Physics Book - User contributions [en]

Wave-Particle Duality

2022-04-24T17:53:18Z

Erinhorbacz: /* History */

===Claimed by Arghya Roy===
'''Wave-particle duality''' is the concept that states every elementary particle behaves like both a wave and a particle.

==The Main Idea==

In the 1920s, a French physicist named [[Louis de Broglie]] suggested that all matter has wave-like properties. This conclusion was largely the result of two landmark experiments that contradicted each other in almost every way. The first experiment was Thomas Young's double slit experiment, which showed light behaved like a wave. The second experiment was by Albert Einstein, who showed, through his research on the photoelectric effect, that light was made up of discrete packets of energy called photons -- which meant that light also behaved as a particle. This contradiction sent the world of physics as humans knew it into panic.

===Double slit experiment===

The [http://micro.magnet.fsu.edu/primer/java/interference/doubleslit/ double slit experiment] is a deceptively simple experiment that was originally conducted by Thomas Young in the 17th century. In the experiment, Young simply sent a beam of light through two slits and observed the pattern on the surface behind the slits. What he saw was an interference pattern that only could have been present if waves were what went inside two slits. The bright spots occur where the amplitudes of the two waves match (both waves are at their peaks) and the dark spots occur when one wave is at its maximum amplitude and the other is at its minimum.

[[File:Double-slit.PNG|Double-slit]]

[[File:Single slit and double slit2.jpg|Single slit and double slit2]]

===Photoelectric effect===

It was known that when light struck a metal, electrons were liberated from the surface. The intuition was that increasing the intensity of light (shining more light) would liberate more electrons. Albert Einstein found something interesting, though. Varying intensity of light had no effect on how many electrons were liberated. Rather, the ''frequency'' of the light determined how many electrons, if any, would be freed. Furthermore, the original theory was that the electrons that would be freed was continuous -- even the smallest amount of light would free some electrons. In fact, this was not the case. Einstein found that there was a minimum threshold frequency that must have been present in order to release electrons at all. This implied there was a ''minimum amount of energy'', or '''quantum''' involved in the interaction. This pointed to the fact that light in fact behaved as particles (called photons) which were packets of these quantum energies. This directly conflicted with the double slit experiment.

[[File:Photoelectric effect.svg|Photoelectric effect]]

[https://phet.colorado.edu/en/simulation/legacy/photoelectric PhET Simulation for Photoelectric effect]

===A Mathematical Model===

Now that we can treat these particles at the quantum level as waves, we can use many different equations from wave mechanics to describe their behavior. One of the most important equations in dealing with wave like properties of these quantum systems and particles is the [https://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation Schrödinger equation]. The Schrödinger equation is the analog of [https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion Newton's second law] ('''F''' = ''m'''''a''') in quantum mechanics, and describes the wave function over time of a system such as a particle moving in a magnetic field. But rather than a simple linear equation, the Schrödinger equation is a linear partial differential equation:

<math>i \hbar \frac{\partial}{\partial t}\Psi(\mathbf{r},t) = \hat H \Psi(\mathbf{r},t)</math>

is the general, relativistic (works for particles moving up to close to the speed of light) equation, where <math>i</math> is the square root of negative 1, <math>ħ</math> is the [https://en.wikipedia.org/wiki/Planck_constant Planck constant] divided by <math>2pi</math>, the symbol ∂/∂t indicates a partial derivative with respect to time, Ψ is the [[wave function]] of the quantum system, and <math>Ĥ</math> is the Hamiltonian operator, which represents the total energy of the wave function at different times.

Using the Schrödinger equation involves using the proper form of the Hamiltonian operator that accounts for the kinetic and potential energy of the particles, and using that operator to then solve the partial differential equation. The output wave function contains information about the system at different times.

==Examples==

The mathematics in solving the Schrodinger equation is quite complicated, but using other simple wave formulas is not very difficult. Two very straightforward formulas involving Planck's constant ''h'', which has a value of <math>6.62607004*10^-34 m^2</math> m^2 kg / s, can be used to relate fundamental properties such as energy ''E'', frequency <math>\nu</math>, and wavelength <math>\lambda</math>.

:<math>E = h \nu</math> (1)

:<math>\lambda = \frac{h}{p} .</math> (2)

Another very useful equation is that the frequency and the wavelength of a particle are inversely proportional, and multiply to the speed of light, ''c''.

:<math>c = \lambda\nu</math> (3)

===Ex. 1===

Microwave ovens emit microwave energy with a wavelength of 12.9 cm. What is the energy of exactly one photon of this microwave radiation?

Here we need to use equations 1 and 3.

Next we define our constants.

<math>c= 2.998*10^8 m/s</math> (this problem wants us to use this number for speed of light), <math>h=6.626*10^34J-s</math>

Now we simply plug in, making sure that our units match (convert 12.9cm to meters = 0.129m)

<math>2.998*10^8 m/s = .129 * v</math>

<math>v = 2,324,031,008 Hz</math>

Now that we found v, we can solve for E.

<math>E = 2,324,031,008 Hz * 6.626*10^-34</math>

<math>E= 1.53990294*10^-24</math>

<math>E= 1.54*10^-24</math>

===Ex. 2===

A radio station broadcasts at a frequency of 590 KHz. What is the wavelength of the radio waves?

We need to use equation 3.

First we convert KHz to Hz.

<math>590</math> KHz = <math>590*10^3</math> Hz

<math>(3*10^8)/(590*10^3)</math> = <math>500</math>m = <math>\lambda</math>

<math>\lambda</math> = 500m.

==Connectedness==

1. How is this topic connected to something that you are interested in?

For a while I had been interested in the strange nature of quantum mechanics. The pure fact that particles could act as waves was simply alluring. In the future it would be great if, even as a biology major, work in a field that had some aspect of quantum research associated.

2. How is it connected to your major?

Extensive, high level research in biology, my major, has shown that during photosynthesis, plants benefit from the quantum properties of the light coming from the sun, and are able to use it to transport energy more efficiently. This groundbreaking discovery could be the key to discovering extremely effective cures for diseases that currently are uncurable or are very costly to treat.

3. Is there an interesting industrial application?

Right now, since quantum computing is not effective or cheap enough for companies to use, industry use is limited. But common lab use is in electron microscopy - it is possible by exploiting the high frequencies of electrons, meaning that one can see objects much smaller than those that can only be seen with visible light.

==History==

Throughout the 1800s, scientists one by one, such as [https://en.wikipedia.org/wiki/John_Dalton John Dalton] and [https://en.wikipedia.org/wiki/Ernest_Rutherford Ernest Rutherford] theorized and discovered elementary particles. Those discoveries in and of themselves were groundbreaking, but of course, scientists pursued these further. It was then that a contradiction arose in two experiments, as mentioned in the above sections, and things went haywire. Newton's classical mechanics had no way of explaining phenomenon like this, so a new field of quantum mechanics was born to study physics of particles on minute scales. The 1900s included scientists like [https://en.wikipedia.org/wiki/Richard_Feynman Richard Feynman] and [https://en.wikipedia.org/wiki/Erwin_Schr%C3%B6dinger Erwin_Schr%C3%B6dinger] (the scientist the above differential equation was named after) that made leaps in QM. Currently, scientists are working on applying [https://en.wikipedia.org/wiki/Quantum_computing quantum effects to computing].

== See also ==

This topic is a big idea in the field of quantum mechanics, but there are many other interesting concepts to further explore:

-[https://en.wikipedia.org/wiki/Quantum_entanglement Quantum entanglement]

-[https://en.wikipedia.org/wiki/Theory_of_everything Theory of everything]

-[https://en.wikipedia.org/wiki/Standard_Model Standard Model]

==References==

All pictures were from Wikimedia Commons, and references are already hyperlinked to key words in the text.

[[Category:Waves]]

Wave-Particle Duality

2022-04-24T17:53:06Z

Erinhorbacz: /* Photoelectric effect */

===Claimed by Arghya Roy===
'''Wave-particle duality''' is the concept that states every elementary particle behaves like both a wave and a particle.

==The Main Idea==

In the 1920s, a French physicist named [[Louis de Broglie]] suggested that all matter has wave-like properties. This conclusion was largely the result of two landmark experiments that contradicted each other in almost every way. The first experiment was Thomas Young's double slit experiment, which showed light behaved like a wave. The second experiment was by Albert Einstein, who showed, through his research on the photoelectric effect, that light was made up of discrete packets of energy called photons -- which meant that light also behaved as a particle. This contradiction sent the world of physics as humans knew it into panic.

===Double slit experiment===

The [http://micro.magnet.fsu.edu/primer/java/interference/doubleslit/ double slit experiment] is a deceptively simple experiment that was originally conducted by Thomas Young in the 17th century. In the experiment, Young simply sent a beam of light through two slits and observed the pattern on the surface behind the slits. What he saw was an interference pattern that only could have been present if waves were what went inside two slits. The bright spots occur where the amplitudes of the two waves match (both waves are at their peaks) and the dark spots occur when one wave is at its maximum amplitude and the other is at its minimum.

[[File:Double-slit.PNG|Double-slit]]

[[File:Single slit and double slit2.jpg|Single slit and double slit2]]

===Photoelectric effect===

It was known that when light struck a metal, electrons were liberated from the surface. The intuition was that increasing the intensity of light (shining more light) would liberate more electrons. Albert Einstein found something interesting, though. Varying intensity of light had no effect on how many electrons were liberated. Rather, the ''frequency'' of the light determined how many electrons, if any, would be freed. Furthermore, the original theory was that the electrons that would be freed was continuous -- even the smallest amount of light would free some electrons. In fact, this was not the case. Einstein found that there was a minimum threshold frequency that must have been present in order to release electrons at all. This implied there was a ''minimum amount of energy'', or '''quantum''' involved in the interaction. This pointed to the fact that light in fact behaved as particles (called photons) which were packets of these quantum energies. This directly conflicted with the double slit experiment.

[[File:Photoelectric effect.svg|Photoelectric effect]]

[https://phet.colorado.edu/en/simulation/legacy/photoelectric PhET Simulation for Photoelectric effect]

===A Mathematical Model===

Now that we can treat these particles at the quantum level as waves, we can use many different equations from wave mechanics to describe their behavior. One of the most important equations in dealing with wave like properties of these quantum systems and particles is the [https://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation Schrödinger equation]. The Schrödinger equation is the analog of [https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion Newton's second law] ('''F''' = ''m'''''a''') in quantum mechanics, and describes the wave function over time of a system such as a particle moving in a magnetic field. But rather than a simple linear equation, the Schrödinger equation is a linear partial differential equation:

<math>i \hbar \frac{\partial}{\partial t}\Psi(\mathbf{r},t) = \hat H \Psi(\mathbf{r},t)</math>

is the general, relativistic (works for particles moving up to close to the speed of light) equation, where <math>i</math> is the square root of negative 1, <math>ħ</math> is the [https://en.wikipedia.org/wiki/Planck_constant Planck constant] divided by <math>2pi</math>, the symbol ∂/∂t indicates a partial derivative with respect to time, Ψ is the [[wave function]] of the quantum system, and <math>Ĥ</math> is the Hamiltonian operator, which represents the total energy of the wave function at different times.

Using the Schrödinger equation involves using the proper form of the Hamiltonian operator that accounts for the kinetic and potential energy of the particles, and using that operator to then solve the partial differential equation. The output wave function contains information about the system at different times.

==Examples==

The mathematics in solving the Schrodinger equation is quite complicated, but using other simple wave formulas is not very difficult. Two very straightforward formulas involving Planck's constant ''h'', which has a value of <math>6.62607004*10^-34 m^2</math> m^2 kg / s, can be used to relate fundamental properties such as energy ''E'', frequency <math>\nu</math>, and wavelength <math>\lambda</math>.

:<math>E = h \nu</math> (1)

:<math>\lambda = \frac{h}{p} .</math> (2)

Another very useful equation is that the frequency and the wavelength of a particle are inversely proportional, and multiply to the speed of light, ''c''.

:<math>c = \lambda\nu</math> (3)

===Ex. 1===

Microwave ovens emit microwave energy with a wavelength of 12.9 cm. What is the energy of exactly one photon of this microwave radiation?

Here we need to use equations 1 and 3.

Next we define our constants.

<math>c= 2.998*10^8 m/s</math> (this problem wants us to use this number for speed of light), <math>h=6.626*10^34J-s</math>

Now we simply plug in, making sure that our units match (convert 12.9cm to meters = 0.129m)

<math>2.998*10^8 m/s = .129 * v</math>

<math>v = 2,324,031,008 Hz</math>

Now that we found v, we can solve for E.

<math>E = 2,324,031,008 Hz * 6.626*10^-34</math>

<math>E= 1.53990294*10^-24</math>

<math>E= 1.54*10^-24</math>

===Ex. 2===

A radio station broadcasts at a frequency of 590 KHz. What is the wavelength of the radio waves?

We need to use equation 3.

First we convert KHz to Hz.

<math>590</math> KHz = <math>590*10^3</math> Hz

<math>(3*10^8)/(590*10^3)</math> = <math>500</math>m = <math>\lambda</math>

<math>\lambda</math> = 500m.

==Connectedness==

1. How is this topic connected to something that you are interested in?

For a while I had been interested in the strange nature of quantum mechanics. The pure fact that particles could act as waves was simply alluring. In the future it would be great if, even as a biology major, work in a field that had some aspect of quantum research associated.

2. How is it connected to your major?

Extensive, high level research in biology, my major, has shown that during photosynthesis, plants benefit from the quantum properties of the light coming from the sun, and are able to use it to transport energy more efficiently. This groundbreaking discovery could be the key to discovering extremely effective cures for diseases that currently are uncurable or are very costly to treat.

3. Is there an interesting industrial application?

Right now, since quantum computing is not effective or cheap enough for companies to use, industry use is limited. But common lab use is in electron microscopy - it is possible by exploiting the high frequencies of electrons, meaning that one can see objects much smaller than those that can only be seen with visible light.

==History==

Throughout the 1800s, scientists one by one, such as [https://en.wikipedia.org/wiki/John_Dalton John Dalton] and [https://en.wikipedia.org/wiki/Ernest_Rutherford Ernest Rutherford] theorized and discovered elementary particles. Those discoveries in and of themselves were groundbreaking, but of course, scientists pursued these further. It was then that a contradiction arose in two experiments, as mentioned in the above sections, and things went haywire. Newton's classical mechanics had no way of explaining phenomenon like this, so a new field of quantum mechanics was born to study physics of particles on minute scales. The 1900s included scientists like [https://en.wikipedia.org/wiki/Richard_Feynman Richard Feynman] and [https://en.wikipedia.org/wiki/Erwin_Schr%C3%B6dinger Erwin_Schr%C3%B6dinger] (the scientist the above differential equation was named after) that made leaps in QM. Currently, scientists are working on applying [https://en.wikipedia.org/wiki/Quantum_computing quantum effects to computing].

(will be expanded by Erin Horbacz 4/14/2022)

== See also ==

This topic is a big idea in the field of quantum mechanics, but there are many other interesting concepts to further explore:

-[https://en.wikipedia.org/wiki/Quantum_entanglement Quantum entanglement]

-[https://en.wikipedia.org/wiki/Theory_of_everything Theory of everything]

-[https://en.wikipedia.org/wiki/Standard_Model Standard Model]

==References==

All pictures were from Wikimedia Commons, and references are already hyperlinked to key words in the text.

[[Category:Waves]]

Atomic Theory

2022-04-21T15:19:42Z

Erinhorbacz: /* References */

Claimed by: Erin Horbacz (4/17/2022)

Atomic theory states that matter is composed of discrete units, called atoms. The word "atom" comes from the Greek word for uncuttable, ''atomos'', since it was believed that if one cut a substance into smaller and smaller pieces, one would reach a point where the substance could not be cut any further. Scientists later discovered that atoms were indeed able to be broken into subatomic, or elementary, particles including protons, neutrons, and electrons. Furthermore, protons and neutrons can be broken down yet again into smaller, elementary particles called [https://en.wikipedia.org/wiki/Quark#:~:text=A%20quark%20(%2Fkw%C9%94%CB%90r,the%20components%20of%20atomic%20nuclei./ quarks]. Atomic theory has evolved greatly over time, but the most recent model stems from quantum mechanics[https://en.wikipedia.org/wiki/Atomic_theory].

==The Main Idea==
===A Mathematical Model===
Mathematical models of atomic processes have become more thorough and sophisticated as knowledge of atomic properties has grown. The goal of a mathematical model is to express the underlying rules that govern atomic processes in a formula that can then predict and describe the behavior of atoms [https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf] (such as is seen with the list of Bohr's mathematical models for the atom). Such fundamental formulas are powerful tools for helping scientists understand the interactions within and processes of both microscopic and macroscopic systems. For example, it was [https://en.wikipedia.org/wiki/Charles-Augustin_de_Coulomb/ Charles-Augustin de Coulomb] who first determined the mathematical equation which could accurately describe the electrostatic potential between charged particles that make up an atom:

<math>
V = \frac{1}{4 \pi \epsilon} \frac{q_1 q_2}{r}
</math>

[[File:bohr_equations.jpg|thumb|Bohr's mathematical model to describe the atom]]

where V is the [https://en.wikipedia.org/wiki/Electric_potential/ electrostatic potential] (in volts), <math> \frac{1}{4 \pi \epsilon} </math> is the [https://en.wikipedia.org/wiki/Coulomb_constant#:~:text=The%20Coulomb%20constant%2C%20the%20electric,%E2%88%922%E2%8B%85C%E2%88%922./ Coulomb constant], <math>q_1 </math> and <math> q_2 </math> are the charges of two particles, and r is the distance between the two particles.

Additionally, stretching of atomic bonds are known to be affected by force fields around an equilibrium point, and they can be modeled according to the equation:

<math>
\Delta V(l) = \frac{1}{2} k_l (l - l_0)^2
</math>

Where <math>\Delta V(l) </math> is the change in potential energy at <math>l</math>, <math>k_1</math> is the spring constant (a proportionality constant), <math>l</math> is the bond length, and <math>l_0</math> is the equilibrium bond length[http://cmt.dur.ac.uk/sjc/thesis_dlc/node45.html].

The use and creation of these formulas is incredibly prominent in simulation modeling. For example, simulations modeling the motion of multiple atoms can use mathematical models such as [https://en.wikipedia.org/wiki/Leapfrog_integration/ Leapfrog integration] and [https://en.wikipedia.org/wiki/Verlet_integration/ Verlet integration] to update particle positions and velocities respectively[https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf].

Perhaps the most important aspect of these mathematical models are their ability to take difficult, abstract concepts and represent them in a form that can be manipulated for further research. The creation of models to describe quantum phenomena makes the information more digestible and the concepts somewhat clearer. In fact, it is often the case that a mathematical model describing quantum behavior helps others think about concepts in different ways. In this manner, many discoveries have resulted from generalizing these models to extend beyond their initial boundaries. For example, the [https://en.wikipedia.org/wiki/Wave%E2%80%93particle_duality#:~:text=Wave%E2%80%93particle%20duality%20is%20the,behaviour%20of%20quantum%2Dscale%20objects./ wave-particle duality] of electrons became known through experiments such as the [https://en.wikipedia.org/wiki/Double-slit_experiment/ double-slit experiment] and the [https://en.wikipedia.org/wiki/Photoelectric_effect/ photoelectric effect]. However, it was Louis de Broglie who considered extending the wave nature to all particles, not just electrons. He discovered that all matter has wave properties, and he formulated the de Broglie wavelength[https://en.wikipedia.org/wiki/Matter_wave]:

<math>
\lambda = \frac{h}{p}
</math>

This formula tells us the wavelength of any particle with a given momentum. This was a huge breakthrough for atomic theory, and is a great example of the usefulness of atomic mathematical models to represent information and inspire new findings.

===A Computational Model===
Understanding the composition and structure of atoms is essential to the study of both microscopic and macroscopic systems. Researchers have made use of atomic information to create what are called atomistic models. These models are used to predict and analyze the behavior of complex systems through knowledge of their most fundamental parts. By understanding how atomic structure affects characteristic properties of atoms, scientists are able to create computational models based on simple microscopic characteristics that simulate complex macroscopic systems. In doing so, they aim to better understand the connection between these macroscopic systems and the underlying atomic structures that govern them [https://www.sciencedirect.com/topics/engineering/atomistic-modeling].

Use of simulations in research has broadened both the volume and complexity of analysis that can be done at any one time. The ability to model atoms through simulations has been an integral part of the research done in diverse areas of science, notably materials science. In this field, atomistic models are often used to predict material properties under certain conditions using information about their nucleus and electron density. For example, professor Gumbart of the physics department of Georgia Tech created an atomistic model that simulates the behavior of atoms by modeling the forces between them as a system of springs. A simulation of this type of model can be found here: https://trinket.io/library/trinkets/a6b3149ef8. Another use of atomistic models is to simulate and analyze important processes such as a nuclear chain reaction; an example of such a simulation can be viewed on [https://javalab.org/en/nuclear_chain_reaction_en/ JavaLab].

Atomistic models use the mathematical models discussed above to computationally represent atomic forces, atomic positions, velocities, and magnetic charges of atoms among other things. The result is an accurate model of quantum processes. Ultimately, the use of such simulations help to understand the collective behavior of atoms and how this behavior affects macroscopic processes (such as deformation and phase change) as well as performance abilities (such as strength of material) [https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf].

Another simulation of atomic spring model: https://www.myphysicslab.com/springs/molecule3-en.html

==History==

===John Dalton: The Law of Multiple Proportions and Atomic Mass===
[[File:Daltons_symbols.gif|thumb|Dalton's concept of atoms and molecules]]
Working from the conservation of mass principle, chemist John Dalton determined the law of multiple proportions to understand how different elements combined in compounds. In 1803, he proposed that each element of the periodic table was composed of identical components, atoms, that were unique to each element. He also suggested that these atoms were not created nor destroyed when one element was combined with another. Dalton's empirical, experimentally-based work marked the first scientific theory of the atom.

Dalton proposed a list of atomic weights in 1805. However, Dalton failed to recognize natural tendencies of elements in nature (for example, oxygen typically exists as a diatomic molecule as <math>\text{O}_2</math>). Dalton was unable to distinguish between atoms and molecules (groups of atoms).

===Amedeo Avogadro: Avogadro's Law===
In 1811, [[Amedeo Avogadro]] studied gases and determined that the amount of volume a gas occupies is not determined by the mass of the gas. This allowed Avogadro to take more accurate atomic measurements of gases than Dalton, and differentiate atoms from molecules.

===Robert Brown: Brownian Motion===
A Scottish botanist, Robert Brown, studied the motion of tiny pollen particles in water in 1827. The particles followed complex paths, dubbed Brownian Motion. As early as 1905, [[Albert Einstein]] used Brownian Motion to predict the size of atoms and molecules.

===J.J. Thomson: The Plum-Pudding Model and Electrons===
[[File:Plum_pudding_model.svg|thumb|Tomson's Plum-Pudding Model]]
Through his work with cathode rays, [[J.J. Thomson]] discovered the electron in 1897, and was the first to learn that atoms weren't actually "uncuttable" as initially thought. Thomson knew that atoms had a net neutral charge, but he only knew that negative particles existed. Thus, Thomson developed the "plum-pudding" model of negatively charged electrons floating in a sea of positive charge. (He likened the relationship of electrons to the sea of positive charge to that of plums in plum pudding.)

===Ernest Rutherford: Gold Foil Experiment and the Nucleus===
In 1909, one of Thomson's students, [[Ernest Rutherford]], determined that the positive charge of atoms was located in a central nucleus. He shot small, positively charged alpha particles at thin sheets of gold foil and noted that some particles were sharply deflected. This deflection could only occur if the positive components of atoms were located in a small area, which Rutherford assumed to be the center. He proposed a planetary model of atoms where a cloud of electrons surrounded a central, positively charged nucleus.

===Niels Bohr: Introducing Quantum Physics===
[[File:Bohr_atom_animation_2.gif|thumb|The Bohr model for a Hydrogen atom with its electron moving between energy levels]]
As quantum mechanics progressed through the work of [[Albert Einstein]] and [[Max Planck]], [[Niels Bohr]] updated the atomic model in 1913 to account for quantum phenomena. Bohr, who was also one of Rutherford's students, suggested that electrostatic forces kept electrons in circular orbit around the positively charged central nucleus. In support of his theory, Bohr examined the behavior of electrons in hydrogen molecules and noted that they followed distinct energy levels. When an electron changed energy levels, it gained or lost energy, which could be emitted in the form of light. While the Bohr model holds true for hydrogen, it isn't accurate for multi-electron elements.

===James Chadwick: Neutrons===
James Chadwick won a Nobel Prize in 1935 for his discovery of the neutron. Starting with Rutherford's work, Chadwick continued experimenting to determine the excess mass in the nucleus that wasn't accounted for by protons. He found that neutrally charged particles, dubbed neutrons, were also inside the nucleus.

===The Current Model: Quantum Physics and Electron Orbitals===
Erwin Schrödinger examined the possibility that moving electrons behaved more like waves than particles, and published "Schrödinger's Equation" in 1926. Although this resolved many issues encountered with the Bohr model, it faced opposition from physicist [[Max Born]]. Instead, Born suggested a wave-particle duality of electrons, which stated that electrons could behave both like a wave and a particle.
As electrons were now given properties of waves, it was impossible to simultaneously determine an electron's exact location and momentum around the nucleus. Werner Heisenberg, first described this phenomena in 1927, and it was later named the Heisenberg Uncertainty Principle. This refuted the Bohr model of the atom, and replaced it with a pattern of probabilities as to where electrons are located around the nucleus. These patterns are referred to as atomic orbitals and come in a variety of shapes (basic spheres, rings, dumbbells, etc.) and the nucleus is always at the center.
[[File:Neon_orbitals.JPG|thumb|center|The first five atomic orbitals: 1s, 2s, 2px, 2py, and 2pz.]]

==Connectedness==
While classical physics applies to large objects moving much slower than the speed of light, modern physics deals with special cases of tiny objects, like atoms, subject to relativistic effects. Atomic theory is vital to understanding many quantum physics concepts that are covered in both Physics 2211 and 2212, like the ball-and-spring model of solids, point charges, and conductivity.

Although one can argue physics applies to just about every aspect of life, and atomic theory is critical to understanding physics, atomic theory has directly influenced material science, power generation, electronics, and even food processing, to name a few.

<gallery>
File:Apollo_synthetic_diamond.jpg|'''Material Science:''' Synthetic diamonds are used for both cosmetic retail and in manufacturing cutting tools.
File:Electrical_and_Mechanical_Services_Department_Headquarters_Photovoltaics.jpg|'''Power:''' Solar cells and power rely on the photovoltaic effect and the wave-particle duality of subatomic particles (like photons).
File:Monokristalines_Silizium_f%C3%BCr_die_Waferherstellung.jpg|'''Electronics:''' Silicon, a popular semiconductor used in electronics, is produced industrially in a single-crystal form.
File:Sodium-chloride-3D-ionic.png|'''Food processing:''' An atomic view of table salt. Purple particles are sodium (Na), and green particles are chlorine (Cl).
File:Nagasakibomb.jpg|'''Defense:''' Nuclear weapons were used during World War II.
File:White_Matter_Connections_Obtained_with_MRI_Tractography.png|'''Medicine:''' MRI's provide doctors critical information without the risks of surgery.
File:Plastic_household_items.jpg|'''Manufacturing:''' Many common household items are made with plastic.
</gallery>

== See also ==

*[[Bohr Model]]
*[[Electronic Energy Levels and Photons]]
*[[Rutherford Experiment and Atomic Collisions]]

===Notable Scientists===
*[[Amedeo Avogadro]]
*[[J.J. Thomson]]
*[[Ernest Rutherford]]
*[[Albert Einstein]]
*[[Max Planck]]
*[[Niels Bohr]]
*[[Max Born]]

===Related Theories===
*[[Quantum Theory]]
*[[Einstein's Theory of Special Relativity]]

===Concept Application===
*[[Ball and Spring Model of Matter]], [[Ball and Spring Model]]
*[[Length and Stiffness of an Interatomic Bond]], [[Young's Modulus]]
*[[Density]], [[Charge]], [[Spin]], and [[Conductivity]]
*[[The Photoelectric Effect]], [[Photons]]
*[[Rest Mass Energy]]
*[[Potential Energy of a Pair of Neutral Atoms]]

===External links===
*Physics Portal description of [https://en.wikipedia.org/wiki/History_of_molecular_theory Molecular Theory] and [https://en.wikipedia.org/wiki/Elementary_particle Subatomic Particles]
*HyperPhysics summary of [http://hyperphysics.phy-astr.gsu.edu/hbase/quacon.html#quacon Quantum Physics]
*Demonstration of the [https://phet.colorado.edu/en/simulation/legacy/hydrogen-atom various models] of a hydrogen atom

==References==

1. “Atomic Theory.” Wikipedia, Wikimedia Foundation, 19 Feb. 2022, https://en.wikipedia.org/wiki/Atomic_theory.

2. Introduction to Atomistic Modeling Xxx Techniques. https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf.

3. Clark, S J. “Atomistic Models.” Atomistic Models, http://cmt.dur.ac.uk/sjc/thesis_dlc/node45.html.

4. Introduction to Atomistic Modeling Xxx Techniques. https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf.

5. “Matter Wave.” Wikipedia, Wikimedia Foundation, 3 Apr. 2022, https://en.wikipedia.org/wiki/Matter_wave.

6. “Atomistic Modeling.” Atomistic Modeling - an Overview | ScienceDirect Topics, https://www.sciencedirect.com/topics/engineering/atomistic-modeling.

7. Introduction to Atomistic Modeling Xxx Techniques. https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf.

Chapter 30 of [https://openstaxcollege.org/files/textbook_version/hi_res_pdf/9/CollegePhysics-OP.pdf OpenStax Textbook]

Physics Portal page on [https://en.wikipedia.org/wiki/Atomic_theory Atomic Theory]

[[Category: Theory]]

Atomic Theory

2022-04-21T15:15:26Z

Erinhorbacz: /* A Computational Model */

Claimed by: Erin Horbacz (4/17/2022)

Atomic theory states that matter is composed of discrete units, called atoms. The word "atom" comes from the Greek word for uncuttable, ''atomos'', since it was believed that if one cut a substance into smaller and smaller pieces, one would reach a point where the substance could not be cut any further. Scientists later discovered that atoms were indeed able to be broken into subatomic, or elementary, particles including protons, neutrons, and electrons. Furthermore, protons and neutrons can be broken down yet again into smaller, elementary particles called [https://en.wikipedia.org/wiki/Quark#:~:text=A%20quark%20(%2Fkw%C9%94%CB%90r,the%20components%20of%20atomic%20nuclei./ quarks]. Atomic theory has evolved greatly over time, but the most recent model stems from quantum mechanics[https://en.wikipedia.org/wiki/Atomic_theory].

==The Main Idea==
===A Mathematical Model===
Mathematical models of atomic processes have become more thorough and sophisticated as knowledge of atomic properties has grown. The goal of a mathematical model is to express the underlying rules that govern atomic processes in a formula that can then predict and describe the behavior of atoms [https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf] (such as is seen with the list of Bohr's mathematical models for the atom). Such fundamental formulas are powerful tools for helping scientists understand the interactions within and processes of both microscopic and macroscopic systems. For example, it was [https://en.wikipedia.org/wiki/Charles-Augustin_de_Coulomb/ Charles-Augustin de Coulomb] who first determined the mathematical equation which could accurately describe the electrostatic potential between charged particles that make up an atom:

<math>
V = \frac{1}{4 \pi \epsilon} \frac{q_1 q_2}{r}
</math>

[[File:bohr_equations.jpg|thumb|Bohr's mathematical model to describe the atom]]

where V is the [https://en.wikipedia.org/wiki/Electric_potential/ electrostatic potential] (in volts), <math> \frac{1}{4 \pi \epsilon} </math> is the [https://en.wikipedia.org/wiki/Coulomb_constant#:~:text=The%20Coulomb%20constant%2C%20the%20electric,%E2%88%922%E2%8B%85C%E2%88%922./ Coulomb constant], <math>q_1 </math> and <math> q_2 </math> are the charges of two particles, and r is the distance between the two particles.

Additionally, stretching of atomic bonds are known to be affected by force fields around an equilibrium point, and they can be modeled according to the equation:

<math>
\Delta V(l) = \frac{1}{2} k_l (l - l_0)^2
</math>

Where <math>\Delta V(l) </math> is the change in potential energy at <math>l</math>, <math>k_1</math> is the spring constant (a proportionality constant), <math>l</math> is the bond length, and <math>l_0</math> is the equilibrium bond length[http://cmt.dur.ac.uk/sjc/thesis_dlc/node45.html].

The use and creation of these formulas is incredibly prominent in simulation modeling. For example, simulations modeling the motion of multiple atoms can use mathematical models such as [https://en.wikipedia.org/wiki/Leapfrog_integration/ Leapfrog integration] and [https://en.wikipedia.org/wiki/Verlet_integration/ Verlet integration] to update particle positions and velocities respectively[https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf].

Perhaps the most important aspect of these mathematical models are their ability to take difficult, abstract concepts and represent them in a form that can be manipulated for further research. The creation of models to describe quantum phenomena makes the information more digestible and the concepts somewhat clearer. In fact, it is often the case that a mathematical model describing quantum behavior helps others think about concepts in different ways. In this manner, many discoveries have resulted from generalizing these models to extend beyond their initial boundaries. For example, the [https://en.wikipedia.org/wiki/Wave%E2%80%93particle_duality#:~:text=Wave%E2%80%93particle%20duality%20is%20the,behaviour%20of%20quantum%2Dscale%20objects./ wave-particle duality] of electrons became known through experiments such as the [https://en.wikipedia.org/wiki/Double-slit_experiment/ double-slit experiment] and the [https://en.wikipedia.org/wiki/Photoelectric_effect/ photoelectric effect]. However, it was Louis de Broglie who considered extending the wave nature to all particles, not just electrons. He discovered that all matter has wave properties, and he formulated the de Broglie wavelength[https://en.wikipedia.org/wiki/Matter_wave]:

<math>
\lambda = \frac{h}{p}
</math>

This formula tells us the wavelength of any particle with a given momentum. This was a huge breakthrough for atomic theory, and is a great example of the usefulness of atomic mathematical models to represent information and inspire new findings.

===A Computational Model===
Understanding the composition and structure of atoms is essential to the study of both microscopic and macroscopic systems. Researchers have made use of atomic information to create what are called atomistic models. These models are used to predict and analyze the behavior of complex systems through knowledge of their most fundamental parts. By understanding how atomic structure affects characteristic properties of atoms, scientists are able to create computational models based on simple microscopic characteristics that simulate complex macroscopic systems. In doing so, they aim to better understand the connection between these macroscopic systems and the underlying atomic structures that govern them [https://www.sciencedirect.com/topics/engineering/atomistic-modeling].

Use of simulations in research has broadened both the volume and complexity of analysis that can be done at any one time. The ability to model atoms through simulations has been an integral part of the research done in diverse areas of science, notably materials science. In this field, atomistic models are often used to predict material properties under certain conditions using information about their nucleus and electron density. For example, professor Gumbart of the physics department of Georgia Tech created an atomistic model that simulates the behavior of atoms by modeling the forces between them as a system of springs. A simulation of this type of model can be found here: https://trinket.io/library/trinkets/a6b3149ef8. Another use of atomistic models is to simulate and analyze important processes such as a nuclear chain reaction; an example of such a simulation can be viewed on [https://javalab.org/en/nuclear_chain_reaction_en/ JavaLab].

Atomistic models use the mathematical models discussed above to computationally represent atomic forces, atomic positions, velocities, and magnetic charges of atoms among other things. The result is an accurate model of quantum processes. Ultimately, the use of such simulations help to understand the collective behavior of atoms and how this behavior affects macroscopic processes (such as deformation and phase change) as well as performance abilities (such as strength of material) [https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf].

Another simulation of atomic spring model: https://www.myphysicslab.com/springs/molecule3-en.html

==History==

===John Dalton: The Law of Multiple Proportions and Atomic Mass===
[[File:Daltons_symbols.gif|thumb|Dalton's concept of atoms and molecules]]
Working from the conservation of mass principle, chemist John Dalton determined the law of multiple proportions to understand how different elements combined in compounds. In 1803, he proposed that each element of the periodic table was composed of identical components, atoms, that were unique to each element. He also suggested that these atoms were not created nor destroyed when one element was combined with another. Dalton's empirical, experimentally-based work marked the first scientific theory of the atom.

Dalton proposed a list of atomic weights in 1805. However, Dalton failed to recognize natural tendencies of elements in nature (for example, oxygen typically exists as a diatomic molecule as <math>\text{O}_2</math>). Dalton was unable to distinguish between atoms and molecules (groups of atoms).

===Amedeo Avogadro: Avogadro's Law===
In 1811, [[Amedeo Avogadro]] studied gases and determined that the amount of volume a gas occupies is not determined by the mass of the gas. This allowed Avogadro to take more accurate atomic measurements of gases than Dalton, and differentiate atoms from molecules.

===Robert Brown: Brownian Motion===
A Scottish botanist, Robert Brown, studied the motion of tiny pollen particles in water in 1827. The particles followed complex paths, dubbed Brownian Motion. As early as 1905, [[Albert Einstein]] used Brownian Motion to predict the size of atoms and molecules.

===J.J. Thomson: The Plum-Pudding Model and Electrons===
[[File:Plum_pudding_model.svg|thumb|Tomson's Plum-Pudding Model]]
Through his work with cathode rays, [[J.J. Thomson]] discovered the electron in 1897, and was the first to learn that atoms weren't actually "uncuttable" as initially thought. Thomson knew that atoms had a net neutral charge, but he only knew that negative particles existed. Thus, Thomson developed the "plum-pudding" model of negatively charged electrons floating in a sea of positive charge. (He likened the relationship of electrons to the sea of positive charge to that of plums in plum pudding.)

===Ernest Rutherford: Gold Foil Experiment and the Nucleus===
In 1909, one of Thomson's students, [[Ernest Rutherford]], determined that the positive charge of atoms was located in a central nucleus. He shot small, positively charged alpha particles at thin sheets of gold foil and noted that some particles were sharply deflected. This deflection could only occur if the positive components of atoms were located in a small area, which Rutherford assumed to be the center. He proposed a planetary model of atoms where a cloud of electrons surrounded a central, positively charged nucleus.

===Niels Bohr: Introducing Quantum Physics===
[[File:Bohr_atom_animation_2.gif|thumb|The Bohr model for a Hydrogen atom with its electron moving between energy levels]]
As quantum mechanics progressed through the work of [[Albert Einstein]] and [[Max Planck]], [[Niels Bohr]] updated the atomic model in 1913 to account for quantum phenomena. Bohr, who was also one of Rutherford's students, suggested that electrostatic forces kept electrons in circular orbit around the positively charged central nucleus. In support of his theory, Bohr examined the behavior of electrons in hydrogen molecules and noted that they followed distinct energy levels. When an electron changed energy levels, it gained or lost energy, which could be emitted in the form of light. While the Bohr model holds true for hydrogen, it isn't accurate for multi-electron elements.

===James Chadwick: Neutrons===
James Chadwick won a Nobel Prize in 1935 for his discovery of the neutron. Starting with Rutherford's work, Chadwick continued experimenting to determine the excess mass in the nucleus that wasn't accounted for by protons. He found that neutrally charged particles, dubbed neutrons, were also inside the nucleus.

===The Current Model: Quantum Physics and Electron Orbitals===
Erwin Schrödinger examined the possibility that moving electrons behaved more like waves than particles, and published "Schrödinger's Equation" in 1926. Although this resolved many issues encountered with the Bohr model, it faced opposition from physicist [[Max Born]]. Instead, Born suggested a wave-particle duality of electrons, which stated that electrons could behave both like a wave and a particle.
As electrons were now given properties of waves, it was impossible to simultaneously determine an electron's exact location and momentum around the nucleus. Werner Heisenberg, first described this phenomena in 1927, and it was later named the Heisenberg Uncertainty Principle. This refuted the Bohr model of the atom, and replaced it with a pattern of probabilities as to where electrons are located around the nucleus. These patterns are referred to as atomic orbitals and come in a variety of shapes (basic spheres, rings, dumbbells, etc.) and the nucleus is always at the center.
[[File:Neon_orbitals.JPG|thumb|center|The first five atomic orbitals: 1s, 2s, 2px, 2py, and 2pz.]]

==Connectedness==
While classical physics applies to large objects moving much slower than the speed of light, modern physics deals with special cases of tiny objects, like atoms, subject to relativistic effects. Atomic theory is vital to understanding many quantum physics concepts that are covered in both Physics 2211 and 2212, like the ball-and-spring model of solids, point charges, and conductivity.

Although one can argue physics applies to just about every aspect of life, and atomic theory is critical to understanding physics, atomic theory has directly influenced material science, power generation, electronics, and even food processing, to name a few.

<gallery>
File:Apollo_synthetic_diamond.jpg|'''Material Science:''' Synthetic diamonds are used for both cosmetic retail and in manufacturing cutting tools.
File:Electrical_and_Mechanical_Services_Department_Headquarters_Photovoltaics.jpg|'''Power:''' Solar cells and power rely on the photovoltaic effect and the wave-particle duality of subatomic particles (like photons).
File:Monokristalines_Silizium_f%C3%BCr_die_Waferherstellung.jpg|'''Electronics:''' Silicon, a popular semiconductor used in electronics, is produced industrially in a single-crystal form.
File:Sodium-chloride-3D-ionic.png|'''Food processing:''' An atomic view of table salt. Purple particles are sodium (Na), and green particles are chlorine (Cl).
File:Nagasakibomb.jpg|'''Defense:''' Nuclear weapons were used during World War II.
File:White_Matter_Connections_Obtained_with_MRI_Tractography.png|'''Medicine:''' MRI's provide doctors critical information without the risks of surgery.
File:Plastic_household_items.jpg|'''Manufacturing:''' Many common household items are made with plastic.
</gallery>

== See also ==

*[[Bohr Model]]
*[[Electronic Energy Levels and Photons]]
*[[Rutherford Experiment and Atomic Collisions]]

===Notable Scientists===
*[[Amedeo Avogadro]]
*[[J.J. Thomson]]
*[[Ernest Rutherford]]
*[[Albert Einstein]]
*[[Max Planck]]
*[[Niels Bohr]]
*[[Max Born]]

===Related Theories===
*[[Quantum Theory]]
*[[Einstein's Theory of Special Relativity]]

===Concept Application===
*[[Ball and Spring Model of Matter]], [[Ball and Spring Model]]
*[[Length and Stiffness of an Interatomic Bond]], [[Young's Modulus]]
*[[Density]], [[Charge]], [[Spin]], and [[Conductivity]]
*[[The Photoelectric Effect]], [[Photons]]
*[[Rest Mass Energy]]
*[[Potential Energy of a Pair of Neutral Atoms]]

===External links===
*Physics Portal description of [https://en.wikipedia.org/wiki/History_of_molecular_theory Molecular Theory] and [https://en.wikipedia.org/wiki/Elementary_particle Subatomic Particles]
*HyperPhysics summary of [http://hyperphysics.phy-astr.gsu.edu/hbase/quacon.html#quacon Quantum Physics]
*Demonstration of the [https://phet.colorado.edu/en/simulation/legacy/hydrogen-atom various models] of a hydrogen atom

==References==

1. “Atomic Theory.” Wikipedia, Wikimedia Foundation, 19 Feb. 2022, https://en.wikipedia.org/wiki/Atomic_theory.

2. Introduction to Atomistic Modeling Xxx Techniques. https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf.

3. Clark, S J. “Atomistic Models.” Atomistic Models, http://cmt.dur.ac.uk/sjc/thesis_dlc/node45.html.

4. Introduction to Atomistic Modeling Xxx Techniques. https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf.

5. “Matter Wave.” Wikipedia, Wikimedia Foundation, 3 Apr. 2022, https://en.wikipedia.org/wiki/Matter_wave.

Chapter 30 of [https://openstaxcollege.org/files/textbook_version/hi_res_pdf/9/CollegePhysics-OP.pdf OpenStax Textbook]

Physics Portal page on [https://en.wikipedia.org/wiki/Atomic_theory Atomic Theory]

[[Category: Theory]]

Atomic Theory

2022-04-21T15:10:28Z

Erinhorbacz: /* A Computational Model */

Claimed by: Erin Horbacz (4/17/2022)

Atomic theory states that matter is composed of discrete units, called atoms. The word "atom" comes from the Greek word for uncuttable, ''atomos'', since it was believed that if one cut a substance into smaller and smaller pieces, one would reach a point where the substance could not be cut any further. Scientists later discovered that atoms were indeed able to be broken into subatomic, or elementary, particles including protons, neutrons, and electrons. Furthermore, protons and neutrons can be broken down yet again into smaller, elementary particles called [https://en.wikipedia.org/wiki/Quark#:~:text=A%20quark%20(%2Fkw%C9%94%CB%90r,the%20components%20of%20atomic%20nuclei./ quarks]. Atomic theory has evolved greatly over time, but the most recent model stems from quantum mechanics[https://en.wikipedia.org/wiki/Atomic_theory].

==The Main Idea==
===A Mathematical Model===
Mathematical models of atomic processes have become more thorough and sophisticated as knowledge of atomic properties has grown. The goal of a mathematical model is to express the underlying rules that govern atomic processes in a formula that can then predict and describe the behavior of atoms [https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf] (such as is seen with the list of Bohr's mathematical models for the atom). Such fundamental formulas are powerful tools for helping scientists understand the interactions within and processes of both microscopic and macroscopic systems. For example, it was [https://en.wikipedia.org/wiki/Charles-Augustin_de_Coulomb/ Charles-Augustin de Coulomb] who first determined the mathematical equation which could accurately describe the electrostatic potential between charged particles that make up an atom:

<math>
V = \frac{1}{4 \pi \epsilon} \frac{q_1 q_2}{r}
</math>

[[File:bohr_equations.jpg|thumb|Bohr's mathematical model to describe the atom]]

where V is the [https://en.wikipedia.org/wiki/Electric_potential/ electrostatic potential] (in volts), <math> \frac{1}{4 \pi \epsilon} </math> is the [https://en.wikipedia.org/wiki/Coulomb_constant#:~:text=The%20Coulomb%20constant%2C%20the%20electric,%E2%88%922%E2%8B%85C%E2%88%922./ Coulomb constant], <math>q_1 </math> and <math> q_2 </math> are the charges of two particles, and r is the distance between the two particles.

Additionally, stretching of atomic bonds are known to be affected by force fields around an equilibrium point, and they can be modeled according to the equation:

<math>
\Delta V(l) = \frac{1}{2} k_l (l - l_0)^2
</math>

Where <math>\Delta V(l) </math> is the change in potential energy at <math>l</math>, <math>k_1</math> is the spring constant (a proportionality constant), <math>l</math> is the bond length, and <math>l_0</math> is the equilibrium bond length[http://cmt.dur.ac.uk/sjc/thesis_dlc/node45.html].

The use and creation of these formulas is incredibly prominent in simulation modeling. For example, simulations modeling the motion of multiple atoms can use mathematical models such as [https://en.wikipedia.org/wiki/Leapfrog_integration/ Leapfrog integration] and [https://en.wikipedia.org/wiki/Verlet_integration/ Verlet integration] to update particle positions and velocities respectively[https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf].

Perhaps the most important aspect of these mathematical models are their ability to take difficult, abstract concepts and represent them in a form that can be manipulated for further research. The creation of models to describe quantum phenomena makes the information more digestible and the concepts somewhat clearer. In fact, it is often the case that a mathematical model describing quantum behavior helps others think about concepts in different ways. In this manner, many discoveries have resulted from generalizing these models to extend beyond their initial boundaries. For example, the [https://en.wikipedia.org/wiki/Wave%E2%80%93particle_duality#:~:text=Wave%E2%80%93particle%20duality%20is%20the,behaviour%20of%20quantum%2Dscale%20objects./ wave-particle duality] of electrons became known through experiments such as the [https://en.wikipedia.org/wiki/Double-slit_experiment/ double-slit experiment] and the [https://en.wikipedia.org/wiki/Photoelectric_effect/ photoelectric effect]. However, it was Louis de Broglie who considered extending the wave nature to all particles, not just electrons. He discovered that all matter has wave properties, and he formulated the de Broglie wavelength[https://en.wikipedia.org/wiki/Matter_wave]:

<math>
\lambda = \frac{h}{p}
</math>

This formula tells us the wavelength of any particle with a given momentum. This was a huge breakthrough for atomic theory, and is a great example of the usefulness of atomic mathematical models to represent information and inspire new findings.

===A Computational Model===
Understanding the composition and structure of atoms is essential to the study of both microscopic and macroscopic systems. Researchers have made use of atomic information to create what are called atomistic models. These models are used to predict and analyze the behavior of complex systems through knowledge of their most fundamental parts. By understanding how atomic structure affects characteristic properties of atoms, scientists are able to create computational models based on simple microscopic characteristics that simulate complex macroscopic systems. In doing so, they aim to better understand the connection between these macroscopic systems and the underlying atomic structures that govern them.

Use of simulations in research has broadened both the volume and complexity of analysis that can be done at any one time. The ability to model atoms through simulations has been an integral part of the research done in diverse areas of science, notably materials science. In this field, atomistic models are often used to predict material properties under certain conditions using information about their nucleus and electron density. For example, professor Gumbart of the physics department of Georgia Tech created an atomistic model that simulates the behavior of atoms by modeling the forces between them as a system of springs. A simulation of this type of model can be found here: https://trinket.io/library/trinkets/a6b3149ef8. Another use of atomistic models is to simulate and analyze important processes such as a nuclear chain reaction; an example of such a simulation can be viewed on [https://javalab.org/en/nuclear_chain_reaction_en/ JavaLab].

Atomistic models use the mathematical models discussed above to computationally represent atomic forces, atomic positions, velocities, and magnetic charges of atoms among other things. The result is an accurate model of quantum processes. Ultimately, the use of such simulations help to understand the collective behavior of atoms and how this behavior affects macroscopic processes (such as deformation and phase change) as well as performance abilities (such as strength of material).

Another simulation of atomic spring model: https://www.myphysicslab.com/springs/molecule3-en.html

==History==

===John Dalton: The Law of Multiple Proportions and Atomic Mass===
[[File:Daltons_symbols.gif|thumb|Dalton's concept of atoms and molecules]]
Working from the conservation of mass principle, chemist John Dalton determined the law of multiple proportions to understand how different elements combined in compounds. In 1803, he proposed that each element of the periodic table was composed of identical components, atoms, that were unique to each element. He also suggested that these atoms were not created nor destroyed when one element was combined with another. Dalton's empirical, experimentally-based work marked the first scientific theory of the atom.

Dalton proposed a list of atomic weights in 1805. However, Dalton failed to recognize natural tendencies of elements in nature (for example, oxygen typically exists as a diatomic molecule as <math>\text{O}_2</math>). Dalton was unable to distinguish between atoms and molecules (groups of atoms).

===Amedeo Avogadro: Avogadro's Law===
In 1811, [[Amedeo Avogadro]] studied gases and determined that the amount of volume a gas occupies is not determined by the mass of the gas. This allowed Avogadro to take more accurate atomic measurements of gases than Dalton, and differentiate atoms from molecules.

===Robert Brown: Brownian Motion===
A Scottish botanist, Robert Brown, studied the motion of tiny pollen particles in water in 1827. The particles followed complex paths, dubbed Brownian Motion. As early as 1905, [[Albert Einstein]] used Brownian Motion to predict the size of atoms and molecules.

===J.J. Thomson: The Plum-Pudding Model and Electrons===
[[File:Plum_pudding_model.svg|thumb|Tomson's Plum-Pudding Model]]
Through his work with cathode rays, [[J.J. Thomson]] discovered the electron in 1897, and was the first to learn that atoms weren't actually "uncuttable" as initially thought. Thomson knew that atoms had a net neutral charge, but he only knew that negative particles existed. Thus, Thomson developed the "plum-pudding" model of negatively charged electrons floating in a sea of positive charge. (He likened the relationship of electrons to the sea of positive charge to that of plums in plum pudding.)

===Ernest Rutherford: Gold Foil Experiment and the Nucleus===
In 1909, one of Thomson's students, [[Ernest Rutherford]], determined that the positive charge of atoms was located in a central nucleus. He shot small, positively charged alpha particles at thin sheets of gold foil and noted that some particles were sharply deflected. This deflection could only occur if the positive components of atoms were located in a small area, which Rutherford assumed to be the center. He proposed a planetary model of atoms where a cloud of electrons surrounded a central, positively charged nucleus.

===Niels Bohr: Introducing Quantum Physics===
[[File:Bohr_atom_animation_2.gif|thumb|The Bohr model for a Hydrogen atom with its electron moving between energy levels]]
As quantum mechanics progressed through the work of [[Albert Einstein]] and [[Max Planck]], [[Niels Bohr]] updated the atomic model in 1913 to account for quantum phenomena. Bohr, who was also one of Rutherford's students, suggested that electrostatic forces kept electrons in circular orbit around the positively charged central nucleus. In support of his theory, Bohr examined the behavior of electrons in hydrogen molecules and noted that they followed distinct energy levels. When an electron changed energy levels, it gained or lost energy, which could be emitted in the form of light. While the Bohr model holds true for hydrogen, it isn't accurate for multi-electron elements.

===James Chadwick: Neutrons===
James Chadwick won a Nobel Prize in 1935 for his discovery of the neutron. Starting with Rutherford's work, Chadwick continued experimenting to determine the excess mass in the nucleus that wasn't accounted for by protons. He found that neutrally charged particles, dubbed neutrons, were also inside the nucleus.

===The Current Model: Quantum Physics and Electron Orbitals===
Erwin Schrödinger examined the possibility that moving electrons behaved more like waves than particles, and published "Schrödinger's Equation" in 1926. Although this resolved many issues encountered with the Bohr model, it faced opposition from physicist [[Max Born]]. Instead, Born suggested a wave-particle duality of electrons, which stated that electrons could behave both like a wave and a particle.
As electrons were now given properties of waves, it was impossible to simultaneously determine an electron's exact location and momentum around the nucleus. Werner Heisenberg, first described this phenomena in 1927, and it was later named the Heisenberg Uncertainty Principle. This refuted the Bohr model of the atom, and replaced it with a pattern of probabilities as to where electrons are located around the nucleus. These patterns are referred to as atomic orbitals and come in a variety of shapes (basic spheres, rings, dumbbells, etc.) and the nucleus is always at the center.
[[File:Neon_orbitals.JPG|thumb|center|The first five atomic orbitals: 1s, 2s, 2px, 2py, and 2pz.]]

==Connectedness==
While classical physics applies to large objects moving much slower than the speed of light, modern physics deals with special cases of tiny objects, like atoms, subject to relativistic effects. Atomic theory is vital to understanding many quantum physics concepts that are covered in both Physics 2211 and 2212, like the ball-and-spring model of solids, point charges, and conductivity.

Although one can argue physics applies to just about every aspect of life, and atomic theory is critical to understanding physics, atomic theory has directly influenced material science, power generation, electronics, and even food processing, to name a few.

<gallery>
File:Apollo_synthetic_diamond.jpg|'''Material Science:''' Synthetic diamonds are used for both cosmetic retail and in manufacturing cutting tools.
File:Electrical_and_Mechanical_Services_Department_Headquarters_Photovoltaics.jpg|'''Power:''' Solar cells and power rely on the photovoltaic effect and the wave-particle duality of subatomic particles (like photons).
File:Monokristalines_Silizium_f%C3%BCr_die_Waferherstellung.jpg|'''Electronics:''' Silicon, a popular semiconductor used in electronics, is produced industrially in a single-crystal form.
File:Sodium-chloride-3D-ionic.png|'''Food processing:''' An atomic view of table salt. Purple particles are sodium (Na), and green particles are chlorine (Cl).
File:Nagasakibomb.jpg|'''Defense:''' Nuclear weapons were used during World War II.
File:White_Matter_Connections_Obtained_with_MRI_Tractography.png|'''Medicine:''' MRI's provide doctors critical information without the risks of surgery.
File:Plastic_household_items.jpg|'''Manufacturing:''' Many common household items are made with plastic.
</gallery>

== See also ==

*[[Bohr Model]]
*[[Electronic Energy Levels and Photons]]
*[[Rutherford Experiment and Atomic Collisions]]

===Notable Scientists===
*[[Amedeo Avogadro]]
*[[J.J. Thomson]]
*[[Ernest Rutherford]]
*[[Albert Einstein]]
*[[Max Planck]]
*[[Niels Bohr]]
*[[Max Born]]

===Related Theories===
*[[Quantum Theory]]
*[[Einstein's Theory of Special Relativity]]

===Concept Application===
*[[Ball and Spring Model of Matter]], [[Ball and Spring Model]]
*[[Length and Stiffness of an Interatomic Bond]], [[Young's Modulus]]
*[[Density]], [[Charge]], [[Spin]], and [[Conductivity]]
*[[The Photoelectric Effect]], [[Photons]]
*[[Rest Mass Energy]]
*[[Potential Energy of a Pair of Neutral Atoms]]

===External links===
*Physics Portal description of [https://en.wikipedia.org/wiki/History_of_molecular_theory Molecular Theory] and [https://en.wikipedia.org/wiki/Elementary_particle Subatomic Particles]
*HyperPhysics summary of [http://hyperphysics.phy-astr.gsu.edu/hbase/quacon.html#quacon Quantum Physics]
*Demonstration of the [https://phet.colorado.edu/en/simulation/legacy/hydrogen-atom various models] of a hydrogen atom

==References==

1. “Atomic Theory.” Wikipedia, Wikimedia Foundation, 19 Feb. 2022, https://en.wikipedia.org/wiki/Atomic_theory.

2. Introduction to Atomistic Modeling Xxx Techniques. https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf.

3. Clark, S J. “Atomistic Models.” Atomistic Models, http://cmt.dur.ac.uk/sjc/thesis_dlc/node45.html.

4. Introduction to Atomistic Modeling Xxx Techniques. https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf.

5. “Matter Wave.” Wikipedia, Wikimedia Foundation, 3 Apr. 2022, https://en.wikipedia.org/wiki/Matter_wave.

Chapter 30 of [https://openstaxcollege.org/files/textbook_version/hi_res_pdf/9/CollegePhysics-OP.pdf OpenStax Textbook]

Physics Portal page on [https://en.wikipedia.org/wiki/Atomic_theory Atomic Theory]

[[Category: Theory]]

Atomic Theory

2022-04-20T14:50:01Z

Erinhorbacz: /* A Computational Model */

Claimed by: Erin Horbacz (4/17/2022)

Atomic theory states that matter is composed of discrete units, called atoms. The word "atom" comes from the Greek word for uncuttable, ''atomos'', since it was believed that if one cut a substance into smaller and smaller pieces, one would reach a point where the substance could not be cut any further. Scientists later discovered that atoms were indeed able to be broken into subatomic, or elementary, particles including protons, neutrons, and electrons. Furthermore, protons and neutrons can be broken down yet again into smaller, elementary particles called [https://en.wikipedia.org/wiki/Quark#:~:text=A%20quark%20(%2Fkw%C9%94%CB%90r,the%20components%20of%20atomic%20nuclei./ quarks]. Atomic theory has evolved greatly over time, but the most recent model stems from quantum mechanics[https://en.wikipedia.org/wiki/Atomic_theory].

==The Main Idea==
===A Mathematical Model===
Mathematical models of atomic processes have become more thorough and sophisticated as knowledge of atomic properties has grown. The goal of a mathematical model is to express the underlying rules that govern atomic processes in a formula that can then predict and describe the behavior of atoms [https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf] (such as is seen with the list of Bohr's mathematical models for the atom). Such fundamental formulas are powerful tools for helping scientists understand the interactions within and processes of both microscopic and macroscopic systems. For example, it was [https://en.wikipedia.org/wiki/Charles-Augustin_de_Coulomb/ Charles-Augustin de Coulomb] who first determined the mathematical equation which could accurately describe the electrostatic potential between charged particles that make up an atom:

<math>
V = \frac{1}{4 \pi \epsilon} \frac{q_1 q_2}{r}
</math>

[[File:bohr_equations.jpg|thumb|Bohr's mathematical model to describe the atom]]

where V is the [https://en.wikipedia.org/wiki/Electric_potential/ electrostatic potential] (in volts), <math> \frac{1}{4 \pi \epsilon} </math> is the [https://en.wikipedia.org/wiki/Coulomb_constant#:~:text=The%20Coulomb%20constant%2C%20the%20electric,%E2%88%922%E2%8B%85C%E2%88%922./ Coulomb constant], <math>q_1 </math> and <math> q_2 </math> are the charges of two particles, and r is the distance between the two particles.

Additionally, stretching of atomic bonds are known to be affected by force fields around an equilibrium point, and they can be modeled according to the equation:

<math>
\Delta V(l) = \frac{1}{2} k_l (l - l_0)^2
</math>

Where <math>\Delta V(l) </math> is the change in potential energy at <math>l</math>, <math>k_1</math> is the spring constant (a proportionality constant), <math>l</math> is the bond length, and <math>l_0</math> is the equilibrium bond length[http://cmt.dur.ac.uk/sjc/thesis_dlc/node45.html].

The use and creation of these formulas is incredibly prominent in simulation modeling. For example, simulations modeling the motion of multiple atoms can use mathematical models such as [https://en.wikipedia.org/wiki/Leapfrog_integration/ Leapfrog integration] and [https://en.wikipedia.org/wiki/Verlet_integration/ Verlet integration] to update particle positions and velocities respectively[https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf].

Perhaps the most important aspect of these mathematical models are their ability to take difficult, abstract concepts and represent them in a form that can be manipulated for further research. The creation of models to describe quantum phenomena makes the information more digestible and the concepts somewhat clearer. In fact, it is often the case that a mathematical model describing quantum behavior helps others think about concepts in different ways. In this manner, many discoveries have resulted from generalizing these models to extend beyond their initial boundaries. For example, the [https://en.wikipedia.org/wiki/Wave%E2%80%93particle_duality#:~:text=Wave%E2%80%93particle%20duality%20is%20the,behaviour%20of%20quantum%2Dscale%20objects./ wave-particle duality] of electrons became known through experiments such as the [https://en.wikipedia.org/wiki/Double-slit_experiment/ double-slit experiment] and the [https://en.wikipedia.org/wiki/Photoelectric_effect/ photoelectric effect]. However, it was Louis de Broglie who considered extending the wave nature to all particles, not just electrons. He discovered that all matter has wave properties, and he formulated the de Broglie wavelength[https://en.wikipedia.org/wiki/Matter_wave]:

<math>
\lambda = \frac{h}{p}
</math>

This formula tells us the wavelength of any particle with a given momentum. This was a huge breakthrough for atomic theory, and is a great example of the usefulness of atomic mathematical models to represent information and inspire new findings.

===A Computational Model===
Understanding the composition and structure of atoms is essential to the study of both microscopic and macroscopic systems. Researchers have made use of atomic information to create what are called atomistic models. These models are used to predict and analyze the behavior of complex systems through knowledge of their most fundamental parts. By understanding how atomic structure affects characteristic properties of atoms, scientists are able to create computational models based on simple microscopic characteristics that simulate complex macroscopic systems. In doing so, they aim to better understand the connection between these macroscopic systems and the underlying atomic structures that govern them.

Use of simulations in research has broadened both the volume and complexity of analysis that can be done at any one time. The ability to model atoms through simulations has been an integral part of the research done in diverse areas of science, notably materials science. In this field, atomistic models are often used to predict material properties under certain conditions using information about their nucleus and electron density. For example, professor Gumbart of the physics department of Georgia Tech created an atomistic model that simulates the behavior of atoms by modeling the forces between them as a system of springs. Another use of atomistic models is to simulate and analyze important processes such as a nuclear chain reaction; an example of such a simulation can be viewed on [https://javalab.org/en/nuclear_chain_reaction_en/ JavaLab].

Atomistic models use the mathematical models discussed above to computationally represent atomic forces, atomic positions, velocities, and magnetic charges of atoms among other things. The result is an accurate model of quantum processes. Ultimately, the use of such simulations help to understand the collective behavior of atoms and how this behavior affects macroscopic processes (such as deformation and phase change) as well as performance abilities (such as strength of material).

Simulation of atomic spring model: https://www.myphysicslab.com/springs/molecule3-en.html

[[<iframe src="https://trinket.io/embed/glowscript/31d0f9ad9e?toggleCode=true" width="100%" height="356" frameborder="0" marginwidth="0" marginheight="0" allowfullscreen></iframe>]]

==History==

===John Dalton: The Law of Multiple Proportions and Atomic Mass===
[[File:Daltons_symbols.gif|thumb|Dalton's concept of atoms and molecules]]
Working from the conservation of mass principle, chemist John Dalton determined the law of multiple proportions to understand how different elements combined in compounds. In 1803, he proposed that each element of the periodic table was composed of identical components, atoms, that were unique to each element. He also suggested that these atoms were not created nor destroyed when one element was combined with another. Dalton's empirical, experimentally-based work marked the first scientific theory of the atom.

Dalton proposed a list of atomic weights in 1805. However, Dalton failed to recognize natural tendencies of elements in nature (for example, oxygen typically exists as a diatomic molecule as <math>\text{O}_2</math>). Dalton was unable to distinguish between atoms and molecules (groups of atoms).

===Amedeo Avogadro: Avogadro's Law===
In 1811, [[Amedeo Avogadro]] studied gases and determined that the amount of volume a gas occupies is not determined by the mass of the gas. This allowed Avogadro to take more accurate atomic measurements of gases than Dalton, and differentiate atoms from molecules.

===Robert Brown: Brownian Motion===
A Scottish botanist, Robert Brown, studied the motion of tiny pollen particles in water in 1827. The particles followed complex paths, dubbed Brownian Motion. As early as 1905, [[Albert Einstein]] used Brownian Motion to predict the size of atoms and molecules.

===J.J. Thomson: The Plum-Pudding Model and Electrons===
[[File:Plum_pudding_model.svg|thumb|Tomson's Plum-Pudding Model]]
Through his work with cathode rays, [[J.J. Thomson]] discovered the electron in 1897, and was the first to learn that atoms weren't actually "uncuttable" as initially thought. Thomson knew that atoms had a net neutral charge, but he only knew that negative particles existed. Thus, Thomson developed the "plum-pudding" model of negatively charged electrons floating in a sea of positive charge. (He likened the relationship of electrons to the sea of positive charge to that of plums in plum pudding.)

===Ernest Rutherford: Gold Foil Experiment and the Nucleus===
In 1909, one of Thomson's students, [[Ernest Rutherford]], determined that the positive charge of atoms was located in a central nucleus. He shot small, positively charged alpha particles at thin sheets of gold foil and noted that some particles were sharply deflected. This deflection could only occur if the positive components of atoms were located in a small area, which Rutherford assumed to be the center. He proposed a planetary model of atoms where a cloud of electrons surrounded a central, positively charged nucleus.

===Niels Bohr: Introducing Quantum Physics===
[[File:Bohr_atom_animation_2.gif|thumb|The Bohr model for a Hydrogen atom with its electron moving between energy levels]]
As quantum mechanics progressed through the work of [[Albert Einstein]] and [[Max Planck]], [[Niels Bohr]] updated the atomic model in 1913 to account for quantum phenomena. Bohr, who was also one of Rutherford's students, suggested that electrostatic forces kept electrons in circular orbit around the positively charged central nucleus. In support of his theory, Bohr examined the behavior of electrons in hydrogen molecules and noted that they followed distinct energy levels. When an electron changed energy levels, it gained or lost energy, which could be emitted in the form of light. While the Bohr model holds true for hydrogen, it isn't accurate for multi-electron elements.

===James Chadwick: Neutrons===
James Chadwick won a Nobel Prize in 1935 for his discovery of the neutron. Starting with Rutherford's work, Chadwick continued experimenting to determine the excess mass in the nucleus that wasn't accounted for by protons. He found that neutrally charged particles, dubbed neutrons, were also inside the nucleus.

===The Current Model: Quantum Physics and Electron Orbitals===
Erwin Schrödinger examined the possibility that moving electrons behaved more like waves than particles, and published "Schrödinger's Equation" in 1926. Although this resolved many issues encountered with the Bohr model, it faced opposition from physicist [[Max Born]]. Instead, Born suggested a wave-particle duality of electrons, which stated that electrons could behave both like a wave and a particle.
As electrons were now given properties of waves, it was impossible to simultaneously determine an electron's exact location and momentum around the nucleus. Werner Heisenberg, first described this phenomena in 1927, and it was later named the Heisenberg Uncertainty Principle. This refuted the Bohr model of the atom, and replaced it with a pattern of probabilities as to where electrons are located around the nucleus. These patterns are referred to as atomic orbitals and come in a variety of shapes (basic spheres, rings, dumbbells, etc.) and the nucleus is always at the center.
[[File:Neon_orbitals.JPG|thumb|center|The first five atomic orbitals: 1s, 2s, 2px, 2py, and 2pz.]]

==Connectedness==
While classical physics applies to large objects moving much slower than the speed of light, modern physics deals with special cases of tiny objects, like atoms, subject to relativistic effects. Atomic theory is vital to understanding many quantum physics concepts that are covered in both Physics 2211 and 2212, like the ball-and-spring model of solids, point charges, and conductivity.

Although one can argue physics applies to just about every aspect of life, and atomic theory is critical to understanding physics, atomic theory has directly influenced material science, power generation, electronics, and even food processing, to name a few.

<gallery>
File:Apollo_synthetic_diamond.jpg|'''Material Science:''' Synthetic diamonds are used for both cosmetic retail and in manufacturing cutting tools.
File:Electrical_and_Mechanical_Services_Department_Headquarters_Photovoltaics.jpg|'''Power:''' Solar cells and power rely on the photovoltaic effect and the wave-particle duality of subatomic particles (like photons).
File:Monokristalines_Silizium_f%C3%BCr_die_Waferherstellung.jpg|'''Electronics:''' Silicon, a popular semiconductor used in electronics, is produced industrially in a single-crystal form.
File:Sodium-chloride-3D-ionic.png|'''Food processing:''' An atomic view of table salt. Purple particles are sodium (Na), and green particles are chlorine (Cl).
File:Nagasakibomb.jpg|'''Defense:''' Nuclear weapons were used during World War II.
File:White_Matter_Connections_Obtained_with_MRI_Tractography.png|'''Medicine:''' MRI's provide doctors critical information without the risks of surgery.
File:Plastic_household_items.jpg|'''Manufacturing:''' Many common household items are made with plastic.
</gallery>

== See also ==

*[[Bohr Model]]
*[[Electronic Energy Levels and Photons]]
*[[Rutherford Experiment and Atomic Collisions]]

===Notable Scientists===
*[[Amedeo Avogadro]]
*[[J.J. Thomson]]
*[[Ernest Rutherford]]
*[[Albert Einstein]]
*[[Max Planck]]
*[[Niels Bohr]]
*[[Max Born]]

===Related Theories===
*[[Quantum Theory]]
*[[Einstein's Theory of Special Relativity]]

===Concept Application===
*[[Ball and Spring Model of Matter]], [[Ball and Spring Model]]
*[[Length and Stiffness of an Interatomic Bond]], [[Young's Modulus]]
*[[Density]], [[Charge]], [[Spin]], and [[Conductivity]]
*[[The Photoelectric Effect]], [[Photons]]
*[[Rest Mass Energy]]
*[[Potential Energy of a Pair of Neutral Atoms]]

===External links===
*Physics Portal description of [https://en.wikipedia.org/wiki/History_of_molecular_theory Molecular Theory] and [https://en.wikipedia.org/wiki/Elementary_particle Subatomic Particles]
*HyperPhysics summary of [http://hyperphysics.phy-astr.gsu.edu/hbase/quacon.html#quacon Quantum Physics]
*Demonstration of the [https://phet.colorado.edu/en/simulation/legacy/hydrogen-atom various models] of a hydrogen atom

==References==

1. “Atomic Theory.” Wikipedia, Wikimedia Foundation, 19 Feb. 2022, https://en.wikipedia.org/wiki/Atomic_theory.

2. Introduction to Atomistic Modeling Xxx Techniques. https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf.

3. Clark, S J. “Atomistic Models.” Atomistic Models, http://cmt.dur.ac.uk/sjc/thesis_dlc/node45.html.

4. Introduction to Atomistic Modeling Xxx Techniques. https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf.

5. “Matter Wave.” Wikipedia, Wikimedia Foundation, 3 Apr. 2022, https://en.wikipedia.org/wiki/Matter_wave.

Chapter 30 of [https://openstaxcollege.org/files/textbook_version/hi_res_pdf/9/CollegePhysics-OP.pdf OpenStax Textbook]

Physics Portal page on [https://en.wikipedia.org/wiki/Atomic_theory Atomic Theory]

[[Category: Theory]]

Atomic Theory

2022-04-19T19:56:30Z

Erinhorbacz: /* A Computational Model */

Claimed by: Erin Horbacz (4/17/2022)

Atomic theory states that matter is composed of discrete units, called atoms. The word "atom" comes from the Greek word for uncuttable, ''atomos'', since it was believed that if one cut a substance into smaller and smaller pieces, one would reach a point where the substance could not be cut any further. Scientists later discovered that atoms were indeed able to be broken into subatomic, or elementary, particles including protons, neutrons, and electrons. Furthermore, protons and neutrons can be broken down yet again into smaller, elementary particles called [https://en.wikipedia.org/wiki/Quark#:~:text=A%20quark%20(%2Fkw%C9%94%CB%90r,the%20components%20of%20atomic%20nuclei./ quarks]. Atomic theory has evolved greatly over time, but the most recent model stems from quantum mechanics[https://en.wikipedia.org/wiki/Atomic_theory].

==The Main Idea==
===A Mathematical Model===
Mathematical models of atomic processes have become more thorough and sophisticated as knowledge of atomic properties has grown. The goal of a mathematical model is to express the underlying rules that govern atomic processes in a formula that can then predict and describe the behavior of atoms [https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf] (such as is seen with the list of Bohr's mathematical models for the atom). Such fundamental formulas are powerful tools for helping scientists understand the interactions within and processes of both microscopic and macroscopic systems. For example, it was [https://en.wikipedia.org/wiki/Charles-Augustin_de_Coulomb/ Charles-Augustin de Coulomb] who first determined the mathematical equation which could accurately describe the electrostatic potential between charged particles that make up an atom:

<math>
V = \frac{1}{4 \pi \epsilon} \frac{q_1 q_2}{r}
</math>

[[File:bohr_equations.jpg|thumb|Bohr's mathematical model to describe the atom]]

where V is the [https://en.wikipedia.org/wiki/Electric_potential/ electrostatic potential] (in volts), <math> \frac{1}{4 \pi \epsilon} </math> is the [https://en.wikipedia.org/wiki/Coulomb_constant#:~:text=The%20Coulomb%20constant%2C%20the%20electric,%E2%88%922%E2%8B%85C%E2%88%922./ Coulomb constant], <math>q_1 </math> and <math> q_2 </math> are the charges of two particles, and r is the distance between the two particles.

Additionally, stretching of atomic bonds are known to be affected by force fields around an equilibrium point, and they can be modeled according to the equation:

<math>
\Delta V(l) = \frac{1}{2} k_l (l - l_0)^2
</math>

Where <math>\Delta V(l) </math> is the change in potential energy at <math>l</math>, <math>k_1</math> is the spring constant (a proportionality constant), <math>l</math> is the bond length, and <math>l_0</math> is the equilibrium bond length[http://cmt.dur.ac.uk/sjc/thesis_dlc/node45.html].

The use and creation of these formulas is incredibly prominent in simulation modeling. For example, simulations modeling the motion of multiple atoms can use mathematical models such as [https://en.wikipedia.org/wiki/Leapfrog_integration/ Leapfrog integration] and [https://en.wikipedia.org/wiki/Verlet_integration/ Verlet integration] to update particle positions and velocities respectively[https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf].

Perhaps the most important aspect of these mathematical models are their ability to take difficult, abstract concepts and represent them in a form that can be manipulated for further research. The creation of models to describe quantum phenomena makes the information more digestible and the concepts somewhat clearer. In fact, it is often the case that a mathematical model describing quantum behavior helps others think about concepts in different ways. In this manner, many discoveries have resulted from generalizing these models to extend beyond their initial boundaries. For example, the [https://en.wikipedia.org/wiki/Wave%E2%80%93particle_duality#:~:text=Wave%E2%80%93particle%20duality%20is%20the,behaviour%20of%20quantum%2Dscale%20objects./ wave-particle duality] of electrons became known through experiments such as the [https://en.wikipedia.org/wiki/Double-slit_experiment/ double-slit experiment] and the [https://en.wikipedia.org/wiki/Photoelectric_effect/ photoelectric effect]. However, it was Louis de Broglie who considered extending the wave nature to all particles, not just electrons. He discovered that all matter has wave properties, and he formulated the de Broglie wavelength[https://en.wikipedia.org/wiki/Matter_wave]:

<math>
\lambda = \frac{h}{p}
</math>

This formula tells us the wavelength of any particle with a given momentum. This was a huge breakthrough for atomic theory, and is a great example of the usefulness of atomic mathematical models to represent information and inspire new findings.

===A Computational Model===
Understanding the composition and structure of atoms is essential to the study of both microscopic and macroscopic systems. Researchers have made use of atomic information to create what are called atomistic models. These models are used to predict and analyze the behavior of complex systems through knowledge of their most fundamental parts. By understanding how atomic structure affects characteristic properties of atoms, scientists are able to create computational models based on simple microscopic characteristics that simulate complex macroscopic systems. In doing so, they aim to better understand the connection between these macroscopic systems and the underlying atomic structures that govern them.

Use of simulations in research has broadened both the volume and complexity of analysis that can be done at any one time. The ability to model atoms through simulations has been an integral part of the research done in diverse areas of science, notably materials science. In this field, atomistic models are often used to predict material properties under certain conditions using information about their nucleus and electron density. For example, professor ABFIEJABF of the physics department of Georgia Tech created an atomistic model that simulates the behavior of atoms in ABFIEJABF. Another use of atomistic models is to simulate and analyze important processes such as a nuclear chain reaction; an example of such a simulation can be viewed on [https://javalab.org/en/nuclear_chain_reaction_en/ JavaLab].

Atomistic models use the mathematical models discussed above to computationally represent atomic forces, atomic positions, velocities, and magnetic charges of atoms among other things. The result is an accurate model of quantum processes. Ultimately, the use of such simulations help to understand the collective behavior of atoms and how this behavior affects macroscopic processes (such as deformation and phase change) as well as performance abilities (such as strength of material).

Simulation of atomic spring model: https://www.myphysicslab.com/springs/molecule3-en.html

[[<iframe src="https://trinket.io/embed/glowscript/31d0f9ad9e?toggleCode=true" width="100%" height="356" frameborder="0" marginwidth="0" marginheight="0" allowfullscreen></iframe>]]

==History==

===John Dalton: The Law of Multiple Proportions and Atomic Mass===
[[File:Daltons_symbols.gif|thumb|Dalton's concept of atoms and molecules]]
Working from the conservation of mass principle, chemist John Dalton determined the law of multiple proportions to understand how different elements combined in compounds. In 1803, he proposed that each element of the periodic table was composed of identical components, atoms, that were unique to each element. He also suggested that these atoms were not created nor destroyed when one element was combined with another. Dalton's empirical, experimentally-based work marked the first scientific theory of the atom.

Dalton proposed a list of atomic weights in 1805. However, Dalton failed to recognize natural tendencies of elements in nature (for example, oxygen typically exists as a diatomic molecule as <math>\text{O}_2</math>). Dalton was unable to distinguish between atoms and molecules (groups of atoms).

===Amedeo Avogadro: Avogadro's Law===
In 1811, [[Amedeo Avogadro]] studied gases and determined that the amount of volume a gas occupies is not determined by the mass of the gas. This allowed Avogadro to take more accurate atomic measurements of gases than Dalton, and differentiate atoms from molecules.

===Robert Brown: Brownian Motion===
A Scottish botanist, Robert Brown, studied the motion of tiny pollen particles in water in 1827. The particles followed complex paths, dubbed Brownian Motion. As early as 1905, [[Albert Einstein]] used Brownian Motion to predict the size of atoms and molecules.

===J.J. Thomson: The Plum-Pudding Model and Electrons===
[[File:Plum_pudding_model.svg|thumb|Tomson's Plum-Pudding Model]]
Through his work with cathode rays, [[J.J. Thomson]] discovered the electron in 1897, and was the first to learn that atoms weren't actually "uncuttable" as initially thought. Thomson knew that atoms had a net neutral charge, but he only knew that negative particles existed. Thus, Thomson developed the "plum-pudding" model of negatively charged electrons floating in a sea of positive charge. (He likened the relationship of electrons to the sea of positive charge to that of plums in plum pudding.)

===Ernest Rutherford: Gold Foil Experiment and the Nucleus===
In 1909, one of Thomson's students, [[Ernest Rutherford]], determined that the positive charge of atoms was located in a central nucleus. He shot small, positively charged alpha particles at thin sheets of gold foil and noted that some particles were sharply deflected. This deflection could only occur if the positive components of atoms were located in a small area, which Rutherford assumed to be the center. He proposed a planetary model of atoms where a cloud of electrons surrounded a central, positively charged nucleus.

===Niels Bohr: Introducing Quantum Physics===
[[File:Bohr_atom_animation_2.gif|thumb|The Bohr model for a Hydrogen atom with its electron moving between energy levels]]
As quantum mechanics progressed through the work of [[Albert Einstein]] and [[Max Planck]], [[Niels Bohr]] updated the atomic model in 1913 to account for quantum phenomena. Bohr, who was also one of Rutherford's students, suggested that electrostatic forces kept electrons in circular orbit around the positively charged central nucleus. In support of his theory, Bohr examined the behavior of electrons in hydrogen molecules and noted that they followed distinct energy levels. When an electron changed energy levels, it gained or lost energy, which could be emitted in the form of light. While the Bohr model holds true for hydrogen, it isn't accurate for multi-electron elements.

===James Chadwick: Neutrons===
James Chadwick won a Nobel Prize in 1935 for his discovery of the neutron. Starting with Rutherford's work, Chadwick continued experimenting to determine the excess mass in the nucleus that wasn't accounted for by protons. He found that neutrally charged particles, dubbed neutrons, were also inside the nucleus.

===The Current Model: Quantum Physics and Electron Orbitals===
Erwin Schrödinger examined the possibility that moving electrons behaved more like waves than particles, and published "Schrödinger's Equation" in 1926. Although this resolved many issues encountered with the Bohr model, it faced opposition from physicist [[Max Born]]. Instead, Born suggested a wave-particle duality of electrons, which stated that electrons could behave both like a wave and a particle.
As electrons were now given properties of waves, it was impossible to simultaneously determine an electron's exact location and momentum around the nucleus. Werner Heisenberg, first described this phenomena in 1927, and it was later named the Heisenberg Uncertainty Principle. This refuted the Bohr model of the atom, and replaced it with a pattern of probabilities as to where electrons are located around the nucleus. These patterns are referred to as atomic orbitals and come in a variety of shapes (basic spheres, rings, dumbbells, etc.) and the nucleus is always at the center.
[[File:Neon_orbitals.JPG|thumb|center|The first five atomic orbitals: 1s, 2s, 2px, 2py, and 2pz.]]

==Connectedness==
While classical physics applies to large objects moving much slower than the speed of light, modern physics deals with special cases of tiny objects, like atoms, subject to relativistic effects. Atomic theory is vital to understanding many quantum physics concepts that are covered in both Physics 2211 and 2212, like the ball-and-spring model of solids, point charges, and conductivity.

Although one can argue physics applies to just about every aspect of life, and atomic theory is critical to understanding physics, atomic theory has directly influenced material science, power generation, electronics, and even food processing, to name a few.

<gallery>
File:Apollo_synthetic_diamond.jpg|'''Material Science:''' Synthetic diamonds are used for both cosmetic retail and in manufacturing cutting tools.
File:Electrical_and_Mechanical_Services_Department_Headquarters_Photovoltaics.jpg|'''Power:''' Solar cells and power rely on the photovoltaic effect and the wave-particle duality of subatomic particles (like photons).
File:Monokristalines_Silizium_f%C3%BCr_die_Waferherstellung.jpg|'''Electronics:''' Silicon, a popular semiconductor used in electronics, is produced industrially in a single-crystal form.
File:Sodium-chloride-3D-ionic.png|'''Food processing:''' An atomic view of table salt. Purple particles are sodium (Na), and green particles are chlorine (Cl).
File:Nagasakibomb.jpg|'''Defense:''' Nuclear weapons were used during World War II.
File:White_Matter_Connections_Obtained_with_MRI_Tractography.png|'''Medicine:''' MRI's provide doctors critical information without the risks of surgery.
File:Plastic_household_items.jpg|'''Manufacturing:''' Many common household items are made with plastic.
</gallery>

== See also ==

*[[Bohr Model]]
*[[Electronic Energy Levels and Photons]]
*[[Rutherford Experiment and Atomic Collisions]]

===Notable Scientists===
*[[Amedeo Avogadro]]
*[[J.J. Thomson]]
*[[Ernest Rutherford]]
*[[Albert Einstein]]
*[[Max Planck]]
*[[Niels Bohr]]
*[[Max Born]]

===Related Theories===
*[[Quantum Theory]]
*[[Einstein's Theory of Special Relativity]]

===Concept Application===
*[[Ball and Spring Model of Matter]], [[Ball and Spring Model]]
*[[Length and Stiffness of an Interatomic Bond]], [[Young's Modulus]]
*[[Density]], [[Charge]], [[Spin]], and [[Conductivity]]
*[[The Photoelectric Effect]], [[Photons]]
*[[Rest Mass Energy]]
*[[Potential Energy of a Pair of Neutral Atoms]]

===External links===
*Physics Portal description of [https://en.wikipedia.org/wiki/History_of_molecular_theory Molecular Theory] and [https://en.wikipedia.org/wiki/Elementary_particle Subatomic Particles]
*HyperPhysics summary of [http://hyperphysics.phy-astr.gsu.edu/hbase/quacon.html#quacon Quantum Physics]
*Demonstration of the [https://phet.colorado.edu/en/simulation/legacy/hydrogen-atom various models] of a hydrogen atom

==References==

1. “Atomic Theory.” Wikipedia, Wikimedia Foundation, 19 Feb. 2022, https://en.wikipedia.org/wiki/Atomic_theory.

2. Introduction to Atomistic Modeling Xxx Techniques. https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf.

3. Clark, S J. “Atomistic Models.” Atomistic Models, http://cmt.dur.ac.uk/sjc/thesis_dlc/node45.html.

4. Introduction to Atomistic Modeling Xxx Techniques. https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf.

5. “Matter Wave.” Wikipedia, Wikimedia Foundation, 3 Apr. 2022, https://en.wikipedia.org/wiki/Matter_wave.

Chapter 30 of [https://openstaxcollege.org/files/textbook_version/hi_res_pdf/9/CollegePhysics-OP.pdf OpenStax Textbook]

Physics Portal page on [https://en.wikipedia.org/wiki/Atomic_theory Atomic Theory]

[[Category: Theory]]

Atomic Theory

2022-04-19T19:55:00Z

Erinhorbacz: /* A Computational Model */

Claimed by: Erin Horbacz (4/17/2022)

Atomic theory states that matter is composed of discrete units, called atoms. The word "atom" comes from the Greek word for uncuttable, ''atomos'', since it was believed that if one cut a substance into smaller and smaller pieces, one would reach a point where the substance could not be cut any further. Scientists later discovered that atoms were indeed able to be broken into subatomic, or elementary, particles including protons, neutrons, and electrons. Furthermore, protons and neutrons can be broken down yet again into smaller, elementary particles called [https://en.wikipedia.org/wiki/Quark#:~:text=A%20quark%20(%2Fkw%C9%94%CB%90r,the%20components%20of%20atomic%20nuclei./ quarks]. Atomic theory has evolved greatly over time, but the most recent model stems from quantum mechanics[https://en.wikipedia.org/wiki/Atomic_theory].

==The Main Idea==
===A Mathematical Model===
Mathematical models of atomic processes have become more thorough and sophisticated as knowledge of atomic properties has grown. The goal of a mathematical model is to express the underlying rules that govern atomic processes in a formula that can then predict and describe the behavior of atoms [https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf] (such as is seen with the list of Bohr's mathematical models for the atom). Such fundamental formulas are powerful tools for helping scientists understand the interactions within and processes of both microscopic and macroscopic systems. For example, it was [https://en.wikipedia.org/wiki/Charles-Augustin_de_Coulomb/ Charles-Augustin de Coulomb] who first determined the mathematical equation which could accurately describe the electrostatic potential between charged particles that make up an atom:

<math>
V = \frac{1}{4 \pi \epsilon} \frac{q_1 q_2}{r}
</math>

[[File:bohr_equations.jpg|thumb|Bohr's mathematical model to describe the atom]]

where V is the [https://en.wikipedia.org/wiki/Electric_potential/ electrostatic potential] (in volts), <math> \frac{1}{4 \pi \epsilon} </math> is the [https://en.wikipedia.org/wiki/Coulomb_constant#:~:text=The%20Coulomb%20constant%2C%20the%20electric,%E2%88%922%E2%8B%85C%E2%88%922./ Coulomb constant], <math>q_1 </math> and <math> q_2 </math> are the charges of two particles, and r is the distance between the two particles.

Additionally, stretching of atomic bonds are known to be affected by force fields around an equilibrium point, and they can be modeled according to the equation:

<math>
\Delta V(l) = \frac{1}{2} k_l (l - l_0)^2
</math>

Where <math>\Delta V(l) </math> is the change in potential energy at <math>l</math>, <math>k_1</math> is the spring constant (a proportionality constant), <math>l</math> is the bond length, and <math>l_0</math> is the equilibrium bond length[http://cmt.dur.ac.uk/sjc/thesis_dlc/node45.html].

The use and creation of these formulas is incredibly prominent in simulation modeling. For example, simulations modeling the motion of multiple atoms can use mathematical models such as [https://en.wikipedia.org/wiki/Leapfrog_integration/ Leapfrog integration] and [https://en.wikipedia.org/wiki/Verlet_integration/ Verlet integration] to update particle positions and velocities respectively[https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf].

Perhaps the most important aspect of these mathematical models are their ability to take difficult, abstract concepts and represent them in a form that can be manipulated for further research. The creation of models to describe quantum phenomena makes the information more digestible and the concepts somewhat clearer. In fact, it is often the case that a mathematical model describing quantum behavior helps others think about concepts in different ways. In this manner, many discoveries have resulted from generalizing these models to extend beyond their initial boundaries. For example, the [https://en.wikipedia.org/wiki/Wave%E2%80%93particle_duality#:~:text=Wave%E2%80%93particle%20duality%20is%20the,behaviour%20of%20quantum%2Dscale%20objects./ wave-particle duality] of electrons became known through experiments such as the [https://en.wikipedia.org/wiki/Double-slit_experiment/ double-slit experiment] and the [https://en.wikipedia.org/wiki/Photoelectric_effect/ photoelectric effect]. However, it was Louis de Broglie who considered extending the wave nature to all particles, not just electrons. He discovered that all matter has wave properties, and he formulated the de Broglie wavelength[https://en.wikipedia.org/wiki/Matter_wave]:

<math>
\lambda = \frac{h}{p}
</math>

This formula tells us the wavelength of any particle with a given momentum. This was a huge breakthrough for atomic theory, and is a great example of the usefulness of atomic mathematical models to represent information and inspire new findings.

===A Computational Model===
Understanding the composition and structure of atoms is essential to the study of both microscopic and macroscopic systems. Researchers have made use of atomic information to create what are called atomistic models. These models are used to predict and analyze the behavior of complex systems through knowledge of their most fundamental parts. By understanding how atomic structure affects characteristic properties of atoms, scientists are able to create computational models based on simple microscopic characteristics that simulate complex macroscopic systems. In doing so, they aim to better understand the connection between these macroscopic systems and the underlying atomic structures that govern them.

Use of simulations in research has broadened both the volume and complexity of analysis that can be done at any one time. The ability to model atoms through simulations has been an integral part of the research done in diverse areas of science, notably materials science. In this field, atomistic models are often used to predict material properties under certain conditions using information about their nucleus and electron density. For example, professor ABFIEJABF of the physics department of Georgia Tech created an atomistic model that simulates the behavior of atoms in ABFIEJABF. Another use of atomistic models is to simulate and analyze important processes such as a nuclear chain reaction; an example of such a simulation can be viewed on [https://javalab.org/en/nuclear_chain_reaction_en/ JavaLab].

Atomistic models use the mathematical models discussed above to computationally represent atomic forces, atomic positions, velocities, and magnetic charges of atoms among other things. The result is an accurate model of quantum processes. Ultimately, the use of such simulations help to understand the collective behavior of atoms and how this behavior affects macroscopic processes (such as deformation and phase change) as well as performance abilities (such as strength of material).

Simulation of atomic spring model: https://www.myphysicslab.com/springs/molecule3-en.html

[[<iframe src="https://trinket.io/embed/glowscript/31d0f9ad9e?outputOnly=true" width="100%" height="356" frameborder="0" marginwidth="0" marginheight="0" allowfullscreen></iframe>]]

==History==

===John Dalton: The Law of Multiple Proportions and Atomic Mass===
[[File:Daltons_symbols.gif|thumb|Dalton's concept of atoms and molecules]]
Working from the conservation of mass principle, chemist John Dalton determined the law of multiple proportions to understand how different elements combined in compounds. In 1803, he proposed that each element of the periodic table was composed of identical components, atoms, that were unique to each element. He also suggested that these atoms were not created nor destroyed when one element was combined with another. Dalton's empirical, experimentally-based work marked the first scientific theory of the atom.

Dalton proposed a list of atomic weights in 1805. However, Dalton failed to recognize natural tendencies of elements in nature (for example, oxygen typically exists as a diatomic molecule as <math>\text{O}_2</math>). Dalton was unable to distinguish between atoms and molecules (groups of atoms).

===Amedeo Avogadro: Avogadro's Law===
In 1811, [[Amedeo Avogadro]] studied gases and determined that the amount of volume a gas occupies is not determined by the mass of the gas. This allowed Avogadro to take more accurate atomic measurements of gases than Dalton, and differentiate atoms from molecules.

===Robert Brown: Brownian Motion===
A Scottish botanist, Robert Brown, studied the motion of tiny pollen particles in water in 1827. The particles followed complex paths, dubbed Brownian Motion. As early as 1905, [[Albert Einstein]] used Brownian Motion to predict the size of atoms and molecules.

===J.J. Thomson: The Plum-Pudding Model and Electrons===
[[File:Plum_pudding_model.svg|thumb|Tomson's Plum-Pudding Model]]
Through his work with cathode rays, [[J.J. Thomson]] discovered the electron in 1897, and was the first to learn that atoms weren't actually "uncuttable" as initially thought. Thomson knew that atoms had a net neutral charge, but he only knew that negative particles existed. Thus, Thomson developed the "plum-pudding" model of negatively charged electrons floating in a sea of positive charge. (He likened the relationship of electrons to the sea of positive charge to that of plums in plum pudding.)

===Ernest Rutherford: Gold Foil Experiment and the Nucleus===
In 1909, one of Thomson's students, [[Ernest Rutherford]], determined that the positive charge of atoms was located in a central nucleus. He shot small, positively charged alpha particles at thin sheets of gold foil and noted that some particles were sharply deflected. This deflection could only occur if the positive components of atoms were located in a small area, which Rutherford assumed to be the center. He proposed a planetary model of atoms where a cloud of electrons surrounded a central, positively charged nucleus.

===Niels Bohr: Introducing Quantum Physics===
[[File:Bohr_atom_animation_2.gif|thumb|The Bohr model for a Hydrogen atom with its electron moving between energy levels]]
As quantum mechanics progressed through the work of [[Albert Einstein]] and [[Max Planck]], [[Niels Bohr]] updated the atomic model in 1913 to account for quantum phenomena. Bohr, who was also one of Rutherford's students, suggested that electrostatic forces kept electrons in circular orbit around the positively charged central nucleus. In support of his theory, Bohr examined the behavior of electrons in hydrogen molecules and noted that they followed distinct energy levels. When an electron changed energy levels, it gained or lost energy, which could be emitted in the form of light. While the Bohr model holds true for hydrogen, it isn't accurate for multi-electron elements.

===James Chadwick: Neutrons===
James Chadwick won a Nobel Prize in 1935 for his discovery of the neutron. Starting with Rutherford's work, Chadwick continued experimenting to determine the excess mass in the nucleus that wasn't accounted for by protons. He found that neutrally charged particles, dubbed neutrons, were also inside the nucleus.

===The Current Model: Quantum Physics and Electron Orbitals===
Erwin Schrödinger examined the possibility that moving electrons behaved more like waves than particles, and published "Schrödinger's Equation" in 1926. Although this resolved many issues encountered with the Bohr model, it faced opposition from physicist [[Max Born]]. Instead, Born suggested a wave-particle duality of electrons, which stated that electrons could behave both like a wave and a particle.
As electrons were now given properties of waves, it was impossible to simultaneously determine an electron's exact location and momentum around the nucleus. Werner Heisenberg, first described this phenomena in 1927, and it was later named the Heisenberg Uncertainty Principle. This refuted the Bohr model of the atom, and replaced it with a pattern of probabilities as to where electrons are located around the nucleus. These patterns are referred to as atomic orbitals and come in a variety of shapes (basic spheres, rings, dumbbells, etc.) and the nucleus is always at the center.
[[File:Neon_orbitals.JPG|thumb|center|The first five atomic orbitals: 1s, 2s, 2px, 2py, and 2pz.]]

==Connectedness==
While classical physics applies to large objects moving much slower than the speed of light, modern physics deals with special cases of tiny objects, like atoms, subject to relativistic effects. Atomic theory is vital to understanding many quantum physics concepts that are covered in both Physics 2211 and 2212, like the ball-and-spring model of solids, point charges, and conductivity.

Although one can argue physics applies to just about every aspect of life, and atomic theory is critical to understanding physics, atomic theory has directly influenced material science, power generation, electronics, and even food processing, to name a few.

<gallery>
File:Apollo_synthetic_diamond.jpg|'''Material Science:''' Synthetic diamonds are used for both cosmetic retail and in manufacturing cutting tools.
File:Electrical_and_Mechanical_Services_Department_Headquarters_Photovoltaics.jpg|'''Power:''' Solar cells and power rely on the photovoltaic effect and the wave-particle duality of subatomic particles (like photons).
File:Monokristalines_Silizium_f%C3%BCr_die_Waferherstellung.jpg|'''Electronics:''' Silicon, a popular semiconductor used in electronics, is produced industrially in a single-crystal form.
File:Sodium-chloride-3D-ionic.png|'''Food processing:''' An atomic view of table salt. Purple particles are sodium (Na), and green particles are chlorine (Cl).
File:Nagasakibomb.jpg|'''Defense:''' Nuclear weapons were used during World War II.
File:White_Matter_Connections_Obtained_with_MRI_Tractography.png|'''Medicine:''' MRI's provide doctors critical information without the risks of surgery.
File:Plastic_household_items.jpg|'''Manufacturing:''' Many common household items are made with plastic.
</gallery>

== See also ==

*[[Bohr Model]]
*[[Electronic Energy Levels and Photons]]
*[[Rutherford Experiment and Atomic Collisions]]

===Notable Scientists===
*[[Amedeo Avogadro]]
*[[J.J. Thomson]]
*[[Ernest Rutherford]]
*[[Albert Einstein]]
*[[Max Planck]]
*[[Niels Bohr]]
*[[Max Born]]

===Related Theories===
*[[Quantum Theory]]
*[[Einstein's Theory of Special Relativity]]

===Concept Application===
*[[Ball and Spring Model of Matter]], [[Ball and Spring Model]]
*[[Length and Stiffness of an Interatomic Bond]], [[Young's Modulus]]
*[[Density]], [[Charge]], [[Spin]], and [[Conductivity]]
*[[The Photoelectric Effect]], [[Photons]]
*[[Rest Mass Energy]]
*[[Potential Energy of a Pair of Neutral Atoms]]

===External links===
*Physics Portal description of [https://en.wikipedia.org/wiki/History_of_molecular_theory Molecular Theory] and [https://en.wikipedia.org/wiki/Elementary_particle Subatomic Particles]
*HyperPhysics summary of [http://hyperphysics.phy-astr.gsu.edu/hbase/quacon.html#quacon Quantum Physics]
*Demonstration of the [https://phet.colorado.edu/en/simulation/legacy/hydrogen-atom various models] of a hydrogen atom

==References==

1. “Atomic Theory.” Wikipedia, Wikimedia Foundation, 19 Feb. 2022, https://en.wikipedia.org/wiki/Atomic_theory.

2. Introduction to Atomistic Modeling Xxx Techniques. https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf.

3. Clark, S J. “Atomistic Models.” Atomistic Models, http://cmt.dur.ac.uk/sjc/thesis_dlc/node45.html.

4. Introduction to Atomistic Modeling Xxx Techniques. https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf.

5. “Matter Wave.” Wikipedia, Wikimedia Foundation, 3 Apr. 2022, https://en.wikipedia.org/wiki/Matter_wave.

Chapter 30 of [https://openstaxcollege.org/files/textbook_version/hi_res_pdf/9/CollegePhysics-OP.pdf OpenStax Textbook]

Physics Portal page on [https://en.wikipedia.org/wiki/Atomic_theory Atomic Theory]

[[Category: Theory]]

Atomic Theory

2022-04-18T03:41:32Z

Erinhorbacz: /* A Computational Model */

Claimed by: Erin Horbacz (4/17/2022)

Atomic theory states that matter is composed of discrete units, called atoms. The word "atom" comes from the Greek word for uncuttable, ''atomos'', since it was believed that if one cut a substance into smaller and smaller pieces, one would reach a point where the substance could not be cut any further. Scientists later discovered that atoms were indeed able to be broken into subatomic, or elementary, particles including protons, neutrons, and electrons. Furthermore, protons and neutrons can be broken down yet again into smaller, elementary particles called [https://en.wikipedia.org/wiki/Quark#:~:text=A%20quark%20(%2Fkw%C9%94%CB%90r,the%20components%20of%20atomic%20nuclei./ quarks]. Atomic theory has evolved greatly over time, but the most recent model stems from quantum mechanics[https://en.wikipedia.org/wiki/Atomic_theory].

==The Main Idea==
===A Mathematical Model===
Mathematical models of atomic processes have become more thorough and sophisticated as knowledge of atomic properties has grown. The goal of a mathematical model is to express the underlying rules that govern atomic processes in a formula that can then predict and describe the behavior of atoms [https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf] (such as is seen with the list of Bohr's mathematical models for the atom). Such fundamental formulas are powerful tools for helping scientists understand the interactions within and processes of both microscopic and macroscopic systems. For example, it was [https://en.wikipedia.org/wiki/Charles-Augustin_de_Coulomb/ Charles-Augustin de Coulomb] who first determined the mathematical equation which could accurately describe the electrostatic potential between charged particles that make up an atom:

<math>
V = \frac{1}{4 \pi \epsilon} \frac{q_1 q_2}{r}
</math>

[[File:bohr_equations.jpg|thumb|Bohr's mathematical model to describe the atom]]

where V is the [https://en.wikipedia.org/wiki/Electric_potential/ electrostatic potential] (in volts), <math> \frac{1}{4 \pi \epsilon} </math> is the [https://en.wikipedia.org/wiki/Coulomb_constant#:~:text=The%20Coulomb%20constant%2C%20the%20electric,%E2%88%922%E2%8B%85C%E2%88%922./ Coulomb constant], <math>q_1 </math> and <math> q_2 </math> are the charges of two particles, and r is the distance between the two particles.

Additionally, stretching of atomic bonds are known to be affected by force fields around an equilibrium point, and they can be modeled according to the equation:

<math>
\Delta V(l) = \frac{1}{2} k_l (l - l_0)^2
</math>

Where <math>\Delta V(l) </math> is the change in potential energy at <math>l</math>, <math>k_1</math> is the spring constant (a proportionality constant), <math>l</math> is the bond length, and <math>l_0</math> is the equilibrium bond length[http://cmt.dur.ac.uk/sjc/thesis_dlc/node45.html].

The use and creation of these formulas is incredibly prominent in simulation modeling. For example, simulations modeling the motion of multiple atoms can use mathematical models such as [https://en.wikipedia.org/wiki/Leapfrog_integration/ Leapfrog integration] and [https://en.wikipedia.org/wiki/Verlet_integration/ Verlet integration] to update particle positions and velocities respectively[https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf].

Perhaps the most important aspect of these mathematical models are their ability to take difficult, abstract concepts and represent them in a form that can be manipulated for further research. The creation of models to describe quantum phenomena makes the information more digestible and the concepts somewhat clearer. In fact, it is often the case that a mathematical model describing quantum behavior helps others think about concepts in different ways. In this manner, many discoveries have resulted from generalizing these models to extend beyond their initial boundaries. For example, the [https://en.wikipedia.org/wiki/Wave%E2%80%93particle_duality#:~:text=Wave%E2%80%93particle%20duality%20is%20the,behaviour%20of%20quantum%2Dscale%20objects./ wave-particle duality] of electrons became known through experiments such as the [https://en.wikipedia.org/wiki/Double-slit_experiment/ double-slit experiment] and the [https://en.wikipedia.org/wiki/Photoelectric_effect/ photoelectric effect]. However, it was Louis de Broglie who considered extending the wave nature to all particles, not just electrons. He discovered that all matter has wave properties, and he formulated the de Broglie wavelength[https://en.wikipedia.org/wiki/Matter_wave]:

<math>
\lambda = \frac{h}{p}
</math>

This formula tells us the wavelength of any particle with a given momentum. This was a huge breakthrough for atomic theory, and is a great example of the usefulness of atomic mathematical models to represent information and inspire new findings.

===A Computational Model===
Understanding the composition and structure of atoms is essential to the study of both microscopic and macroscopic systems. Researchers have made use of atomic information to create what are called atomistic models. These models are used to predict and analyze the behavior of complex systems through knowledge of their most fundamental parts. By understanding how atomic structure affects characteristic properties of atoms, scientists are able to create computational models based on simple microscopic characteristics that simulate complex macroscopic systems. In doing so, they aim to better understand the connection between these macroscopic systems and the underlying atomic structures that govern them.

Use of simulations in research has broadened both the volume and complexity of analysis that can be done at any one time. The ability to model atoms through simulations has been an integral part of the research done in diverse areas of science, notably materials science. In this field, atomistic models are often used to predict material properties under certain conditions using information about their nucleus and electron density. For example, professor ABFIEJABF of the physics department of Georgia Tech created an atomistic model that simulates the behavior of atoms in ABFIEJABF. Another use of atomistic models is to simulate and analyze important processes such as a nuclear chain reaction; an example of such a simulation can be viewed on [https://javalab.org/en/nuclear_chain_reaction_en/ JavaLab].

Atomistic models use the mathematical models discussed above to computationally represent atomic forces, atomic positions, velocities, and magnetic charges of atoms among other things. The result is an accurate model of quantum processes. Ultimately, the use of such simulations help to understand the collective behavior of atoms and how this behavior affects macroscopic processes (such as deformation and phase change) as well as performance abilities (such as strength of material).

Simulation of atomic spring model: https://www.myphysicslab.com/springs/molecule3-en.html

==History==

===John Dalton: The Law of Multiple Proportions and Atomic Mass===
[[File:Daltons_symbols.gif|thumb|Dalton's concept of atoms and molecules]]
Working from the conservation of mass principle, chemist John Dalton determined the law of multiple proportions to understand how different elements combined in compounds. In 1803, he proposed that each element of the periodic table was composed of identical components, atoms, that were unique to each element. He also suggested that these atoms were not created nor destroyed when one element was combined with another. Dalton's empirical, experimentally-based work marked the first scientific theory of the atom.

Dalton proposed a list of atomic weights in 1805. However, Dalton failed to recognize natural tendencies of elements in nature (for example, oxygen typically exists as a diatomic molecule as <math>\text{O}_2</math>). Dalton was unable to distinguish between atoms and molecules (groups of atoms).

===Amedeo Avogadro: Avogadro's Law===
In 1811, [[Amedeo Avogadro]] studied gases and determined that the amount of volume a gas occupies is not determined by the mass of the gas. This allowed Avogadro to take more accurate atomic measurements of gases than Dalton, and differentiate atoms from molecules.

===Robert Brown: Brownian Motion===
A Scottish botanist, Robert Brown, studied the motion of tiny pollen particles in water in 1827. The particles followed complex paths, dubbed Brownian Motion. As early as 1905, [[Albert Einstein]] used Brownian Motion to predict the size of atoms and molecules.

===J.J. Thomson: The Plum-Pudding Model and Electrons===
[[File:Plum_pudding_model.svg|thumb|Tomson's Plum-Pudding Model]]
Through his work with cathode rays, [[J.J. Thomson]] discovered the electron in 1897, and was the first to learn that atoms weren't actually "uncuttable" as initially thought. Thomson knew that atoms had a net neutral charge, but he only knew that negative particles existed. Thus, Thomson developed the "plum-pudding" model of negatively charged electrons floating in a sea of positive charge. (He likened the relationship of electrons to the sea of positive charge to that of plums in plum pudding.)

===Ernest Rutherford: Gold Foil Experiment and the Nucleus===
In 1909, one of Thomson's students, [[Ernest Rutherford]], determined that the positive charge of atoms was located in a central nucleus. He shot small, positively charged alpha particles at thin sheets of gold foil and noted that some particles were sharply deflected. This deflection could only occur if the positive components of atoms were located in a small area, which Rutherford assumed to be the center. He proposed a planetary model of atoms where a cloud of electrons surrounded a central, positively charged nucleus.

===Niels Bohr: Introducing Quantum Physics===
[[File:Bohr_atom_animation_2.gif|thumb|The Bohr model for a Hydrogen atom with its electron moving between energy levels]]
As quantum mechanics progressed through the work of [[Albert Einstein]] and [[Max Planck]], [[Niels Bohr]] updated the atomic model in 1913 to account for quantum phenomena. Bohr, who was also one of Rutherford's students, suggested that electrostatic forces kept electrons in circular orbit around the positively charged central nucleus. In support of his theory, Bohr examined the behavior of electrons in hydrogen molecules and noted that they followed distinct energy levels. When an electron changed energy levels, it gained or lost energy, which could be emitted in the form of light. While the Bohr model holds true for hydrogen, it isn't accurate for multi-electron elements.

===James Chadwick: Neutrons===
James Chadwick won a Nobel Prize in 1935 for his discovery of the neutron. Starting with Rutherford's work, Chadwick continued experimenting to determine the excess mass in the nucleus that wasn't accounted for by protons. He found that neutrally charged particles, dubbed neutrons, were also inside the nucleus.

===The Current Model: Quantum Physics and Electron Orbitals===
Erwin Schrödinger examined the possibility that moving electrons behaved more like waves than particles, and published "Schrödinger's Equation" in 1926. Although this resolved many issues encountered with the Bohr model, it faced opposition from physicist [[Max Born]]. Instead, Born suggested a wave-particle duality of electrons, which stated that electrons could behave both like a wave and a particle.
As electrons were now given properties of waves, it was impossible to simultaneously determine an electron's exact location and momentum around the nucleus. Werner Heisenberg, first described this phenomena in 1927, and it was later named the Heisenberg Uncertainty Principle. This refuted the Bohr model of the atom, and replaced it with a pattern of probabilities as to where electrons are located around the nucleus. These patterns are referred to as atomic orbitals and come in a variety of shapes (basic spheres, rings, dumbbells, etc.) and the nucleus is always at the center.
[[File:Neon_orbitals.JPG|thumb|center|The first five atomic orbitals: 1s, 2s, 2px, 2py, and 2pz.]]

==Connectedness==
While classical physics applies to large objects moving much slower than the speed of light, modern physics deals with special cases of tiny objects, like atoms, subject to relativistic effects. Atomic theory is vital to understanding many quantum physics concepts that are covered in both Physics 2211 and 2212, like the ball-and-spring model of solids, point charges, and conductivity.

Although one can argue physics applies to just about every aspect of life, and atomic theory is critical to understanding physics, atomic theory has directly influenced material science, power generation, electronics, and even food processing, to name a few.

<gallery>
File:Apollo_synthetic_diamond.jpg|'''Material Science:''' Synthetic diamonds are used for both cosmetic retail and in manufacturing cutting tools.
File:Electrical_and_Mechanical_Services_Department_Headquarters_Photovoltaics.jpg|'''Power:''' Solar cells and power rely on the photovoltaic effect and the wave-particle duality of subatomic particles (like photons).
File:Monokristalines_Silizium_f%C3%BCr_die_Waferherstellung.jpg|'''Electronics:''' Silicon, a popular semiconductor used in electronics, is produced industrially in a single-crystal form.
File:Sodium-chloride-3D-ionic.png|'''Food processing:''' An atomic view of table salt. Purple particles are sodium (Na), and green particles are chlorine (Cl).
File:Nagasakibomb.jpg|'''Defense:''' Nuclear weapons were used during World War II.
File:White_Matter_Connections_Obtained_with_MRI_Tractography.png|'''Medicine:''' MRI's provide doctors critical information without the risks of surgery.
File:Plastic_household_items.jpg|'''Manufacturing:''' Many common household items are made with plastic.
</gallery>

== See also ==

*[[Bohr Model]]
*[[Electronic Energy Levels and Photons]]
*[[Rutherford Experiment and Atomic Collisions]]

===Notable Scientists===
*[[Amedeo Avogadro]]
*[[J.J. Thomson]]
*[[Ernest Rutherford]]
*[[Albert Einstein]]
*[[Max Planck]]
*[[Niels Bohr]]
*[[Max Born]]

===Related Theories===
*[[Quantum Theory]]
*[[Einstein's Theory of Special Relativity]]

===Concept Application===
*[[Ball and Spring Model of Matter]], [[Ball and Spring Model]]
*[[Length and Stiffness of an Interatomic Bond]], [[Young's Modulus]]
*[[Density]], [[Charge]], [[Spin]], and [[Conductivity]]
*[[The Photoelectric Effect]], [[Photons]]
*[[Rest Mass Energy]]
*[[Potential Energy of a Pair of Neutral Atoms]]

===External links===
*Physics Portal description of [https://en.wikipedia.org/wiki/History_of_molecular_theory Molecular Theory] and [https://en.wikipedia.org/wiki/Elementary_particle Subatomic Particles]
*HyperPhysics summary of [http://hyperphysics.phy-astr.gsu.edu/hbase/quacon.html#quacon Quantum Physics]
*Demonstration of the [https://phet.colorado.edu/en/simulation/legacy/hydrogen-atom various models] of a hydrogen atom

==References==

1. “Atomic Theory.” Wikipedia, Wikimedia Foundation, 19 Feb. 2022, https://en.wikipedia.org/wiki/Atomic_theory.

2. Introduction to Atomistic Modeling Xxx Techniques. https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf.

3. Clark, S J. “Atomistic Models.” Atomistic Models, http://cmt.dur.ac.uk/sjc/thesis_dlc/node45.html.

4. Introduction to Atomistic Modeling Xxx Techniques. https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf.

5. “Matter Wave.” Wikipedia, Wikimedia Foundation, 3 Apr. 2022, https://en.wikipedia.org/wiki/Matter_wave.

Chapter 30 of [https://openstaxcollege.org/files/textbook_version/hi_res_pdf/9/CollegePhysics-OP.pdf OpenStax Textbook]

Physics Portal page on [https://en.wikipedia.org/wiki/Atomic_theory Atomic Theory]

[[Category: Theory]]

Atomic Theory

2022-04-18T03:40:48Z

Erinhorbacz: /* A Computational Model */

Claimed by: Erin Horbacz (4/17/2022)

Atomic theory states that matter is composed of discrete units, called atoms. The word "atom" comes from the Greek word for uncuttable, ''atomos'', since it was believed that if one cut a substance into smaller and smaller pieces, one would reach a point where the substance could not be cut any further. Scientists later discovered that atoms were indeed able to be broken into subatomic, or elementary, particles including protons, neutrons, and electrons. Furthermore, protons and neutrons can be broken down yet again into smaller, elementary particles called [https://en.wikipedia.org/wiki/Quark#:~:text=A%20quark%20(%2Fkw%C9%94%CB%90r,the%20components%20of%20atomic%20nuclei./ quarks]. Atomic theory has evolved greatly over time, but the most recent model stems from quantum mechanics[https://en.wikipedia.org/wiki/Atomic_theory].

==The Main Idea==
===A Mathematical Model===
Mathematical models of atomic processes have become more thorough and sophisticated as knowledge of atomic properties has grown. The goal of a mathematical model is to express the underlying rules that govern atomic processes in a formula that can then predict and describe the behavior of atoms [https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf] (such as is seen with the list of Bohr's mathematical models for the atom). Such fundamental formulas are powerful tools for helping scientists understand the interactions within and processes of both microscopic and macroscopic systems. For example, it was [https://en.wikipedia.org/wiki/Charles-Augustin_de_Coulomb/ Charles-Augustin de Coulomb] who first determined the mathematical equation which could accurately describe the electrostatic potential between charged particles that make up an atom:

<math>
V = \frac{1}{4 \pi \epsilon} \frac{q_1 q_2}{r}
</math>

[[File:bohr_equations.jpg|thumb|Bohr's mathematical model to describe the atom]]

where V is the [https://en.wikipedia.org/wiki/Electric_potential/ electrostatic potential] (in volts), <math> \frac{1}{4 \pi \epsilon} </math> is the [https://en.wikipedia.org/wiki/Coulomb_constant#:~:text=The%20Coulomb%20constant%2C%20the%20electric,%E2%88%922%E2%8B%85C%E2%88%922./ Coulomb constant], <math>q_1 </math> and <math> q_2 </math> are the charges of two particles, and r is the distance between the two particles.

Additionally, stretching of atomic bonds are known to be affected by force fields around an equilibrium point, and they can be modeled according to the equation:

<math>
\Delta V(l) = \frac{1}{2} k_l (l - l_0)^2
</math>

Where <math>\Delta V(l) </math> is the change in potential energy at <math>l</math>, <math>k_1</math> is the spring constant (a proportionality constant), <math>l</math> is the bond length, and <math>l_0</math> is the equilibrium bond length[http://cmt.dur.ac.uk/sjc/thesis_dlc/node45.html].

The use and creation of these formulas is incredibly prominent in simulation modeling. For example, simulations modeling the motion of multiple atoms can use mathematical models such as [https://en.wikipedia.org/wiki/Leapfrog_integration/ Leapfrog integration] and [https://en.wikipedia.org/wiki/Verlet_integration/ Verlet integration] to update particle positions and velocities respectively[https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf].

Perhaps the most important aspect of these mathematical models are their ability to take difficult, abstract concepts and represent them in a form that can be manipulated for further research. The creation of models to describe quantum phenomena makes the information more digestible and the concepts somewhat clearer. In fact, it is often the case that a mathematical model describing quantum behavior helps others think about concepts in different ways. In this manner, many discoveries have resulted from generalizing these models to extend beyond their initial boundaries. For example, the [https://en.wikipedia.org/wiki/Wave%E2%80%93particle_duality#:~:text=Wave%E2%80%93particle%20duality%20is%20the,behaviour%20of%20quantum%2Dscale%20objects./ wave-particle duality] of electrons became known through experiments such as the [https://en.wikipedia.org/wiki/Double-slit_experiment/ double-slit experiment] and the [https://en.wikipedia.org/wiki/Photoelectric_effect/ photoelectric effect]. However, it was Louis de Broglie who considered extending the wave nature to all particles, not just electrons. He discovered that all matter has wave properties, and he formulated the de Broglie wavelength[https://en.wikipedia.org/wiki/Matter_wave]:

<math>
\lambda = \frac{h}{p}
</math>

This formula tells us the wavelength of any particle with a given momentum. This was a huge breakthrough for atomic theory, and is a great example of the usefulness of atomic mathematical models to represent information and inspire new findings.

===A Computational Model===
Understanding the composition and structure of atoms is essential to the study of both microscopic and macroscopic systems. Researchers have made use of atomic information to create what are called atomistic models. These models are used to predict and analyze the behavior of complex systems through knowledge of their most fundamental parts. By understanding how atomic structure affects characteristic properties of atoms, scientists are able to create computational models based on simple microscopic characteristics that simulate complex macroscopic systems. In doing so, they aim to better understand the connection between these macroscopic systems and the underlying atomic structures that govern them.

Use of simulations in research has broadened both the volume and complexity of analysis that can be done at any one time. The ability to model atoms through simulations has been an integral part of the research done in diverse areas of science, notably materials science. In this field, atomistic models are often used to predict material properties under certain conditions using information about their nucleus and electron density. For example, professor ABFIEJABF of the physics department of Georgia Tech created an atomistic model that simulates the behavior of atoms in ABFIEJABF. Another use of atomistic models is to simulate and analyze important processes such as a nuclear chain reaction; an example of such a simulation can be viewed on [https://javalab.org/en/nuclear_chain_reaction_en/ JavaLab].

Atomistic models use the mathematical models discussed above to computationally represent atomic forces, atomic positions, velocities, and magnetic charges of atoms among other things. The result is an accurate model of quantum processes. Ultimately, the use of such simulations help to understand the collective behavior of atoms and how this behavior affects macroscopic processes (such as deformation and phase change) as well as performance abilities (such as strength of material).

Simulation of atomic spring model: [https://www.myphysicslab.com/springs/molecule3-en.html]

==History==

===John Dalton: The Law of Multiple Proportions and Atomic Mass===
[[File:Daltons_symbols.gif|thumb|Dalton's concept of atoms and molecules]]
Working from the conservation of mass principle, chemist John Dalton determined the law of multiple proportions to understand how different elements combined in compounds. In 1803, he proposed that each element of the periodic table was composed of identical components, atoms, that were unique to each element. He also suggested that these atoms were not created nor destroyed when one element was combined with another. Dalton's empirical, experimentally-based work marked the first scientific theory of the atom.

Dalton proposed a list of atomic weights in 1805. However, Dalton failed to recognize natural tendencies of elements in nature (for example, oxygen typically exists as a diatomic molecule as <math>\text{O}_2</math>). Dalton was unable to distinguish between atoms and molecules (groups of atoms).

===Amedeo Avogadro: Avogadro's Law===
In 1811, [[Amedeo Avogadro]] studied gases and determined that the amount of volume a gas occupies is not determined by the mass of the gas. This allowed Avogadro to take more accurate atomic measurements of gases than Dalton, and differentiate atoms from molecules.

===Robert Brown: Brownian Motion===
A Scottish botanist, Robert Brown, studied the motion of tiny pollen particles in water in 1827. The particles followed complex paths, dubbed Brownian Motion. As early as 1905, [[Albert Einstein]] used Brownian Motion to predict the size of atoms and molecules.

===J.J. Thomson: The Plum-Pudding Model and Electrons===
[[File:Plum_pudding_model.svg|thumb|Tomson's Plum-Pudding Model]]
Through his work with cathode rays, [[J.J. Thomson]] discovered the electron in 1897, and was the first to learn that atoms weren't actually "uncuttable" as initially thought. Thomson knew that atoms had a net neutral charge, but he only knew that negative particles existed. Thus, Thomson developed the "plum-pudding" model of negatively charged electrons floating in a sea of positive charge. (He likened the relationship of electrons to the sea of positive charge to that of plums in plum pudding.)

===Ernest Rutherford: Gold Foil Experiment and the Nucleus===
In 1909, one of Thomson's students, [[Ernest Rutherford]], determined that the positive charge of atoms was located in a central nucleus. He shot small, positively charged alpha particles at thin sheets of gold foil and noted that some particles were sharply deflected. This deflection could only occur if the positive components of atoms were located in a small area, which Rutherford assumed to be the center. He proposed a planetary model of atoms where a cloud of electrons surrounded a central, positively charged nucleus.

===Niels Bohr: Introducing Quantum Physics===
[[File:Bohr_atom_animation_2.gif|thumb|The Bohr model for a Hydrogen atom with its electron moving between energy levels]]
As quantum mechanics progressed through the work of [[Albert Einstein]] and [[Max Planck]], [[Niels Bohr]] updated the atomic model in 1913 to account for quantum phenomena. Bohr, who was also one of Rutherford's students, suggested that electrostatic forces kept electrons in circular orbit around the positively charged central nucleus. In support of his theory, Bohr examined the behavior of electrons in hydrogen molecules and noted that they followed distinct energy levels. When an electron changed energy levels, it gained or lost energy, which could be emitted in the form of light. While the Bohr model holds true for hydrogen, it isn't accurate for multi-electron elements.

===James Chadwick: Neutrons===
James Chadwick won a Nobel Prize in 1935 for his discovery of the neutron. Starting with Rutherford's work, Chadwick continued experimenting to determine the excess mass in the nucleus that wasn't accounted for by protons. He found that neutrally charged particles, dubbed neutrons, were also inside the nucleus.

===The Current Model: Quantum Physics and Electron Orbitals===
Erwin Schrödinger examined the possibility that moving electrons behaved more like waves than particles, and published "Schrödinger's Equation" in 1926. Although this resolved many issues encountered with the Bohr model, it faced opposition from physicist [[Max Born]]. Instead, Born suggested a wave-particle duality of electrons, which stated that electrons could behave both like a wave and a particle.
As electrons were now given properties of waves, it was impossible to simultaneously determine an electron's exact location and momentum around the nucleus. Werner Heisenberg, first described this phenomena in 1927, and it was later named the Heisenberg Uncertainty Principle. This refuted the Bohr model of the atom, and replaced it with a pattern of probabilities as to where electrons are located around the nucleus. These patterns are referred to as atomic orbitals and come in a variety of shapes (basic spheres, rings, dumbbells, etc.) and the nucleus is always at the center.
[[File:Neon_orbitals.JPG|thumb|center|The first five atomic orbitals: 1s, 2s, 2px, 2py, and 2pz.]]

==Connectedness==
While classical physics applies to large objects moving much slower than the speed of light, modern physics deals with special cases of tiny objects, like atoms, subject to relativistic effects. Atomic theory is vital to understanding many quantum physics concepts that are covered in both Physics 2211 and 2212, like the ball-and-spring model of solids, point charges, and conductivity.

Although one can argue physics applies to just about every aspect of life, and atomic theory is critical to understanding physics, atomic theory has directly influenced material science, power generation, electronics, and even food processing, to name a few.

<gallery>
File:Apollo_synthetic_diamond.jpg|'''Material Science:''' Synthetic diamonds are used for both cosmetic retail and in manufacturing cutting tools.
File:Electrical_and_Mechanical_Services_Department_Headquarters_Photovoltaics.jpg|'''Power:''' Solar cells and power rely on the photovoltaic effect and the wave-particle duality of subatomic particles (like photons).
File:Monokristalines_Silizium_f%C3%BCr_die_Waferherstellung.jpg|'''Electronics:''' Silicon, a popular semiconductor used in electronics, is produced industrially in a single-crystal form.
File:Sodium-chloride-3D-ionic.png|'''Food processing:''' An atomic view of table salt. Purple particles are sodium (Na), and green particles are chlorine (Cl).
File:Nagasakibomb.jpg|'''Defense:''' Nuclear weapons were used during World War II.
File:White_Matter_Connections_Obtained_with_MRI_Tractography.png|'''Medicine:''' MRI's provide doctors critical information without the risks of surgery.
File:Plastic_household_items.jpg|'''Manufacturing:''' Many common household items are made with plastic.
</gallery>

== See also ==

*[[Bohr Model]]
*[[Electronic Energy Levels and Photons]]
*[[Rutherford Experiment and Atomic Collisions]]

===Notable Scientists===
*[[Amedeo Avogadro]]
*[[J.J. Thomson]]
*[[Ernest Rutherford]]
*[[Albert Einstein]]
*[[Max Planck]]
*[[Niels Bohr]]
*[[Max Born]]

===Related Theories===
*[[Quantum Theory]]
*[[Einstein's Theory of Special Relativity]]

===Concept Application===
*[[Ball and Spring Model of Matter]], [[Ball and Spring Model]]
*[[Length and Stiffness of an Interatomic Bond]], [[Young's Modulus]]
*[[Density]], [[Charge]], [[Spin]], and [[Conductivity]]
*[[The Photoelectric Effect]], [[Photons]]
*[[Rest Mass Energy]]
*[[Potential Energy of a Pair of Neutral Atoms]]

===External links===
*Physics Portal description of [https://en.wikipedia.org/wiki/History_of_molecular_theory Molecular Theory] and [https://en.wikipedia.org/wiki/Elementary_particle Subatomic Particles]
*HyperPhysics summary of [http://hyperphysics.phy-astr.gsu.edu/hbase/quacon.html#quacon Quantum Physics]
*Demonstration of the [https://phet.colorado.edu/en/simulation/legacy/hydrogen-atom various models] of a hydrogen atom

==References==

1. “Atomic Theory.” Wikipedia, Wikimedia Foundation, 19 Feb. 2022, https://en.wikipedia.org/wiki/Atomic_theory.

2. Introduction to Atomistic Modeling Xxx Techniques. https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf.

3. Clark, S J. “Atomistic Models.” Atomistic Models, http://cmt.dur.ac.uk/sjc/thesis_dlc/node45.html.

4. Introduction to Atomistic Modeling Xxx Techniques. https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf.

5. “Matter Wave.” Wikipedia, Wikimedia Foundation, 3 Apr. 2022, https://en.wikipedia.org/wiki/Matter_wave.

Chapter 30 of [https://openstaxcollege.org/files/textbook_version/hi_res_pdf/9/CollegePhysics-OP.pdf OpenStax Textbook]

Physics Portal page on [https://en.wikipedia.org/wiki/Atomic_theory Atomic Theory]

[[Category: Theory]]

Atomic Theory

2022-04-18T03:35:37Z

Erinhorbacz: /* A Mathematical Model */

Claimed by: Erin Horbacz (4/17/2022)

Atomic theory states that matter is composed of discrete units, called atoms. The word "atom" comes from the Greek word for uncuttable, ''atomos'', since it was believed that if one cut a substance into smaller and smaller pieces, one would reach a point where the substance could not be cut any further. Scientists later discovered that atoms were indeed able to be broken into subatomic, or elementary, particles including protons, neutrons, and electrons. Furthermore, protons and neutrons can be broken down yet again into smaller, elementary particles called [https://en.wikipedia.org/wiki/Quark#:~:text=A%20quark%20(%2Fkw%C9%94%CB%90r,the%20components%20of%20atomic%20nuclei./ quarks]. Atomic theory has evolved greatly over time, but the most recent model stems from quantum mechanics[https://en.wikipedia.org/wiki/Atomic_theory].

==The Main Idea==
===A Mathematical Model===
Mathematical models of atomic processes have become more thorough and sophisticated as knowledge of atomic properties has grown. The goal of a mathematical model is to express the underlying rules that govern atomic processes in a formula that can then predict and describe the behavior of atoms [https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf] (such as is seen with the list of Bohr's mathematical models for the atom). Such fundamental formulas are powerful tools for helping scientists understand the interactions within and processes of both microscopic and macroscopic systems. For example, it was [https://en.wikipedia.org/wiki/Charles-Augustin_de_Coulomb/ Charles-Augustin de Coulomb] who first determined the mathematical equation which could accurately describe the electrostatic potential between charged particles that make up an atom:

<math>
V = \frac{1}{4 \pi \epsilon} \frac{q_1 q_2}{r}
</math>

[[File:bohr_equations.jpg|thumb|Bohr's mathematical model to describe the atom]]

where V is the [https://en.wikipedia.org/wiki/Electric_potential/ electrostatic potential] (in volts), <math> \frac{1}{4 \pi \epsilon} </math> is the [https://en.wikipedia.org/wiki/Coulomb_constant#:~:text=The%20Coulomb%20constant%2C%20the%20electric,%E2%88%922%E2%8B%85C%E2%88%922./ Coulomb constant], <math>q_1 </math> and <math> q_2 </math> are the charges of two particles, and r is the distance between the two particles.

Additionally, stretching of atomic bonds are known to be affected by force fields around an equilibrium point, and they can be modeled according to the equation:

<math>
\Delta V(l) = \frac{1}{2} k_l (l - l_0)^2
</math>

Where <math>\Delta V(l) </math> is the change in potential energy at <math>l</math>, <math>k_1</math> is the spring constant (a proportionality constant), <math>l</math> is the bond length, and <math>l_0</math> is the equilibrium bond length[http://cmt.dur.ac.uk/sjc/thesis_dlc/node45.html].

The use and creation of these formulas is incredibly prominent in simulation modeling. For example, simulations modeling the motion of multiple atoms can use mathematical models such as [https://en.wikipedia.org/wiki/Leapfrog_integration/ Leapfrog integration] and [https://en.wikipedia.org/wiki/Verlet_integration/ Verlet integration] to update particle positions and velocities respectively[https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf].

Perhaps the most important aspect of these mathematical models are their ability to take difficult, abstract concepts and represent them in a form that can be manipulated for further research. The creation of models to describe quantum phenomena makes the information more digestible and the concepts somewhat clearer. In fact, it is often the case that a mathematical model describing quantum behavior helps others think about concepts in different ways. In this manner, many discoveries have resulted from generalizing these models to extend beyond their initial boundaries. For example, the [https://en.wikipedia.org/wiki/Wave%E2%80%93particle_duality#:~:text=Wave%E2%80%93particle%20duality%20is%20the,behaviour%20of%20quantum%2Dscale%20objects./ wave-particle duality] of electrons became known through experiments such as the [https://en.wikipedia.org/wiki/Double-slit_experiment/ double-slit experiment] and the [https://en.wikipedia.org/wiki/Photoelectric_effect/ photoelectric effect]. However, it was Louis de Broglie who considered extending the wave nature to all particles, not just electrons. He discovered that all matter has wave properties, and he formulated the de Broglie wavelength[https://en.wikipedia.org/wiki/Matter_wave]:

<math>
\lambda = \frac{h}{p}
</math>

This formula tells us the wavelength of any particle with a given momentum. This was a huge breakthrough for atomic theory, and is a great example of the usefulness of atomic mathematical models to represent information and inspire new findings.

===A Computational Model===
Understanding the composition and structure of atoms is essential to the study of both microscopic and macroscopic systems. Researchers have made use of atomic information to create what are called atomistic models. These models are used to predict and analyze the behavior of complex systems through knowledge of their most fundamental parts. By understanding how atomic structure affects characteristic properties of atoms, scientists are able to create computational models based on simple microscopic characteristics that simulate complex macroscopic systems. In doing so, they aim to better understand the connection between these macroscopic systems and the underlying atomic structures that govern them.

Use of simulations in research has broadened both the volume and complexity of analysis that can be done at any one time. The ability to model atoms through simulations has been an integral part of the research done in diverse areas of science, notably materials science. In this field, atomistic models are often used to predict material properties under certain conditions using information about their nucleus and electron density. For example, professor ABFIEJABF of the physics department of Georgia Tech created an atomistic model that simulates the behavior of atoms in ABFIEJABF. Another use of atomistic models is to simulate and analyze important processes such as a nuclear chain reaction; an example of such a simulation can be viewed on [https://javalab.org/en/nuclear_chain_reaction_en/ JavaLab].

Atomistic models use the mathematical models discussed above to computationally represent atomic forces, atomic positions, velocities, and magnetic charges of atoms among other things. The result is an accurate model of quantum processes. Ultimately, the use of such simulations help to understand the collective behavior of atoms and how this behavior affects macroscopic processes (such as deformation and phase change) as well as performance abilities (such as strength of material).
[[File:https://www.youtube.com/embed/jhGhSXAqXmU?start=30|thumb]]

==History==

===John Dalton: The Law of Multiple Proportions and Atomic Mass===
[[File:Daltons_symbols.gif|thumb|Dalton's concept of atoms and molecules]]
Working from the conservation of mass principle, chemist John Dalton determined the law of multiple proportions to understand how different elements combined in compounds. In 1803, he proposed that each element of the periodic table was composed of identical components, atoms, that were unique to each element. He also suggested that these atoms were not created nor destroyed when one element was combined with another. Dalton's empirical, experimentally-based work marked the first scientific theory of the atom.

Dalton proposed a list of atomic weights in 1805. However, Dalton failed to recognize natural tendencies of elements in nature (for example, oxygen typically exists as a diatomic molecule as <math>\text{O}_2</math>). Dalton was unable to distinguish between atoms and molecules (groups of atoms).

===Amedeo Avogadro: Avogadro's Law===
In 1811, [[Amedeo Avogadro]] studied gases and determined that the amount of volume a gas occupies is not determined by the mass of the gas. This allowed Avogadro to take more accurate atomic measurements of gases than Dalton, and differentiate atoms from molecules.

===Robert Brown: Brownian Motion===
A Scottish botanist, Robert Brown, studied the motion of tiny pollen particles in water in 1827. The particles followed complex paths, dubbed Brownian Motion. As early as 1905, [[Albert Einstein]] used Brownian Motion to predict the size of atoms and molecules.

===J.J. Thomson: The Plum-Pudding Model and Electrons===
[[File:Plum_pudding_model.svg|thumb|Tomson's Plum-Pudding Model]]
Through his work with cathode rays, [[J.J. Thomson]] discovered the electron in 1897, and was the first to learn that atoms weren't actually "uncuttable" as initially thought. Thomson knew that atoms had a net neutral charge, but he only knew that negative particles existed. Thus, Thomson developed the "plum-pudding" model of negatively charged electrons floating in a sea of positive charge. (He likened the relationship of electrons to the sea of positive charge to that of plums in plum pudding.)

===Ernest Rutherford: Gold Foil Experiment and the Nucleus===
In 1909, one of Thomson's students, [[Ernest Rutherford]], determined that the positive charge of atoms was located in a central nucleus. He shot small, positively charged alpha particles at thin sheets of gold foil and noted that some particles were sharply deflected. This deflection could only occur if the positive components of atoms were located in a small area, which Rutherford assumed to be the center. He proposed a planetary model of atoms where a cloud of electrons surrounded a central, positively charged nucleus.

===Niels Bohr: Introducing Quantum Physics===
[[File:Bohr_atom_animation_2.gif|thumb|The Bohr model for a Hydrogen atom with its electron moving between energy levels]]
As quantum mechanics progressed through the work of [[Albert Einstein]] and [[Max Planck]], [[Niels Bohr]] updated the atomic model in 1913 to account for quantum phenomena. Bohr, who was also one of Rutherford's students, suggested that electrostatic forces kept electrons in circular orbit around the positively charged central nucleus. In support of his theory, Bohr examined the behavior of electrons in hydrogen molecules and noted that they followed distinct energy levels. When an electron changed energy levels, it gained or lost energy, which could be emitted in the form of light. While the Bohr model holds true for hydrogen, it isn't accurate for multi-electron elements.

===James Chadwick: Neutrons===
James Chadwick won a Nobel Prize in 1935 for his discovery of the neutron. Starting with Rutherford's work, Chadwick continued experimenting to determine the excess mass in the nucleus that wasn't accounted for by protons. He found that neutrally charged particles, dubbed neutrons, were also inside the nucleus.

===The Current Model: Quantum Physics and Electron Orbitals===
Erwin Schrödinger examined the possibility that moving electrons behaved more like waves than particles, and published "Schrödinger's Equation" in 1926. Although this resolved many issues encountered with the Bohr model, it faced opposition from physicist [[Max Born]]. Instead, Born suggested a wave-particle duality of electrons, which stated that electrons could behave both like a wave and a particle.
As electrons were now given properties of waves, it was impossible to simultaneously determine an electron's exact location and momentum around the nucleus. Werner Heisenberg, first described this phenomena in 1927, and it was later named the Heisenberg Uncertainty Principle. This refuted the Bohr model of the atom, and replaced it with a pattern of probabilities as to where electrons are located around the nucleus. These patterns are referred to as atomic orbitals and come in a variety of shapes (basic spheres, rings, dumbbells, etc.) and the nucleus is always at the center.
[[File:Neon_orbitals.JPG|thumb|center|The first five atomic orbitals: 1s, 2s, 2px, 2py, and 2pz.]]

==Connectedness==
While classical physics applies to large objects moving much slower than the speed of light, modern physics deals with special cases of tiny objects, like atoms, subject to relativistic effects. Atomic theory is vital to understanding many quantum physics concepts that are covered in both Physics 2211 and 2212, like the ball-and-spring model of solids, point charges, and conductivity.

Although one can argue physics applies to just about every aspect of life, and atomic theory is critical to understanding physics, atomic theory has directly influenced material science, power generation, electronics, and even food processing, to name a few.

<gallery>
File:Apollo_synthetic_diamond.jpg|'''Material Science:''' Synthetic diamonds are used for both cosmetic retail and in manufacturing cutting tools.
File:Electrical_and_Mechanical_Services_Department_Headquarters_Photovoltaics.jpg|'''Power:''' Solar cells and power rely on the photovoltaic effect and the wave-particle duality of subatomic particles (like photons).
File:Monokristalines_Silizium_f%C3%BCr_die_Waferherstellung.jpg|'''Electronics:''' Silicon, a popular semiconductor used in electronics, is produced industrially in a single-crystal form.
File:Sodium-chloride-3D-ionic.png|'''Food processing:''' An atomic view of table salt. Purple particles are sodium (Na), and green particles are chlorine (Cl).
File:Nagasakibomb.jpg|'''Defense:''' Nuclear weapons were used during World War II.
File:White_Matter_Connections_Obtained_with_MRI_Tractography.png|'''Medicine:''' MRI's provide doctors critical information without the risks of surgery.
File:Plastic_household_items.jpg|'''Manufacturing:''' Many common household items are made with plastic.
</gallery>

== See also ==

*[[Bohr Model]]
*[[Electronic Energy Levels and Photons]]
*[[Rutherford Experiment and Atomic Collisions]]

===Notable Scientists===
*[[Amedeo Avogadro]]
*[[J.J. Thomson]]
*[[Ernest Rutherford]]
*[[Albert Einstein]]
*[[Max Planck]]
*[[Niels Bohr]]
*[[Max Born]]

===Related Theories===
*[[Quantum Theory]]
*[[Einstein's Theory of Special Relativity]]

===Concept Application===
*[[Ball and Spring Model of Matter]], [[Ball and Spring Model]]
*[[Length and Stiffness of an Interatomic Bond]], [[Young's Modulus]]
*[[Density]], [[Charge]], [[Spin]], and [[Conductivity]]
*[[The Photoelectric Effect]], [[Photons]]
*[[Rest Mass Energy]]
*[[Potential Energy of a Pair of Neutral Atoms]]

===External links===
*Physics Portal description of [https://en.wikipedia.org/wiki/History_of_molecular_theory Molecular Theory] and [https://en.wikipedia.org/wiki/Elementary_particle Subatomic Particles]
*HyperPhysics summary of [http://hyperphysics.phy-astr.gsu.edu/hbase/quacon.html#quacon Quantum Physics]
*Demonstration of the [https://phet.colorado.edu/en/simulation/legacy/hydrogen-atom various models] of a hydrogen atom

==References==

1. “Atomic Theory.” Wikipedia, Wikimedia Foundation, 19 Feb. 2022, https://en.wikipedia.org/wiki/Atomic_theory.

2. Introduction to Atomistic Modeling Xxx Techniques. https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf.

3. Clark, S J. “Atomistic Models.” Atomistic Models, http://cmt.dur.ac.uk/sjc/thesis_dlc/node45.html.

4. Introduction to Atomistic Modeling Xxx Techniques. https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf.

5. “Matter Wave.” Wikipedia, Wikimedia Foundation, 3 Apr. 2022, https://en.wikipedia.org/wiki/Matter_wave.

Chapter 30 of [https://openstaxcollege.org/files/textbook_version/hi_res_pdf/9/CollegePhysics-OP.pdf OpenStax Textbook]

Physics Portal page on [https://en.wikipedia.org/wiki/Atomic_theory Atomic Theory]

[[Category: Theory]]

Atomic Theory

2022-04-18T03:25:30Z

Erinhorbacz: /* A Computational Model */

Claimed by: Erin Horbacz (4/17/2022)

Atomic theory states that matter is composed of discrete units, called atoms. The word "atom" comes from the Greek word for uncuttable, ''atomos'', since it was believed that if one cut a substance into smaller and smaller pieces, one would reach a point where the substance could not be cut any further. Scientists later discovered that atoms were indeed able to be broken into subatomic, or elementary, particles including protons, neutrons, and electrons. Furthermore, protons and neutrons can be broken down yet again into smaller, elementary particles called [https://en.wikipedia.org/wiki/Quark#:~:text=A%20quark%20(%2Fkw%C9%94%CB%90r,the%20components%20of%20atomic%20nuclei./ quarks]. Atomic theory has evolved greatly over time, but the most recent model stems from quantum mechanics[https://en.wikipedia.org/wiki/Atomic_theory].

==The Main Idea==
===A Mathematical Model===
Mathematical models of atomic processes have become more thorough and sophisticated as knowledge of atomic properties has grown. The goal of a mathematical model is to express the underlying rules that govern atomic processes in a formula that can then predict and describe the behavior of atoms [https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf] (such as is seen with the list of Bohr's mathematical models for the atom). Such fundamental formulas are powerful tools for helping scientists understand the interactions within and processes of both microscopic and macroscopic systems. For example, it was [https://en.wikipedia.org/wiki/Charles-Augustin_de_Coulomb/ Charles-Augustin de Coulomb] who first determined the mathematical equation which could accurately describe the electrostatic potential between charged particles that make up an atom:

<math>
V = \frac{1}{4 \pi \epsilon} \frac{q_1 q_2}{r}
</math>

[[File:de-broglie-equation.png|thumb|Bohr's mathematical model to describe the atom]]

where V is the [https://en.wikipedia.org/wiki/Electric_potential/ electrostatic potential] (in volts), <math> \frac{1}{4 \pi \epsilon} </math> is the [https://en.wikipedia.org/wiki/Coulomb_constant#:~:text=The%20Coulomb%20constant%2C%20the%20electric,%E2%88%922%E2%8B%85C%E2%88%922./ Coulomb constant], <math>q_1 </math> and <math> q_2 </math> are the charges of two particles, and r is the distance between the two particles.

Additionally, stretching of atomic bonds are known to be affected by force fields around an equilibrium point, and they can be modeled according to the equation:

<math>
\Delta V(l) = \frac{1}{2} k_l (l - l_0)^2
</math>

Where <math>\Delta V(l) </math> is the change in potential energy at <math>l</math>, <math>k_1</math> is the spring constant (a proportionality constant), <math>l</math> is the bond length, and <math>l_0</math> is the equilibrium bond length[http://cmt.dur.ac.uk/sjc/thesis_dlc/node45.html].

The use and creation of these formulas is incredibly prominent in simulation modeling. For example, simulations modeling the motion of multiple atoms can use mathematical models such as [https://en.wikipedia.org/wiki/Leapfrog_integration/ Leapfrog integration] and [https://en.wikipedia.org/wiki/Verlet_integration/ Verlet integration] to update particle positions and velocities respectively[https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf].

Perhaps the most important aspect of these mathematical models are their ability to take difficult, abstract concepts and represent them in a form that can be manipulated for further research. The creation of models to describe quantum phenomena makes the information more digestible and the concepts somewhat clearer. In fact, it is often the case that a mathematical model describing quantum behavior helps others think about concepts in different ways. In this manner, many discoveries have resulted from generalizing these models to extend beyond their initial boundaries. For example, the [https://en.wikipedia.org/wiki/Wave%E2%80%93particle_duality#:~:text=Wave%E2%80%93particle%20duality%20is%20the,behaviour%20of%20quantum%2Dscale%20objects./ wave-particle duality] of electrons became known through experiments such as the [https://en.wikipedia.org/wiki/Double-slit_experiment/ double-slit experiment] and the [https://en.wikipedia.org/wiki/Photoelectric_effect/ photoelectric effect]. However, it was Louis de Broglie who considered extending the wave nature to all particles, not just electrons. He discovered that all matter has wave properties, and he formulated the de Broglie wavelength[https://en.wikipedia.org/wiki/Matter_wave]:

<math>
\lambda = \frac{h}{p}
</math>

This formula tells us the wavelength of any particle with a given momentum. This was a huge breakthrough for atomic theory, and is a great example of the usefulness of atomic mathematical models to represent information and inspire new findings.

===A Computational Model===
Understanding the composition and structure of atoms is essential to the study of both microscopic and macroscopic systems. Researchers have made use of atomic information to create what are called atomistic models. These models are used to predict and analyze the behavior of complex systems through knowledge of their most fundamental parts. By understanding how atomic structure affects characteristic properties of atoms, scientists are able to create computational models based on simple microscopic characteristics that simulate complex macroscopic systems. In doing so, they aim to better understand the connection between these macroscopic systems and the underlying atomic structures that govern them.

Use of simulations in research has broadened both the volume and complexity of analysis that can be done at any one time. The ability to model atoms through simulations has been an integral part of the research done in diverse areas of science, notably materials science. In this field, atomistic models are often used to predict material properties under certain conditions using information about their nucleus and electron density. For example, professor ABFIEJABF of the physics department of Georgia Tech created an atomistic model that simulates the behavior of atoms in ABFIEJABF. Another use of atomistic models is to simulate and analyze important processes such as a nuclear chain reaction; an example of such a simulation can be viewed on [https://javalab.org/en/nuclear_chain_reaction_en/ JavaLab].

Atomistic models use the mathematical models discussed above to computationally represent atomic forces, atomic positions, velocities, and magnetic charges of atoms among other things. The result is an accurate model of quantum processes. Ultimately, the use of such simulations help to understand the collective behavior of atoms and how this behavior affects macroscopic processes (such as deformation and phase change) as well as performance abilities (such as strength of material).
[[File:https://www.youtube.com/embed/jhGhSXAqXmU?start=30|thumb]]

==History==

===John Dalton: The Law of Multiple Proportions and Atomic Mass===
[[File:Daltons_symbols.gif|thumb|Dalton's concept of atoms and molecules]]
Working from the conservation of mass principle, chemist John Dalton determined the law of multiple proportions to understand how different elements combined in compounds. In 1803, he proposed that each element of the periodic table was composed of identical components, atoms, that were unique to each element. He also suggested that these atoms were not created nor destroyed when one element was combined with another. Dalton's empirical, experimentally-based work marked the first scientific theory of the atom.

Dalton proposed a list of atomic weights in 1805. However, Dalton failed to recognize natural tendencies of elements in nature (for example, oxygen typically exists as a diatomic molecule as <math>\text{O}_2</math>). Dalton was unable to distinguish between atoms and molecules (groups of atoms).

===Amedeo Avogadro: Avogadro's Law===
In 1811, [[Amedeo Avogadro]] studied gases and determined that the amount of volume a gas occupies is not determined by the mass of the gas. This allowed Avogadro to take more accurate atomic measurements of gases than Dalton, and differentiate atoms from molecules.

===Robert Brown: Brownian Motion===
A Scottish botanist, Robert Brown, studied the motion of tiny pollen particles in water in 1827. The particles followed complex paths, dubbed Brownian Motion. As early as 1905, [[Albert Einstein]] used Brownian Motion to predict the size of atoms and molecules.

===J.J. Thomson: The Plum-Pudding Model and Electrons===
[[File:Plum_pudding_model.svg|thumb|Tomson's Plum-Pudding Model]]
Through his work with cathode rays, [[J.J. Thomson]] discovered the electron in 1897, and was the first to learn that atoms weren't actually "uncuttable" as initially thought. Thomson knew that atoms had a net neutral charge, but he only knew that negative particles existed. Thus, Thomson developed the "plum-pudding" model of negatively charged electrons floating in a sea of positive charge. (He likened the relationship of electrons to the sea of positive charge to that of plums in plum pudding.)

===Ernest Rutherford: Gold Foil Experiment and the Nucleus===
In 1909, one of Thomson's students, [[Ernest Rutherford]], determined that the positive charge of atoms was located in a central nucleus. He shot small, positively charged alpha particles at thin sheets of gold foil and noted that some particles were sharply deflected. This deflection could only occur if the positive components of atoms were located in a small area, which Rutherford assumed to be the center. He proposed a planetary model of atoms where a cloud of electrons surrounded a central, positively charged nucleus.

===Niels Bohr: Introducing Quantum Physics===
[[File:Bohr_atom_animation_2.gif|thumb|The Bohr model for a Hydrogen atom with its electron moving between energy levels]]
As quantum mechanics progressed through the work of [[Albert Einstein]] and [[Max Planck]], [[Niels Bohr]] updated the atomic model in 1913 to account for quantum phenomena. Bohr, who was also one of Rutherford's students, suggested that electrostatic forces kept electrons in circular orbit around the positively charged central nucleus. In support of his theory, Bohr examined the behavior of electrons in hydrogen molecules and noted that they followed distinct energy levels. When an electron changed energy levels, it gained or lost energy, which could be emitted in the form of light. While the Bohr model holds true for hydrogen, it isn't accurate for multi-electron elements.

===James Chadwick: Neutrons===
James Chadwick won a Nobel Prize in 1935 for his discovery of the neutron. Starting with Rutherford's work, Chadwick continued experimenting to determine the excess mass in the nucleus that wasn't accounted for by protons. He found that neutrally charged particles, dubbed neutrons, were also inside the nucleus.

===The Current Model: Quantum Physics and Electron Orbitals===
Erwin Schrödinger examined the possibility that moving electrons behaved more like waves than particles, and published "Schrödinger's Equation" in 1926. Although this resolved many issues encountered with the Bohr model, it faced opposition from physicist [[Max Born]]. Instead, Born suggested a wave-particle duality of electrons, which stated that electrons could behave both like a wave and a particle.
As electrons were now given properties of waves, it was impossible to simultaneously determine an electron's exact location and momentum around the nucleus. Werner Heisenberg, first described this phenomena in 1927, and it was later named the Heisenberg Uncertainty Principle. This refuted the Bohr model of the atom, and replaced it with a pattern of probabilities as to where electrons are located around the nucleus. These patterns are referred to as atomic orbitals and come in a variety of shapes (basic spheres, rings, dumbbells, etc.) and the nucleus is always at the center.
[[File:Neon_orbitals.JPG|thumb|center|The first five atomic orbitals: 1s, 2s, 2px, 2py, and 2pz.]]

==Connectedness==
While classical physics applies to large objects moving much slower than the speed of light, modern physics deals with special cases of tiny objects, like atoms, subject to relativistic effects. Atomic theory is vital to understanding many quantum physics concepts that are covered in both Physics 2211 and 2212, like the ball-and-spring model of solids, point charges, and conductivity.

Although one can argue physics applies to just about every aspect of life, and atomic theory is critical to understanding physics, atomic theory has directly influenced material science, power generation, electronics, and even food processing, to name a few.

<gallery>
File:Apollo_synthetic_diamond.jpg|'''Material Science:''' Synthetic diamonds are used for both cosmetic retail and in manufacturing cutting tools.
File:Electrical_and_Mechanical_Services_Department_Headquarters_Photovoltaics.jpg|'''Power:''' Solar cells and power rely on the photovoltaic effect and the wave-particle duality of subatomic particles (like photons).
File:Monokristalines_Silizium_f%C3%BCr_die_Waferherstellung.jpg|'''Electronics:''' Silicon, a popular semiconductor used in electronics, is produced industrially in a single-crystal form.
File:Sodium-chloride-3D-ionic.png|'''Food processing:''' An atomic view of table salt. Purple particles are sodium (Na), and green particles are chlorine (Cl).
File:Nagasakibomb.jpg|'''Defense:''' Nuclear weapons were used during World War II.
File:White_Matter_Connections_Obtained_with_MRI_Tractography.png|'''Medicine:''' MRI's provide doctors critical information without the risks of surgery.
File:Plastic_household_items.jpg|'''Manufacturing:''' Many common household items are made with plastic.
</gallery>

== See also ==

*[[Bohr Model]]
*[[Electronic Energy Levels and Photons]]
*[[Rutherford Experiment and Atomic Collisions]]

===Notable Scientists===
*[[Amedeo Avogadro]]
*[[J.J. Thomson]]
*[[Ernest Rutherford]]
*[[Albert Einstein]]
*[[Max Planck]]
*[[Niels Bohr]]
*[[Max Born]]

===Related Theories===
*[[Quantum Theory]]
*[[Einstein's Theory of Special Relativity]]

===Concept Application===
*[[Ball and Spring Model of Matter]], [[Ball and Spring Model]]
*[[Length and Stiffness of an Interatomic Bond]], [[Young's Modulus]]
*[[Density]], [[Charge]], [[Spin]], and [[Conductivity]]
*[[The Photoelectric Effect]], [[Photons]]
*[[Rest Mass Energy]]
*[[Potential Energy of a Pair of Neutral Atoms]]

===External links===
*Physics Portal description of [https://en.wikipedia.org/wiki/History_of_molecular_theory Molecular Theory] and [https://en.wikipedia.org/wiki/Elementary_particle Subatomic Particles]
*HyperPhysics summary of [http://hyperphysics.phy-astr.gsu.edu/hbase/quacon.html#quacon Quantum Physics]
*Demonstration of the [https://phet.colorado.edu/en/simulation/legacy/hydrogen-atom various models] of a hydrogen atom

==References==

1. “Atomic Theory.” Wikipedia, Wikimedia Foundation, 19 Feb. 2022, https://en.wikipedia.org/wiki/Atomic_theory.

2. Introduction to Atomistic Modeling Xxx Techniques. https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf.

3. Clark, S J. “Atomistic Models.” Atomistic Models, http://cmt.dur.ac.uk/sjc/thesis_dlc/node45.html.

4. Introduction to Atomistic Modeling Xxx Techniques. https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf.

5. “Matter Wave.” Wikipedia, Wikimedia Foundation, 3 Apr. 2022, https://en.wikipedia.org/wiki/Matter_wave.

Chapter 30 of [https://openstaxcollege.org/files/textbook_version/hi_res_pdf/9/CollegePhysics-OP.pdf OpenStax Textbook]

Physics Portal page on [https://en.wikipedia.org/wiki/Atomic_theory Atomic Theory]

[[Category: Theory]]

Atomic Theory

2022-04-18T03:24:45Z

Erinhorbacz: /* A Computational Model */

Claimed by: Erin Horbacz (4/17/2022)

Atomic theory states that matter is composed of discrete units, called atoms. The word "atom" comes from the Greek word for uncuttable, ''atomos'', since it was believed that if one cut a substance into smaller and smaller pieces, one would reach a point where the substance could not be cut any further. Scientists later discovered that atoms were indeed able to be broken into subatomic, or elementary, particles including protons, neutrons, and electrons. Furthermore, protons and neutrons can be broken down yet again into smaller, elementary particles called [https://en.wikipedia.org/wiki/Quark#:~:text=A%20quark%20(%2Fkw%C9%94%CB%90r,the%20components%20of%20atomic%20nuclei./ quarks]. Atomic theory has evolved greatly over time, but the most recent model stems from quantum mechanics[https://en.wikipedia.org/wiki/Atomic_theory].

==The Main Idea==
===A Mathematical Model===
Mathematical models of atomic processes have become more thorough and sophisticated as knowledge of atomic properties has grown. The goal of a mathematical model is to express the underlying rules that govern atomic processes in a formula that can then predict and describe the behavior of atoms [https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf] (such as is seen with the list of Bohr's mathematical models for the atom). Such fundamental formulas are powerful tools for helping scientists understand the interactions within and processes of both microscopic and macroscopic systems. For example, it was [https://en.wikipedia.org/wiki/Charles-Augustin_de_Coulomb/ Charles-Augustin de Coulomb] who first determined the mathematical equation which could accurately describe the electrostatic potential between charged particles that make up an atom:

<math>
V = \frac{1}{4 \pi \epsilon} \frac{q_1 q_2}{r}
</math>

[[File:de-broglie-equation.png|thumb|Bohr's mathematical model to describe the atom]]

where V is the [https://en.wikipedia.org/wiki/Electric_potential/ electrostatic potential] (in volts), <math> \frac{1}{4 \pi \epsilon} </math> is the [https://en.wikipedia.org/wiki/Coulomb_constant#:~:text=The%20Coulomb%20constant%2C%20the%20electric,%E2%88%922%E2%8B%85C%E2%88%922./ Coulomb constant], <math>q_1 </math> and <math> q_2 </math> are the charges of two particles, and r is the distance between the two particles.

Additionally, stretching of atomic bonds are known to be affected by force fields around an equilibrium point, and they can be modeled according to the equation:

<math>
\Delta V(l) = \frac{1}{2} k_l (l - l_0)^2
</math>

Where <math>\Delta V(l) </math> is the change in potential energy at <math>l</math>, <math>k_1</math> is the spring constant (a proportionality constant), <math>l</math> is the bond length, and <math>l_0</math> is the equilibrium bond length[http://cmt.dur.ac.uk/sjc/thesis_dlc/node45.html].

The use and creation of these formulas is incredibly prominent in simulation modeling. For example, simulations modeling the motion of multiple atoms can use mathematical models such as [https://en.wikipedia.org/wiki/Leapfrog_integration/ Leapfrog integration] and [https://en.wikipedia.org/wiki/Verlet_integration/ Verlet integration] to update particle positions and velocities respectively[https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf].

Perhaps the most important aspect of these mathematical models are their ability to take difficult, abstract concepts and represent them in a form that can be manipulated for further research. The creation of models to describe quantum phenomena makes the information more digestible and the concepts somewhat clearer. In fact, it is often the case that a mathematical model describing quantum behavior helps others think about concepts in different ways. In this manner, many discoveries have resulted from generalizing these models to extend beyond their initial boundaries. For example, the [https://en.wikipedia.org/wiki/Wave%E2%80%93particle_duality#:~:text=Wave%E2%80%93particle%20duality%20is%20the,behaviour%20of%20quantum%2Dscale%20objects./ wave-particle duality] of electrons became known through experiments such as the [https://en.wikipedia.org/wiki/Double-slit_experiment/ double-slit experiment] and the [https://en.wikipedia.org/wiki/Photoelectric_effect/ photoelectric effect]. However, it was Louis de Broglie who considered extending the wave nature to all particles, not just electrons. He discovered that all matter has wave properties, and he formulated the de Broglie wavelength[https://en.wikipedia.org/wiki/Matter_wave]:

<math>
\lambda = \frac{h}{p}
</math>

This formula tells us the wavelength of any particle with a given momentum. This was a huge breakthrough for atomic theory, and is a great example of the usefulness of atomic mathematical models to represent information and inspire new findings.

===A Computational Model===
Understanding the composition and structure of atoms is essential to the study of both microscopic and macroscopic systems. Researchers have made use of atomic information to create what are called atomistic models. These models are used to predict and analyze the behavior of complex systems through knowledge of their most fundamental parts. By understanding how atomic structure affects characteristic properties of atoms, scientists are able to create computational models based on simple microscopic characteristics that simulate complex macroscopic systems. In doing so, they aim to better understand the connection between these macroscopic systems and the underlying atomic structures that govern them.

Use of simulations in research has broadened both the volume and complexity of analysis that can be done at any one time. The ability to model atoms through simulations has been an integral part of the research done in diverse areas of science, notably materials science. In this field, atomistic models are often used to predict material properties under certain conditions using information about their nucleus and electron density. For example, professor ABFIEJABF of the physics department of Georgia Tech created an atomistic model that simulates the behavior of atoms in ABFIEJABF. Another use of atomistic models is to simulate and analyze important processes such as a nuclear chain reaction; an example of such a simulation can be viewed on [https://javalab.org/en/nuclear_chain_reaction_en/ JavaLab].

Atomistic models use the mathematical models discussed above to computationally represent atomic forces, atomic positions, velocities, and magnetic charges of atoms among other things. The result is an accurate model of quantum processes. Ultimately, the use of such simulations help to understand the collective behavior of atoms and how this behavior affects macroscopic processes (such as deformation and phase change) as well as performance abilities (such as strength of material).
[[https://www.youtube.com/embed/jhGhSXAqXmU?start=30|thumb]]

==History==

===John Dalton: The Law of Multiple Proportions and Atomic Mass===
[[File:Daltons_symbols.gif|thumb|Dalton's concept of atoms and molecules]]
Working from the conservation of mass principle, chemist John Dalton determined the law of multiple proportions to understand how different elements combined in compounds. In 1803, he proposed that each element of the periodic table was composed of identical components, atoms, that were unique to each element. He also suggested that these atoms were not created nor destroyed when one element was combined with another. Dalton's empirical, experimentally-based work marked the first scientific theory of the atom.

Dalton proposed a list of atomic weights in 1805. However, Dalton failed to recognize natural tendencies of elements in nature (for example, oxygen typically exists as a diatomic molecule as <math>\text{O}_2</math>). Dalton was unable to distinguish between atoms and molecules (groups of atoms).

===Amedeo Avogadro: Avogadro's Law===
In 1811, [[Amedeo Avogadro]] studied gases and determined that the amount of volume a gas occupies is not determined by the mass of the gas. This allowed Avogadro to take more accurate atomic measurements of gases than Dalton, and differentiate atoms from molecules.

===Robert Brown: Brownian Motion===
A Scottish botanist, Robert Brown, studied the motion of tiny pollen particles in water in 1827. The particles followed complex paths, dubbed Brownian Motion. As early as 1905, [[Albert Einstein]] used Brownian Motion to predict the size of atoms and molecules.

===J.J. Thomson: The Plum-Pudding Model and Electrons===
[[File:Plum_pudding_model.svg|thumb|Tomson's Plum-Pudding Model]]
Through his work with cathode rays, [[J.J. Thomson]] discovered the electron in 1897, and was the first to learn that atoms weren't actually "uncuttable" as initially thought. Thomson knew that atoms had a net neutral charge, but he only knew that negative particles existed. Thus, Thomson developed the "plum-pudding" model of negatively charged electrons floating in a sea of positive charge. (He likened the relationship of electrons to the sea of positive charge to that of plums in plum pudding.)

===Ernest Rutherford: Gold Foil Experiment and the Nucleus===
In 1909, one of Thomson's students, [[Ernest Rutherford]], determined that the positive charge of atoms was located in a central nucleus. He shot small, positively charged alpha particles at thin sheets of gold foil and noted that some particles were sharply deflected. This deflection could only occur if the positive components of atoms were located in a small area, which Rutherford assumed to be the center. He proposed a planetary model of atoms where a cloud of electrons surrounded a central, positively charged nucleus.

===Niels Bohr: Introducing Quantum Physics===
[[File:Bohr_atom_animation_2.gif|thumb|The Bohr model for a Hydrogen atom with its electron moving between energy levels]]
As quantum mechanics progressed through the work of [[Albert Einstein]] and [[Max Planck]], [[Niels Bohr]] updated the atomic model in 1913 to account for quantum phenomena. Bohr, who was also one of Rutherford's students, suggested that electrostatic forces kept electrons in circular orbit around the positively charged central nucleus. In support of his theory, Bohr examined the behavior of electrons in hydrogen molecules and noted that they followed distinct energy levels. When an electron changed energy levels, it gained or lost energy, which could be emitted in the form of light. While the Bohr model holds true for hydrogen, it isn't accurate for multi-electron elements.

===James Chadwick: Neutrons===
James Chadwick won a Nobel Prize in 1935 for his discovery of the neutron. Starting with Rutherford's work, Chadwick continued experimenting to determine the excess mass in the nucleus that wasn't accounted for by protons. He found that neutrally charged particles, dubbed neutrons, were also inside the nucleus.

===The Current Model: Quantum Physics and Electron Orbitals===
Erwin Schrödinger examined the possibility that moving electrons behaved more like waves than particles, and published "Schrödinger's Equation" in 1926. Although this resolved many issues encountered with the Bohr model, it faced opposition from physicist [[Max Born]]. Instead, Born suggested a wave-particle duality of electrons, which stated that electrons could behave both like a wave and a particle.
As electrons were now given properties of waves, it was impossible to simultaneously determine an electron's exact location and momentum around the nucleus. Werner Heisenberg, first described this phenomena in 1927, and it was later named the Heisenberg Uncertainty Principle. This refuted the Bohr model of the atom, and replaced it with a pattern of probabilities as to where electrons are located around the nucleus. These patterns are referred to as atomic orbitals and come in a variety of shapes (basic spheres, rings, dumbbells, etc.) and the nucleus is always at the center.
[[File:Neon_orbitals.JPG|thumb|center|The first five atomic orbitals: 1s, 2s, 2px, 2py, and 2pz.]]

==Connectedness==
While classical physics applies to large objects moving much slower than the speed of light, modern physics deals with special cases of tiny objects, like atoms, subject to relativistic effects. Atomic theory is vital to understanding many quantum physics concepts that are covered in both Physics 2211 and 2212, like the ball-and-spring model of solids, point charges, and conductivity.

Although one can argue physics applies to just about every aspect of life, and atomic theory is critical to understanding physics, atomic theory has directly influenced material science, power generation, electronics, and even food processing, to name a few.

<gallery>
File:Apollo_synthetic_diamond.jpg|'''Material Science:''' Synthetic diamonds are used for both cosmetic retail and in manufacturing cutting tools.
File:Electrical_and_Mechanical_Services_Department_Headquarters_Photovoltaics.jpg|'''Power:''' Solar cells and power rely on the photovoltaic effect and the wave-particle duality of subatomic particles (like photons).
File:Monokristalines_Silizium_f%C3%BCr_die_Waferherstellung.jpg|'''Electronics:''' Silicon, a popular semiconductor used in electronics, is produced industrially in a single-crystal form.
File:Sodium-chloride-3D-ionic.png|'''Food processing:''' An atomic view of table salt. Purple particles are sodium (Na), and green particles are chlorine (Cl).
File:Nagasakibomb.jpg|'''Defense:''' Nuclear weapons were used during World War II.
File:White_Matter_Connections_Obtained_with_MRI_Tractography.png|'''Medicine:''' MRI's provide doctors critical information without the risks of surgery.
File:Plastic_household_items.jpg|'''Manufacturing:''' Many common household items are made with plastic.
</gallery>

== See also ==

*[[Bohr Model]]
*[[Electronic Energy Levels and Photons]]
*[[Rutherford Experiment and Atomic Collisions]]

===Notable Scientists===
*[[Amedeo Avogadro]]
*[[J.J. Thomson]]
*[[Ernest Rutherford]]
*[[Albert Einstein]]
*[[Max Planck]]
*[[Niels Bohr]]
*[[Max Born]]

===Related Theories===
*[[Quantum Theory]]
*[[Einstein's Theory of Special Relativity]]

===Concept Application===
*[[Ball and Spring Model of Matter]], [[Ball and Spring Model]]
*[[Length and Stiffness of an Interatomic Bond]], [[Young's Modulus]]
*[[Density]], [[Charge]], [[Spin]], and [[Conductivity]]
*[[The Photoelectric Effect]], [[Photons]]
*[[Rest Mass Energy]]
*[[Potential Energy of a Pair of Neutral Atoms]]

===External links===
*Physics Portal description of [https://en.wikipedia.org/wiki/History_of_molecular_theory Molecular Theory] and [https://en.wikipedia.org/wiki/Elementary_particle Subatomic Particles]
*HyperPhysics summary of [http://hyperphysics.phy-astr.gsu.edu/hbase/quacon.html#quacon Quantum Physics]
*Demonstration of the [https://phet.colorado.edu/en/simulation/legacy/hydrogen-atom various models] of a hydrogen atom

==References==

1. “Atomic Theory.” Wikipedia, Wikimedia Foundation, 19 Feb. 2022, https://en.wikipedia.org/wiki/Atomic_theory.

2. Introduction to Atomistic Modeling Xxx Techniques. https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf.

3. Clark, S J. “Atomistic Models.” Atomistic Models, http://cmt.dur.ac.uk/sjc/thesis_dlc/node45.html.

4. Introduction to Atomistic Modeling Xxx Techniques. https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf.

5. “Matter Wave.” Wikipedia, Wikimedia Foundation, 3 Apr. 2022, https://en.wikipedia.org/wiki/Matter_wave.

Chapter 30 of [https://openstaxcollege.org/files/textbook_version/hi_res_pdf/9/CollegePhysics-OP.pdf OpenStax Textbook]

Physics Portal page on [https://en.wikipedia.org/wiki/Atomic_theory Atomic Theory]

[[Category: Theory]]

Atomic Theory

2022-04-18T03:24:13Z

Erinhorbacz: /* A Computational Model */

Claimed by: Erin Horbacz (4/17/2022)

Atomic theory states that matter is composed of discrete units, called atoms. The word "atom" comes from the Greek word for uncuttable, ''atomos'', since it was believed that if one cut a substance into smaller and smaller pieces, one would reach a point where the substance could not be cut any further. Scientists later discovered that atoms were indeed able to be broken into subatomic, or elementary, particles including protons, neutrons, and electrons. Furthermore, protons and neutrons can be broken down yet again into smaller, elementary particles called [https://en.wikipedia.org/wiki/Quark#:~:text=A%20quark%20(%2Fkw%C9%94%CB%90r,the%20components%20of%20atomic%20nuclei./ quarks]. Atomic theory has evolved greatly over time, but the most recent model stems from quantum mechanics[https://en.wikipedia.org/wiki/Atomic_theory].

==The Main Idea==
===A Mathematical Model===
Mathematical models of atomic processes have become more thorough and sophisticated as knowledge of atomic properties has grown. The goal of a mathematical model is to express the underlying rules that govern atomic processes in a formula that can then predict and describe the behavior of atoms [https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf] (such as is seen with the list of Bohr's mathematical models for the atom). Such fundamental formulas are powerful tools for helping scientists understand the interactions within and processes of both microscopic and macroscopic systems. For example, it was [https://en.wikipedia.org/wiki/Charles-Augustin_de_Coulomb/ Charles-Augustin de Coulomb] who first determined the mathematical equation which could accurately describe the electrostatic potential between charged particles that make up an atom:

<math>
V = \frac{1}{4 \pi \epsilon} \frac{q_1 q_2}{r}
</math>

[[File:de-broglie-equation.png|thumb|Bohr's mathematical model to describe the atom]]

where V is the [https://en.wikipedia.org/wiki/Electric_potential/ electrostatic potential] (in volts), <math> \frac{1}{4 \pi \epsilon} </math> is the [https://en.wikipedia.org/wiki/Coulomb_constant#:~:text=The%20Coulomb%20constant%2C%20the%20electric,%E2%88%922%E2%8B%85C%E2%88%922./ Coulomb constant], <math>q_1 </math> and <math> q_2 </math> are the charges of two particles, and r is the distance between the two particles.

Additionally, stretching of atomic bonds are known to be affected by force fields around an equilibrium point, and they can be modeled according to the equation:

<math>
\Delta V(l) = \frac{1}{2} k_l (l - l_0)^2
</math>

Where <math>\Delta V(l) </math> is the change in potential energy at <math>l</math>, <math>k_1</math> is the spring constant (a proportionality constant), <math>l</math> is the bond length, and <math>l_0</math> is the equilibrium bond length[http://cmt.dur.ac.uk/sjc/thesis_dlc/node45.html].

The use and creation of these formulas is incredibly prominent in simulation modeling. For example, simulations modeling the motion of multiple atoms can use mathematical models such as [https://en.wikipedia.org/wiki/Leapfrog_integration/ Leapfrog integration] and [https://en.wikipedia.org/wiki/Verlet_integration/ Verlet integration] to update particle positions and velocities respectively[https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf].

Perhaps the most important aspect of these mathematical models are their ability to take difficult, abstract concepts and represent them in a form that can be manipulated for further research. The creation of models to describe quantum phenomena makes the information more digestible and the concepts somewhat clearer. In fact, it is often the case that a mathematical model describing quantum behavior helps others think about concepts in different ways. In this manner, many discoveries have resulted from generalizing these models to extend beyond their initial boundaries. For example, the [https://en.wikipedia.org/wiki/Wave%E2%80%93particle_duality#:~:text=Wave%E2%80%93particle%20duality%20is%20the,behaviour%20of%20quantum%2Dscale%20objects./ wave-particle duality] of electrons became known through experiments such as the [https://en.wikipedia.org/wiki/Double-slit_experiment/ double-slit experiment] and the [https://en.wikipedia.org/wiki/Photoelectric_effect/ photoelectric effect]. However, it was Louis de Broglie who considered extending the wave nature to all particles, not just electrons. He discovered that all matter has wave properties, and he formulated the de Broglie wavelength[https://en.wikipedia.org/wiki/Matter_wave]:

<math>
\lambda = \frac{h}{p}
</math>

This formula tells us the wavelength of any particle with a given momentum. This was a huge breakthrough for atomic theory, and is a great example of the usefulness of atomic mathematical models to represent information and inspire new findings.

===A Computational Model===
Understanding the composition and structure of atoms is essential to the study of both microscopic and macroscopic systems. Researchers have made use of atomic information to create what are called atomistic models. These models are used to predict and analyze the behavior of complex systems through knowledge of their most fundamental parts. By understanding how atomic structure affects characteristic properties of atoms, scientists are able to create computational models based on simple microscopic characteristics that simulate complex macroscopic systems. In doing so, they aim to better understand the connection between these macroscopic systems and the underlying atomic structures that govern them.

Use of simulations in research has broadened both the volume and complexity of analysis that can be done at any one time. The ability to model atoms through simulations has been an integral part of the research done in diverse areas of science, notably materials science. In this field, atomistic models are often used to predict material properties under certain conditions using information about their nucleus and electron density. For example, professor ABFIEJABF of the physics department of Georgia Tech created an atomistic model that simulates the behavior of atoms in ABFIEJABF. Another use of atomistic models is to simulate and analyze important processes such as a nuclear chain reaction; an example of such a simulation can be viewed on [https://javalab.org/en/nuclear_chain_reaction_en/ JavaLab].

Atomistic models use the mathematical models discussed above to computationally represent atomic forces, atomic positions, velocities, and magnetic charges of atoms among other things. The result is an accurate model of quantum processes. Ultimately, the use of such simulations help to understand the collective behavior of atoms and how this behavior affects macroscopic processes (such as deformation and phase change) as well as performance abilities (such as strength of material).
[[<iframe width="560" height="315" src="https://www.youtube.com/embed/jhGhSXAqXmU?start=30" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>|thumb]]

==History==

===John Dalton: The Law of Multiple Proportions and Atomic Mass===
[[File:Daltons_symbols.gif|thumb|Dalton's concept of atoms and molecules]]
Working from the conservation of mass principle, chemist John Dalton determined the law of multiple proportions to understand how different elements combined in compounds. In 1803, he proposed that each element of the periodic table was composed of identical components, atoms, that were unique to each element. He also suggested that these atoms were not created nor destroyed when one element was combined with another. Dalton's empirical, experimentally-based work marked the first scientific theory of the atom.

Dalton proposed a list of atomic weights in 1805. However, Dalton failed to recognize natural tendencies of elements in nature (for example, oxygen typically exists as a diatomic molecule as <math>\text{O}_2</math>). Dalton was unable to distinguish between atoms and molecules (groups of atoms).

===Amedeo Avogadro: Avogadro's Law===
In 1811, [[Amedeo Avogadro]] studied gases and determined that the amount of volume a gas occupies is not determined by the mass of the gas. This allowed Avogadro to take more accurate atomic measurements of gases than Dalton, and differentiate atoms from molecules.

===Robert Brown: Brownian Motion===
A Scottish botanist, Robert Brown, studied the motion of tiny pollen particles in water in 1827. The particles followed complex paths, dubbed Brownian Motion. As early as 1905, [[Albert Einstein]] used Brownian Motion to predict the size of atoms and molecules.

===J.J. Thomson: The Plum-Pudding Model and Electrons===
[[File:Plum_pudding_model.svg|thumb|Tomson's Plum-Pudding Model]]
Through his work with cathode rays, [[J.J. Thomson]] discovered the electron in 1897, and was the first to learn that atoms weren't actually "uncuttable" as initially thought. Thomson knew that atoms had a net neutral charge, but he only knew that negative particles existed. Thus, Thomson developed the "plum-pudding" model of negatively charged electrons floating in a sea of positive charge. (He likened the relationship of electrons to the sea of positive charge to that of plums in plum pudding.)

===Ernest Rutherford: Gold Foil Experiment and the Nucleus===
In 1909, one of Thomson's students, [[Ernest Rutherford]], determined that the positive charge of atoms was located in a central nucleus. He shot small, positively charged alpha particles at thin sheets of gold foil and noted that some particles were sharply deflected. This deflection could only occur if the positive components of atoms were located in a small area, which Rutherford assumed to be the center. He proposed a planetary model of atoms where a cloud of electrons surrounded a central, positively charged nucleus.

===Niels Bohr: Introducing Quantum Physics===
[[File:Bohr_atom_animation_2.gif|thumb|The Bohr model for a Hydrogen atom with its electron moving between energy levels]]
As quantum mechanics progressed through the work of [[Albert Einstein]] and [[Max Planck]], [[Niels Bohr]] updated the atomic model in 1913 to account for quantum phenomena. Bohr, who was also one of Rutherford's students, suggested that electrostatic forces kept electrons in circular orbit around the positively charged central nucleus. In support of his theory, Bohr examined the behavior of electrons in hydrogen molecules and noted that they followed distinct energy levels. When an electron changed energy levels, it gained or lost energy, which could be emitted in the form of light. While the Bohr model holds true for hydrogen, it isn't accurate for multi-electron elements.

===James Chadwick: Neutrons===
James Chadwick won a Nobel Prize in 1935 for his discovery of the neutron. Starting with Rutherford's work, Chadwick continued experimenting to determine the excess mass in the nucleus that wasn't accounted for by protons. He found that neutrally charged particles, dubbed neutrons, were also inside the nucleus.

===The Current Model: Quantum Physics and Electron Orbitals===
Erwin Schrödinger examined the possibility that moving electrons behaved more like waves than particles, and published "Schrödinger's Equation" in 1926. Although this resolved many issues encountered with the Bohr model, it faced opposition from physicist [[Max Born]]. Instead, Born suggested a wave-particle duality of electrons, which stated that electrons could behave both like a wave and a particle.
As electrons were now given properties of waves, it was impossible to simultaneously determine an electron's exact location and momentum around the nucleus. Werner Heisenberg, first described this phenomena in 1927, and it was later named the Heisenberg Uncertainty Principle. This refuted the Bohr model of the atom, and replaced it with a pattern of probabilities as to where electrons are located around the nucleus. These patterns are referred to as atomic orbitals and come in a variety of shapes (basic spheres, rings, dumbbells, etc.) and the nucleus is always at the center.
[[File:Neon_orbitals.JPG|thumb|center|The first five atomic orbitals: 1s, 2s, 2px, 2py, and 2pz.]]

==Connectedness==
While classical physics applies to large objects moving much slower than the speed of light, modern physics deals with special cases of tiny objects, like atoms, subject to relativistic effects. Atomic theory is vital to understanding many quantum physics concepts that are covered in both Physics 2211 and 2212, like the ball-and-spring model of solids, point charges, and conductivity.

Although one can argue physics applies to just about every aspect of life, and atomic theory is critical to understanding physics, atomic theory has directly influenced material science, power generation, electronics, and even food processing, to name a few.

<gallery>
File:Apollo_synthetic_diamond.jpg|'''Material Science:''' Synthetic diamonds are used for both cosmetic retail and in manufacturing cutting tools.
File:Electrical_and_Mechanical_Services_Department_Headquarters_Photovoltaics.jpg|'''Power:''' Solar cells and power rely on the photovoltaic effect and the wave-particle duality of subatomic particles (like photons).
File:Monokristalines_Silizium_f%C3%BCr_die_Waferherstellung.jpg|'''Electronics:''' Silicon, a popular semiconductor used in electronics, is produced industrially in a single-crystal form.
File:Sodium-chloride-3D-ionic.png|'''Food processing:''' An atomic view of table salt. Purple particles are sodium (Na), and green particles are chlorine (Cl).
File:Nagasakibomb.jpg|'''Defense:''' Nuclear weapons were used during World War II.
File:White_Matter_Connections_Obtained_with_MRI_Tractography.png|'''Medicine:''' MRI's provide doctors critical information without the risks of surgery.
File:Plastic_household_items.jpg|'''Manufacturing:''' Many common household items are made with plastic.
</gallery>

== See also ==

*[[Bohr Model]]
*[[Electronic Energy Levels and Photons]]
*[[Rutherford Experiment and Atomic Collisions]]

===Notable Scientists===
*[[Amedeo Avogadro]]
*[[J.J. Thomson]]
*[[Ernest Rutherford]]
*[[Albert Einstein]]
*[[Max Planck]]
*[[Niels Bohr]]
*[[Max Born]]

===Related Theories===
*[[Quantum Theory]]
*[[Einstein's Theory of Special Relativity]]

===Concept Application===
*[[Ball and Spring Model of Matter]], [[Ball and Spring Model]]
*[[Length and Stiffness of an Interatomic Bond]], [[Young's Modulus]]
*[[Density]], [[Charge]], [[Spin]], and [[Conductivity]]
*[[The Photoelectric Effect]], [[Photons]]
*[[Rest Mass Energy]]
*[[Potential Energy of a Pair of Neutral Atoms]]

===External links===
*Physics Portal description of [https://en.wikipedia.org/wiki/History_of_molecular_theory Molecular Theory] and [https://en.wikipedia.org/wiki/Elementary_particle Subatomic Particles]
*HyperPhysics summary of [http://hyperphysics.phy-astr.gsu.edu/hbase/quacon.html#quacon Quantum Physics]
*Demonstration of the [https://phet.colorado.edu/en/simulation/legacy/hydrogen-atom various models] of a hydrogen atom

==References==

1. “Atomic Theory.” Wikipedia, Wikimedia Foundation, 19 Feb. 2022, https://en.wikipedia.org/wiki/Atomic_theory.

2. Introduction to Atomistic Modeling Xxx Techniques. https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf.

3. Clark, S J. “Atomistic Models.” Atomistic Models, http://cmt.dur.ac.uk/sjc/thesis_dlc/node45.html.

4. Introduction to Atomistic Modeling Xxx Techniques. https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf.

5. “Matter Wave.” Wikipedia, Wikimedia Foundation, 3 Apr. 2022, https://en.wikipedia.org/wiki/Matter_wave.

Chapter 30 of [https://openstaxcollege.org/files/textbook_version/hi_res_pdf/9/CollegePhysics-OP.pdf OpenStax Textbook]

Physics Portal page on [https://en.wikipedia.org/wiki/Atomic_theory Atomic Theory]

[[Category: Theory]]

File:Javalab20220417180453.png

2022-04-18T03:04:52Z

Erinhorbacz: testing

== Summary ==
testing

Atomic Theory

2022-04-18T03:01:02Z

Erinhorbacz: /* A Mathematical Model */

Claimed by: Erin Horbacz (4/17/2022)

Atomic theory states that matter is composed of discrete units, called atoms. The word "atom" comes from the Greek word for uncuttable, ''atomos'', since it was believed that if one cut a substance into smaller and smaller pieces, one would reach a point where the substance could not be cut any further. Scientists later discovered that atoms were indeed able to be broken into subatomic, or elementary, particles including protons, neutrons, and electrons. Furthermore, protons and neutrons can be broken down yet again into smaller, elementary particles called [https://en.wikipedia.org/wiki/Quark#:~:text=A%20quark%20(%2Fkw%C9%94%CB%90r,the%20components%20of%20atomic%20nuclei./ quarks]. Atomic theory has evolved greatly over time, but the most recent model stems from quantum mechanics[https://en.wikipedia.org/wiki/Atomic_theory].

==The Main Idea==
===A Mathematical Model===
Mathematical models of atomic processes have become more thorough and sophisticated as knowledge of atomic properties has grown. The goal of a mathematical model is to express the underlying rules that govern atomic processes in a formula that can then predict and describe the behavior of atoms [https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf] (such as is seen with the list of Bohr's mathematical models for the atom). Such fundamental formulas are powerful tools for helping scientists understand the interactions within and processes of both microscopic and macroscopic systems. For example, it was [https://en.wikipedia.org/wiki/Charles-Augustin_de_Coulomb/ Charles-Augustin de Coulomb] who first determined the mathematical equation which could accurately describe the electrostatic potential between charged particles that make up an atom:

<math>
V = \frac{1}{4 \pi \epsilon} \frac{q_1 q_2}{r}
</math>

[[File:de-broglie-equation.png|thumb|Bohr's mathematical model to describe the atom]]

where V is the [https://en.wikipedia.org/wiki/Electric_potential/ electrostatic potential] (in volts), <math> \frac{1}{4 \pi \epsilon} </math> is the [https://en.wikipedia.org/wiki/Coulomb_constant#:~:text=The%20Coulomb%20constant%2C%20the%20electric,%E2%88%922%E2%8B%85C%E2%88%922./ Coulomb constant], <math>q_1 </math> and <math> q_2 </math> are the charges of two particles, and r is the distance between the two particles.

Additionally, stretching of atomic bonds are known to be affected by force fields around an equilibrium point, and they can be modeled according to the equation:

<math>
\Delta V(l) = \frac{1}{2} k_l (l - l_0)^2
</math>

Where <math>\Delta V(l) </math> is the change in potential energy at <math>l</math>, <math>k_1</math> is the spring constant (a proportionality constant), <math>l</math> is the bond length, and <math>l_0</math> is the equilibrium bond length[http://cmt.dur.ac.uk/sjc/thesis_dlc/node45.html].

The use and creation of these formulas is incredibly prominent in simulation modeling. For example, simulations modeling the motion of multiple atoms can use mathematical models such as [https://en.wikipedia.org/wiki/Leapfrog_integration/ Leapfrog integration] and [https://en.wikipedia.org/wiki/Verlet_integration/ Verlet integration] to update particle positions and velocities respectively[https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf].

Perhaps the most important aspect of these mathematical models are their ability to take difficult, abstract concepts and represent them in a form that can be manipulated for further research. The creation of models to describe quantum phenomena makes the information more digestible and the concepts somewhat clearer. In fact, it is often the case that a mathematical model describing quantum behavior helps others think about concepts in different ways. In this manner, many discoveries have resulted from generalizing these models to extend beyond their initial boundaries. For example, the [https://en.wikipedia.org/wiki/Wave%E2%80%93particle_duality#:~:text=Wave%E2%80%93particle%20duality%20is%20the,behaviour%20of%20quantum%2Dscale%20objects./ wave-particle duality] of electrons became known through experiments such as the [https://en.wikipedia.org/wiki/Double-slit_experiment/ double-slit experiment] and the [https://en.wikipedia.org/wiki/Photoelectric_effect/ photoelectric effect]. However, it was Louis de Broglie who considered extending the wave nature to all particles, not just electrons. He discovered that all matter has wave properties, and he formulated the de Broglie wavelength[https://en.wikipedia.org/wiki/Matter_wave]:

<math>
\lambda = \frac{h}{p}
</math>

This formula tells us the wavelength of any particle with a given momentum. This was a huge breakthrough for atomic theory, and is a great example of the usefulness of atomic mathematical models to represent information and inspire new findings.

===A Computational Model===
Understanding the composition and structure of atoms is essential to the study of both microscopic and macroscopic systems. Researchers have made use of atomic information to create what are called atomistic models. These models are used to predict and analyze the behavior of complex systems through knowledge of their most fundamental parts. By understanding how atomic structure affects characteristic properties of atoms, scientists are able to create computational models based on simple microscopic characteristics that simulate complex macroscopic systems. In doing so, they aim to better understand the connection between these macroscopic systems and the underlying atomic structures that govern them.

Use of simulations in research has broadened both the volume and complexity of analysis that can be done at any one time. The ability to model atoms through simulations has been an integral part of the research done in diverse areas of science, notably materials science. In this field, atomistic models are often used to predict material properties under certain conditions using information about their nucleus and electron density. For example, professor ABFIEJABF of the physics department of Georgia Tech created an atomistic model that simulates the behavior of atoms in ABFIEJABF. Another use of atomistic models is to simulate and analyze important processes such as a nuclear chain reaction; an example of such a simulation can be viewed on [https://javalab.org/en/nuclear_chain_reaction_en/ JavaLab].

Atomistic models use the mathematical models discussed above to computationally represent atomic forces, atomic positions, velocities, and magnetic charges of atoms among other things. The result is an accurate model of quantum processes. Ultimately, the use of such simulations help to understand the collective behavior of atoms and how this behavior affects macroscopic processes (such as deformation and phase change) as well as performance abilities (such as strength of material).

==History==

===John Dalton: The Law of Multiple Proportions and Atomic Mass===
[[File:Daltons_symbols.gif|thumb|Dalton's concept of atoms and molecules]]
Working from the conservation of mass principle, chemist John Dalton determined the law of multiple proportions to understand how different elements combined in compounds. In 1803, he proposed that each element of the periodic table was composed of identical components, atoms, that were unique to each element. He also suggested that these atoms were not created nor destroyed when one element was combined with another. Dalton's empirical, experimentally-based work marked the first scientific theory of the atom.

Dalton proposed a list of atomic weights in 1805. However, Dalton failed to recognize natural tendencies of elements in nature (for example, oxygen typically exists as a diatomic molecule as <math>\text{O}_2</math>). Dalton was unable to distinguish between atoms and molecules (groups of atoms).

===Amedeo Avogadro: Avogadro's Law===
In 1811, [[Amedeo Avogadro]] studied gases and determined that the amount of volume a gas occupies is not determined by the mass of the gas. This allowed Avogadro to take more accurate atomic measurements of gases than Dalton, and differentiate atoms from molecules.

===Robert Brown: Brownian Motion===
A Scottish botanist, Robert Brown, studied the motion of tiny pollen particles in water in 1827. The particles followed complex paths, dubbed Brownian Motion. As early as 1905, [[Albert Einstein]] used Brownian Motion to predict the size of atoms and molecules.

===J.J. Thomson: The Plum-Pudding Model and Electrons===
[[File:Plum_pudding_model.svg|thumb|Tomson's Plum-Pudding Model]]
Through his work with cathode rays, [[J.J. Thomson]] discovered the electron in 1897, and was the first to learn that atoms weren't actually "uncuttable" as initially thought. Thomson knew that atoms had a net neutral charge, but he only knew that negative particles existed. Thus, Thomson developed the "plum-pudding" model of negatively charged electrons floating in a sea of positive charge. (He likened the relationship of electrons to the sea of positive charge to that of plums in plum pudding.)

===Ernest Rutherford: Gold Foil Experiment and the Nucleus===
In 1909, one of Thomson's students, [[Ernest Rutherford]], determined that the positive charge of atoms was located in a central nucleus. He shot small, positively charged alpha particles at thin sheets of gold foil and noted that some particles were sharply deflected. This deflection could only occur if the positive components of atoms were located in a small area, which Rutherford assumed to be the center. He proposed a planetary model of atoms where a cloud of electrons surrounded a central, positively charged nucleus.

===Niels Bohr: Introducing Quantum Physics===
[[File:Bohr_atom_animation_2.gif|thumb|The Bohr model for a Hydrogen atom with its electron moving between energy levels]]
As quantum mechanics progressed through the work of [[Albert Einstein]] and [[Max Planck]], [[Niels Bohr]] updated the atomic model in 1913 to account for quantum phenomena. Bohr, who was also one of Rutherford's students, suggested that electrostatic forces kept electrons in circular orbit around the positively charged central nucleus. In support of his theory, Bohr examined the behavior of electrons in hydrogen molecules and noted that they followed distinct energy levels. When an electron changed energy levels, it gained or lost energy, which could be emitted in the form of light. While the Bohr model holds true for hydrogen, it isn't accurate for multi-electron elements.

===James Chadwick: Neutrons===
James Chadwick won a Nobel Prize in 1935 for his discovery of the neutron. Starting with Rutherford's work, Chadwick continued experimenting to determine the excess mass in the nucleus that wasn't accounted for by protons. He found that neutrally charged particles, dubbed neutrons, were also inside the nucleus.

===The Current Model: Quantum Physics and Electron Orbitals===
Erwin Schrödinger examined the possibility that moving electrons behaved more like waves than particles, and published "Schrödinger's Equation" in 1926. Although this resolved many issues encountered with the Bohr model, it faced opposition from physicist [[Max Born]]. Instead, Born suggested a wave-particle duality of electrons, which stated that electrons could behave both like a wave and a particle.
As electrons were now given properties of waves, it was impossible to simultaneously determine an electron's exact location and momentum around the nucleus. Werner Heisenberg, first described this phenomena in 1927, and it was later named the Heisenberg Uncertainty Principle. This refuted the Bohr model of the atom, and replaced it with a pattern of probabilities as to where electrons are located around the nucleus. These patterns are referred to as atomic orbitals and come in a variety of shapes (basic spheres, rings, dumbbells, etc.) and the nucleus is always at the center.
[[File:Neon_orbitals.JPG|thumb|center|The first five atomic orbitals: 1s, 2s, 2px, 2py, and 2pz.]]

==Connectedness==
While classical physics applies to large objects moving much slower than the speed of light, modern physics deals with special cases of tiny objects, like atoms, subject to relativistic effects. Atomic theory is vital to understanding many quantum physics concepts that are covered in both Physics 2211 and 2212, like the ball-and-spring model of solids, point charges, and conductivity.

Although one can argue physics applies to just about every aspect of life, and atomic theory is critical to understanding physics, atomic theory has directly influenced material science, power generation, electronics, and even food processing, to name a few.

<gallery>
File:Apollo_synthetic_diamond.jpg|'''Material Science:''' Synthetic diamonds are used for both cosmetic retail and in manufacturing cutting tools.
File:Electrical_and_Mechanical_Services_Department_Headquarters_Photovoltaics.jpg|'''Power:''' Solar cells and power rely on the photovoltaic effect and the wave-particle duality of subatomic particles (like photons).
File:Monokristalines_Silizium_f%C3%BCr_die_Waferherstellung.jpg|'''Electronics:''' Silicon, a popular semiconductor used in electronics, is produced industrially in a single-crystal form.
File:Sodium-chloride-3D-ionic.png|'''Food processing:''' An atomic view of table salt. Purple particles are sodium (Na), and green particles are chlorine (Cl).
File:Nagasakibomb.jpg|'''Defense:''' Nuclear weapons were used during World War II.
File:White_Matter_Connections_Obtained_with_MRI_Tractography.png|'''Medicine:''' MRI's provide doctors critical information without the risks of surgery.
File:Plastic_household_items.jpg|'''Manufacturing:''' Many common household items are made with plastic.
</gallery>

== See also ==

*[[Bohr Model]]
*[[Electronic Energy Levels and Photons]]
*[[Rutherford Experiment and Atomic Collisions]]

===Notable Scientists===
*[[Amedeo Avogadro]]
*[[J.J. Thomson]]
*[[Ernest Rutherford]]
*[[Albert Einstein]]
*[[Max Planck]]
*[[Niels Bohr]]
*[[Max Born]]

===Related Theories===
*[[Quantum Theory]]
*[[Einstein's Theory of Special Relativity]]

===Concept Application===
*[[Ball and Spring Model of Matter]], [[Ball and Spring Model]]
*[[Length and Stiffness of an Interatomic Bond]], [[Young's Modulus]]
*[[Density]], [[Charge]], [[Spin]], and [[Conductivity]]
*[[The Photoelectric Effect]], [[Photons]]
*[[Rest Mass Energy]]
*[[Potential Energy of a Pair of Neutral Atoms]]

===External links===
*Physics Portal description of [https://en.wikipedia.org/wiki/History_of_molecular_theory Molecular Theory] and [https://en.wikipedia.org/wiki/Elementary_particle Subatomic Particles]
*HyperPhysics summary of [http://hyperphysics.phy-astr.gsu.edu/hbase/quacon.html#quacon Quantum Physics]
*Demonstration of the [https://phet.colorado.edu/en/simulation/legacy/hydrogen-atom various models] of a hydrogen atom

==References==

1. “Atomic Theory.” Wikipedia, Wikimedia Foundation, 19 Feb. 2022, https://en.wikipedia.org/wiki/Atomic_theory.

2. Introduction to Atomistic Modeling Xxx Techniques. https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf.

3. Clark, S J. “Atomistic Models.” Atomistic Models, http://cmt.dur.ac.uk/sjc/thesis_dlc/node45.html.

4. Introduction to Atomistic Modeling Xxx Techniques. https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf.

5. “Matter Wave.” Wikipedia, Wikimedia Foundation, 3 Apr. 2022, https://en.wikipedia.org/wiki/Matter_wave.

Chapter 30 of [https://openstaxcollege.org/files/textbook_version/hi_res_pdf/9/CollegePhysics-OP.pdf OpenStax Textbook]

Physics Portal page on [https://en.wikipedia.org/wiki/Atomic_theory Atomic Theory]

[[Category: Theory]]

File:De-broglie-equation.png

2022-04-18T03:00:15Z

Erinhorbacz: list of de Broglie equations

== Summary ==
list of de Broglie equations

Atomic Theory

2022-04-18T02:57:50Z

Erinhorbacz: /* A Mathematical Model */

Claimed by: Erin Horbacz (4/17/2022)

Atomic theory states that matter is composed of discrete units, called atoms. The word "atom" comes from the Greek word for uncuttable, ''atomos'', since it was believed that if one cut a substance into smaller and smaller pieces, one would reach a point where the substance could not be cut any further. Scientists later discovered that atoms were indeed able to be broken into subatomic, or elementary, particles including protons, neutrons, and electrons. Furthermore, protons and neutrons can be broken down yet again into smaller, elementary particles called [https://en.wikipedia.org/wiki/Quark#:~:text=A%20quark%20(%2Fkw%C9%94%CB%90r,the%20components%20of%20atomic%20nuclei./ quarks]. Atomic theory has evolved greatly over time, but the most recent model stems from quantum mechanics[https://en.wikipedia.org/wiki/Atomic_theory].

==The Main Idea==
===A Mathematical Model===
Mathematical models of atomic processes have become more thorough and sophisticated as knowledge of atomic properties has grown. The goal of a mathematical model is to express the underlying rules that govern atomic processes in a formula that can then predict and describe the behavior of atoms [https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf] (such as is seen with the list of Bohr's mathematical models for the atom). Such fundamental formulas are powerful tools for helping scientists understand the interactions within and processes of both microscopic and macroscopic systems. For example, it was [https://en.wikipedia.org/wiki/Charles-Augustin_de_Coulomb/ Charles-Augustin de Coulomb] who first determined the mathematical equation which could accurately describe the electrostatic potential between charged particles that make up an atom:

<math>
V = \frac{1}{4 \pi \epsilon} \frac{q_1 q_2}{r}
</math>

[[File:bohr_equations.jpg|thumb|Bohr's mathematical model to describe the atom]]

where V is the [https://en.wikipedia.org/wiki/Electric_potential/ electrostatic potential] (in volts), <math> \frac{1}{4 \pi \epsilon} </math> is the [https://en.wikipedia.org/wiki/Coulomb_constant#:~:text=The%20Coulomb%20constant%2C%20the%20electric,%E2%88%922%E2%8B%85C%E2%88%922./ Coulomb constant], <math>q_1 </math> and <math> q_2 </math> are the charges of two particles, and r is the distance between the two particles.

Additionally, stretching of atomic bonds are known to be affected by force fields around an equilibrium point, and they can be modeled according to the equation:

<math>
\Delta V(l) = \frac{1}{2} k_l (l - l_0)^2
</math>

Where <math>\Delta V(l) </math> is the change in potential energy at <math>l</math>, <math>k_1</math> is the spring constant (a proportionality constant), <math>l</math> is the bond length, and <math>l_0</math> is the equilibrium bond length[http://cmt.dur.ac.uk/sjc/thesis_dlc/node45.html].

The use and creation of these formulas is incredibly prominent in simulation modeling. For example, simulations modeling the motion of multiple atoms can use mathematical models such as [https://en.wikipedia.org/wiki/Leapfrog_integration/ Leapfrog integration] and [https://en.wikipedia.org/wiki/Verlet_integration/ Verlet integration] to update particle positions and velocities respectively[https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf].

Perhaps the most important aspect of these mathematical models are their ability to take difficult, abstract concepts and represent them in a form that can be manipulated for further research. The creation of models to describe quantum phenomena makes the information more digestible and the concepts somewhat clearer. In fact, it is often the case that a mathematical model describing quantum behavior helps others think about concepts in different ways. In this manner, many discoveries have resulted from generalizing these models to extend beyond their initial boundaries. For example, the [https://en.wikipedia.org/wiki/Wave%E2%80%93particle_duality#:~:text=Wave%E2%80%93particle%20duality%20is%20the,behaviour%20of%20quantum%2Dscale%20objects./ wave-particle duality] of electrons became known through experiments such as the [https://en.wikipedia.org/wiki/Double-slit_experiment/ double-slit experiment] and the [https://en.wikipedia.org/wiki/Photoelectric_effect/ photoelectric effect]. However, it was Louis de Broglie who considered extending the wave nature to all particles, not just electrons. He discovered that all matter has wave properties, and he formulated the de Broglie wavelength[https://en.wikipedia.org/wiki/Matter_wave]:

<math>
\lambda = \frac{h}{p}
</math>

This formula tells us the wavelength of any particle with a given momentum. This was a huge breakthrough for atomic theory, and is a great example of the usefulness of atomic mathematical models to represent information and inspire new findings.

===A Computational Model===
Understanding the composition and structure of atoms is essential to the study of both microscopic and macroscopic systems. Researchers have made use of atomic information to create what are called atomistic models. These models are used to predict and analyze the behavior of complex systems through knowledge of their most fundamental parts. By understanding how atomic structure affects characteristic properties of atoms, scientists are able to create computational models based on simple microscopic characteristics that simulate complex macroscopic systems. In doing so, they aim to better understand the connection between these macroscopic systems and the underlying atomic structures that govern them.

Use of simulations in research has broadened both the volume and complexity of analysis that can be done at any one time. The ability to model atoms through simulations has been an integral part of the research done in diverse areas of science, notably materials science. In this field, atomistic models are often used to predict material properties under certain conditions using information about their nucleus and electron density. For example, professor ABFIEJABF of the physics department of Georgia Tech created an atomistic model that simulates the behavior of atoms in ABFIEJABF. Another use of atomistic models is to simulate and analyze important processes such as a nuclear chain reaction; an example of such a simulation can be viewed on [https://javalab.org/en/nuclear_chain_reaction_en/ JavaLab].

Atomistic models use the mathematical models discussed above to computationally represent atomic forces, atomic positions, velocities, and magnetic charges of atoms among other things. The result is an accurate model of quantum processes. Ultimately, the use of such simulations help to understand the collective behavior of atoms and how this behavior affects macroscopic processes (such as deformation and phase change) as well as performance abilities (such as strength of material).

==History==

===John Dalton: The Law of Multiple Proportions and Atomic Mass===
[[File:Daltons_symbols.gif|thumb|Dalton's concept of atoms and molecules]]
Working from the conservation of mass principle, chemist John Dalton determined the law of multiple proportions to understand how different elements combined in compounds. In 1803, he proposed that each element of the periodic table was composed of identical components, atoms, that were unique to each element. He also suggested that these atoms were not created nor destroyed when one element was combined with another. Dalton's empirical, experimentally-based work marked the first scientific theory of the atom.

Dalton proposed a list of atomic weights in 1805. However, Dalton failed to recognize natural tendencies of elements in nature (for example, oxygen typically exists as a diatomic molecule as <math>\text{O}_2</math>). Dalton was unable to distinguish between atoms and molecules (groups of atoms).

===Amedeo Avogadro: Avogadro's Law===
In 1811, [[Amedeo Avogadro]] studied gases and determined that the amount of volume a gas occupies is not determined by the mass of the gas. This allowed Avogadro to take more accurate atomic measurements of gases than Dalton, and differentiate atoms from molecules.

===Robert Brown: Brownian Motion===
A Scottish botanist, Robert Brown, studied the motion of tiny pollen particles in water in 1827. The particles followed complex paths, dubbed Brownian Motion. As early as 1905, [[Albert Einstein]] used Brownian Motion to predict the size of atoms and molecules.

===J.J. Thomson: The Plum-Pudding Model and Electrons===
[[File:Plum_pudding_model.svg|thumb|Tomson's Plum-Pudding Model]]
Through his work with cathode rays, [[J.J. Thomson]] discovered the electron in 1897, and was the first to learn that atoms weren't actually "uncuttable" as initially thought. Thomson knew that atoms had a net neutral charge, but he only knew that negative particles existed. Thus, Thomson developed the "plum-pudding" model of negatively charged electrons floating in a sea of positive charge. (He likened the relationship of electrons to the sea of positive charge to that of plums in plum pudding.)

===Ernest Rutherford: Gold Foil Experiment and the Nucleus===
In 1909, one of Thomson's students, [[Ernest Rutherford]], determined that the positive charge of atoms was located in a central nucleus. He shot small, positively charged alpha particles at thin sheets of gold foil and noted that some particles were sharply deflected. This deflection could only occur if the positive components of atoms were located in a small area, which Rutherford assumed to be the center. He proposed a planetary model of atoms where a cloud of electrons surrounded a central, positively charged nucleus.

===Niels Bohr: Introducing Quantum Physics===
[[File:Bohr_atom_animation_2.gif|thumb|The Bohr model for a Hydrogen atom with its electron moving between energy levels]]
As quantum mechanics progressed through the work of [[Albert Einstein]] and [[Max Planck]], [[Niels Bohr]] updated the atomic model in 1913 to account for quantum phenomena. Bohr, who was also one of Rutherford's students, suggested that electrostatic forces kept electrons in circular orbit around the positively charged central nucleus. In support of his theory, Bohr examined the behavior of electrons in hydrogen molecules and noted that they followed distinct energy levels. When an electron changed energy levels, it gained or lost energy, which could be emitted in the form of light. While the Bohr model holds true for hydrogen, it isn't accurate for multi-electron elements.

===James Chadwick: Neutrons===
James Chadwick won a Nobel Prize in 1935 for his discovery of the neutron. Starting with Rutherford's work, Chadwick continued experimenting to determine the excess mass in the nucleus that wasn't accounted for by protons. He found that neutrally charged particles, dubbed neutrons, were also inside the nucleus.

===The Current Model: Quantum Physics and Electron Orbitals===
Erwin Schrödinger examined the possibility that moving electrons behaved more like waves than particles, and published "Schrödinger's Equation" in 1926. Although this resolved many issues encountered with the Bohr model, it faced opposition from physicist [[Max Born]]. Instead, Born suggested a wave-particle duality of electrons, which stated that electrons could behave both like a wave and a particle.
As electrons were now given properties of waves, it was impossible to simultaneously determine an electron's exact location and momentum around the nucleus. Werner Heisenberg, first described this phenomena in 1927, and it was later named the Heisenberg Uncertainty Principle. This refuted the Bohr model of the atom, and replaced it with a pattern of probabilities as to where electrons are located around the nucleus. These patterns are referred to as atomic orbitals and come in a variety of shapes (basic spheres, rings, dumbbells, etc.) and the nucleus is always at the center.
[[File:Neon_orbitals.JPG|thumb|center|The first five atomic orbitals: 1s, 2s, 2px, 2py, and 2pz.]]

==Connectedness==
While classical physics applies to large objects moving much slower than the speed of light, modern physics deals with special cases of tiny objects, like atoms, subject to relativistic effects. Atomic theory is vital to understanding many quantum physics concepts that are covered in both Physics 2211 and 2212, like the ball-and-spring model of solids, point charges, and conductivity.

Although one can argue physics applies to just about every aspect of life, and atomic theory is critical to understanding physics, atomic theory has directly influenced material science, power generation, electronics, and even food processing, to name a few.

<gallery>
File:Apollo_synthetic_diamond.jpg|'''Material Science:''' Synthetic diamonds are used for both cosmetic retail and in manufacturing cutting tools.
File:Electrical_and_Mechanical_Services_Department_Headquarters_Photovoltaics.jpg|'''Power:''' Solar cells and power rely on the photovoltaic effect and the wave-particle duality of subatomic particles (like photons).
File:Monokristalines_Silizium_f%C3%BCr_die_Waferherstellung.jpg|'''Electronics:''' Silicon, a popular semiconductor used in electronics, is produced industrially in a single-crystal form.
File:Sodium-chloride-3D-ionic.png|'''Food processing:''' An atomic view of table salt. Purple particles are sodium (Na), and green particles are chlorine (Cl).
File:Nagasakibomb.jpg|'''Defense:''' Nuclear weapons were used during World War II.
File:White_Matter_Connections_Obtained_with_MRI_Tractography.png|'''Medicine:''' MRI's provide doctors critical information without the risks of surgery.
File:Plastic_household_items.jpg|'''Manufacturing:''' Many common household items are made with plastic.
</gallery>

== See also ==

*[[Bohr Model]]
*[[Electronic Energy Levels and Photons]]
*[[Rutherford Experiment and Atomic Collisions]]

===Notable Scientists===
*[[Amedeo Avogadro]]
*[[J.J. Thomson]]
*[[Ernest Rutherford]]
*[[Albert Einstein]]
*[[Max Planck]]
*[[Niels Bohr]]
*[[Max Born]]

===Related Theories===
*[[Quantum Theory]]
*[[Einstein's Theory of Special Relativity]]

===Concept Application===
*[[Ball and Spring Model of Matter]], [[Ball and Spring Model]]
*[[Length and Stiffness of an Interatomic Bond]], [[Young's Modulus]]
*[[Density]], [[Charge]], [[Spin]], and [[Conductivity]]
*[[The Photoelectric Effect]], [[Photons]]
*[[Rest Mass Energy]]
*[[Potential Energy of a Pair of Neutral Atoms]]

===External links===
*Physics Portal description of [https://en.wikipedia.org/wiki/History_of_molecular_theory Molecular Theory] and [https://en.wikipedia.org/wiki/Elementary_particle Subatomic Particles]
*HyperPhysics summary of [http://hyperphysics.phy-astr.gsu.edu/hbase/quacon.html#quacon Quantum Physics]
*Demonstration of the [https://phet.colorado.edu/en/simulation/legacy/hydrogen-atom various models] of a hydrogen atom

==References==

1. “Atomic Theory.” Wikipedia, Wikimedia Foundation, 19 Feb. 2022, https://en.wikipedia.org/wiki/Atomic_theory.

2. Introduction to Atomistic Modeling Xxx Techniques. https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf.

3. Clark, S J. “Atomistic Models.” Atomistic Models, http://cmt.dur.ac.uk/sjc/thesis_dlc/node45.html.

4. Introduction to Atomistic Modeling Xxx Techniques. https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf.

5. “Matter Wave.” Wikipedia, Wikimedia Foundation, 3 Apr. 2022, https://en.wikipedia.org/wiki/Matter_wave.

Chapter 30 of [https://openstaxcollege.org/files/textbook_version/hi_res_pdf/9/CollegePhysics-OP.pdf OpenStax Textbook]

Physics Portal page on [https://en.wikipedia.org/wiki/Atomic_theory Atomic Theory]

[[Category: Theory]]

Atomic Theory

2022-04-18T02:50:51Z

Erinhorbacz: /* A Mathematical Model */

Claimed by: Erin Horbacz (4/17/2022)

Atomic theory states that matter is composed of discrete units, called atoms. The word "atom" comes from the Greek word for uncuttable, ''atomos'', since it was believed that if one cut a substance into smaller and smaller pieces, one would reach a point where the substance could not be cut any further. Scientists later discovered that atoms were indeed able to be broken into subatomic, or elementary, particles including protons, neutrons, and electrons. Furthermore, protons and neutrons can be broken down yet again into smaller, elementary particles called [https://en.wikipedia.org/wiki/Quark#:~:text=A%20quark%20(%2Fkw%C9%94%CB%90r,the%20components%20of%20atomic%20nuclei./ quarks]. Atomic theory has evolved greatly over time, but the most recent model stems from quantum mechanics[https://en.wikipedia.org/wiki/Atomic_theory].

==The Main Idea==
===A Mathematical Model===
Mathematical models of atomic processes have become more thorough and sophisticated as knowledge of atomic properties has grown. The goal of a mathematical model is to express the underlying rules that govern atomic processes in a formula that can then predict and describe the behavior of atoms [https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf] (such as is seen with the list of Bohr's mathematical models for the atom). Such fundamental formulas are powerful tools for helping scientists understand the interactions within and processes of both microscopic and macroscopic systems. For example, it was [https://en.wikipedia.org/wiki/Charles-Augustin_de_Coulomb/ Charles-Augustin de Coulomb] who first determined the mathematical equation which could accurately describe the electrostatic potential between charged particles that make up an atom:

<math>
V = \frac{1}{4 \pi \epsilon} \frac{q_1 q_2}{r}
</math>

[[bohr_equations.jpg|thumb|Bohr's mathematical model to describe the atom]]

where V is the [https://en.wikipedia.org/wiki/Electric_potential/ electrostatic potential] (in volts), <math> \frac{1}{4 \pi \epsilon} </math> is the [https://en.wikipedia.org/wiki/Coulomb_constant#:~:text=The%20Coulomb%20constant%2C%20the%20electric,%E2%88%922%E2%8B%85C%E2%88%922./ Coulomb constant], <math>q_1 </math> and <math> q_2 </math> are the charges of two particles, and r is the distance between the two particles.

Additionally, stretching of atomic bonds are known to be affected by force fields around an equilibrium point, and they can be modeled according to the equation:

<math>
\Delta V(l) = \frac{1}{2} k_l (l - l_0)^2
</math>

Where <math>\Delta V(l) </math> is the change in potential energy at <math>l</math>, <math>k_1</math> is the spring constant (a proportionality constant), <math>l</math> is the bond length, and <math>l_0</math> is the equilibrium bond length[http://cmt.dur.ac.uk/sjc/thesis_dlc/node45.html].

The use and creation of these formulas is incredibly prominent in simulation modeling. For example, simulations modeling the motion of multiple atoms can use mathematical models such as [https://en.wikipedia.org/wiki/Leapfrog_integration/ Leapfrog integration] and [https://en.wikipedia.org/wiki/Verlet_integration/ Verlet integration] to update particle positions and velocities respectively[https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf].

Perhaps the most important aspect of these mathematical models are their ability to take difficult, abstract concepts and represent them in a form that can be manipulated for further research. The creation of models to describe quantum phenomena makes the information more digestible and the concepts somewhat clearer. In fact, it is often the case that a mathematical model describing quantum behavior helps others think about concepts in different ways. In this manner, many discoveries have resulted from generalizing these models to extend beyond their initial boundaries. For example, the [https://en.wikipedia.org/wiki/Wave%E2%80%93particle_duality#:~:text=Wave%E2%80%93particle%20duality%20is%20the,behaviour%20of%20quantum%2Dscale%20objects./ wave-particle duality] of electrons became known through experiments such as the [https://en.wikipedia.org/wiki/Double-slit_experiment/ double-slit experiment] and the [https://en.wikipedia.org/wiki/Photoelectric_effect/ photoelectric effect]. However, it was Louis de Broglie who considered extending the wave nature to all particles, not just electrons. He discovered that all matter has wave properties, and he formulated the de Broglie wavelength[https://en.wikipedia.org/wiki/Matter_wave]:

<math>
\lambda = \frac{h}{p}
</math>

This formula tells us the wavelength of any particle with a given momentum. This was a huge breakthrough for atomic theory, and is a great example of the usefulness of atomic mathematical models to represent information and inspire new findings.

===A Computational Model===
Understanding the composition and structure of atoms is essential to the study of both microscopic and macroscopic systems. Researchers have made use of atomic information to create what are called atomistic models. These models are used to predict and analyze the behavior of complex systems through knowledge of their most fundamental parts. By understanding how atomic structure affects characteristic properties of atoms, scientists are able to create computational models based on simple microscopic characteristics that simulate complex macroscopic systems. In doing so, they aim to better understand the connection between these macroscopic systems and the underlying atomic structures that govern them.

Use of simulations in research has broadened both the volume and complexity of analysis that can be done at any one time. The ability to model atoms through simulations has been an integral part of the research done in diverse areas of science, notably materials science. In this field, atomistic models are often used to predict material properties under certain conditions using information about their nucleus and electron density. For example, professor ABFIEJABF of the physics department of Georgia Tech created an atomistic model that simulates the behavior of atoms in ABFIEJABF. Another use of atomistic models is to simulate and analyze important processes such as a nuclear chain reaction; an example of such a simulation can be viewed on [https://javalab.org/en/nuclear_chain_reaction_en/ JavaLab].

Atomistic models use the mathematical models discussed above to computationally represent atomic forces, atomic positions, velocities, and magnetic charges of atoms among other things. The result is an accurate model of quantum processes. Ultimately, the use of such simulations help to understand the collective behavior of atoms and how this behavior affects macroscopic processes (such as deformation and phase change) as well as performance abilities (such as strength of material).

==History==

===John Dalton: The Law of Multiple Proportions and Atomic Mass===
[[File:Daltons_symbols.gif|thumb|Dalton's concept of atoms and molecules]]
Working from the conservation of mass principle, chemist John Dalton determined the law of multiple proportions to understand how different elements combined in compounds. In 1803, he proposed that each element of the periodic table was composed of identical components, atoms, that were unique to each element. He also suggested that these atoms were not created nor destroyed when one element was combined with another. Dalton's empirical, experimentally-based work marked the first scientific theory of the atom.

Dalton proposed a list of atomic weights in 1805. However, Dalton failed to recognize natural tendencies of elements in nature (for example, oxygen typically exists as a diatomic molecule as <math>\text{O}_2</math>). Dalton was unable to distinguish between atoms and molecules (groups of atoms).

===Amedeo Avogadro: Avogadro's Law===
In 1811, [[Amedeo Avogadro]] studied gases and determined that the amount of volume a gas occupies is not determined by the mass of the gas. This allowed Avogadro to take more accurate atomic measurements of gases than Dalton, and differentiate atoms from molecules.

===Robert Brown: Brownian Motion===
A Scottish botanist, Robert Brown, studied the motion of tiny pollen particles in water in 1827. The particles followed complex paths, dubbed Brownian Motion. As early as 1905, [[Albert Einstein]] used Brownian Motion to predict the size of atoms and molecules.

===J.J. Thomson: The Plum-Pudding Model and Electrons===
[[File:Plum_pudding_model.svg|thumb|Tomson's Plum-Pudding Model]]
Through his work with cathode rays, [[J.J. Thomson]] discovered the electron in 1897, and was the first to learn that atoms weren't actually "uncuttable" as initially thought. Thomson knew that atoms had a net neutral charge, but he only knew that negative particles existed. Thus, Thomson developed the "plum-pudding" model of negatively charged electrons floating in a sea of positive charge. (He likened the relationship of electrons to the sea of positive charge to that of plums in plum pudding.)

===Ernest Rutherford: Gold Foil Experiment and the Nucleus===
In 1909, one of Thomson's students, [[Ernest Rutherford]], determined that the positive charge of atoms was located in a central nucleus. He shot small, positively charged alpha particles at thin sheets of gold foil and noted that some particles were sharply deflected. This deflection could only occur if the positive components of atoms were located in a small area, which Rutherford assumed to be the center. He proposed a planetary model of atoms where a cloud of electrons surrounded a central, positively charged nucleus.

===Niels Bohr: Introducing Quantum Physics===
[[File:Bohr_atom_animation_2.gif|thumb|The Bohr model for a Hydrogen atom with its electron moving between energy levels]]
As quantum mechanics progressed through the work of [[Albert Einstein]] and [[Max Planck]], [[Niels Bohr]] updated the atomic model in 1913 to account for quantum phenomena. Bohr, who was also one of Rutherford's students, suggested that electrostatic forces kept electrons in circular orbit around the positively charged central nucleus. In support of his theory, Bohr examined the behavior of electrons in hydrogen molecules and noted that they followed distinct energy levels. When an electron changed energy levels, it gained or lost energy, which could be emitted in the form of light. While the Bohr model holds true for hydrogen, it isn't accurate for multi-electron elements.

===James Chadwick: Neutrons===
James Chadwick won a Nobel Prize in 1935 for his discovery of the neutron. Starting with Rutherford's work, Chadwick continued experimenting to determine the excess mass in the nucleus that wasn't accounted for by protons. He found that neutrally charged particles, dubbed neutrons, were also inside the nucleus.

===The Current Model: Quantum Physics and Electron Orbitals===
Erwin Schrödinger examined the possibility that moving electrons behaved more like waves than particles, and published "Schrödinger's Equation" in 1926. Although this resolved many issues encountered with the Bohr model, it faced opposition from physicist [[Max Born]]. Instead, Born suggested a wave-particle duality of electrons, which stated that electrons could behave both like a wave and a particle.
As electrons were now given properties of waves, it was impossible to simultaneously determine an electron's exact location and momentum around the nucleus. Werner Heisenberg, first described this phenomena in 1927, and it was later named the Heisenberg Uncertainty Principle. This refuted the Bohr model of the atom, and replaced it with a pattern of probabilities as to where electrons are located around the nucleus. These patterns are referred to as atomic orbitals and come in a variety of shapes (basic spheres, rings, dumbbells, etc.) and the nucleus is always at the center.
[[File:Neon_orbitals.JPG|thumb|center|The first five atomic orbitals: 1s, 2s, 2px, 2py, and 2pz.]]

==Connectedness==
While classical physics applies to large objects moving much slower than the speed of light, modern physics deals with special cases of tiny objects, like atoms, subject to relativistic effects. Atomic theory is vital to understanding many quantum physics concepts that are covered in both Physics 2211 and 2212, like the ball-and-spring model of solids, point charges, and conductivity.

Although one can argue physics applies to just about every aspect of life, and atomic theory is critical to understanding physics, atomic theory has directly influenced material science, power generation, electronics, and even food processing, to name a few.

<gallery>
File:Apollo_synthetic_diamond.jpg|'''Material Science:''' Synthetic diamonds are used for both cosmetic retail and in manufacturing cutting tools.
File:Electrical_and_Mechanical_Services_Department_Headquarters_Photovoltaics.jpg|'''Power:''' Solar cells and power rely on the photovoltaic effect and the wave-particle duality of subatomic particles (like photons).
File:Monokristalines_Silizium_f%C3%BCr_die_Waferherstellung.jpg|'''Electronics:''' Silicon, a popular semiconductor used in electronics, is produced industrially in a single-crystal form.
File:Sodium-chloride-3D-ionic.png|'''Food processing:''' An atomic view of table salt. Purple particles are sodium (Na), and green particles are chlorine (Cl).
File:Nagasakibomb.jpg|'''Defense:''' Nuclear weapons were used during World War II.
File:White_Matter_Connections_Obtained_with_MRI_Tractography.png|'''Medicine:''' MRI's provide doctors critical information without the risks of surgery.
File:Plastic_household_items.jpg|'''Manufacturing:''' Many common household items are made with plastic.
</gallery>

== See also ==

*[[Bohr Model]]
*[[Electronic Energy Levels and Photons]]
*[[Rutherford Experiment and Atomic Collisions]]

===Notable Scientists===
*[[Amedeo Avogadro]]
*[[J.J. Thomson]]
*[[Ernest Rutherford]]
*[[Albert Einstein]]
*[[Max Planck]]
*[[Niels Bohr]]
*[[Max Born]]

===Related Theories===
*[[Quantum Theory]]
*[[Einstein's Theory of Special Relativity]]

===Concept Application===
*[[Ball and Spring Model of Matter]], [[Ball and Spring Model]]
*[[Length and Stiffness of an Interatomic Bond]], [[Young's Modulus]]
*[[Density]], [[Charge]], [[Spin]], and [[Conductivity]]
*[[The Photoelectric Effect]], [[Photons]]
*[[Rest Mass Energy]]
*[[Potential Energy of a Pair of Neutral Atoms]]

===External links===
*Physics Portal description of [https://en.wikipedia.org/wiki/History_of_molecular_theory Molecular Theory] and [https://en.wikipedia.org/wiki/Elementary_particle Subatomic Particles]
*HyperPhysics summary of [http://hyperphysics.phy-astr.gsu.edu/hbase/quacon.html#quacon Quantum Physics]
*Demonstration of the [https://phet.colorado.edu/en/simulation/legacy/hydrogen-atom various models] of a hydrogen atom

==References==

1. “Atomic Theory.” Wikipedia, Wikimedia Foundation, 19 Feb. 2022, https://en.wikipedia.org/wiki/Atomic_theory.

2. Introduction to Atomistic Modeling Xxx Techniques. https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf.

3. Clark, S J. “Atomistic Models.” Atomistic Models, http://cmt.dur.ac.uk/sjc/thesis_dlc/node45.html.

4. Introduction to Atomistic Modeling Xxx Techniques. https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf.

5. “Matter Wave.” Wikipedia, Wikimedia Foundation, 3 Apr. 2022, https://en.wikipedia.org/wiki/Matter_wave.

Chapter 30 of [https://openstaxcollege.org/files/textbook_version/hi_res_pdf/9/CollegePhysics-OP.pdf OpenStax Textbook]

Physics Portal page on [https://en.wikipedia.org/wiki/Atomic_theory Atomic Theory]

[[Category: Theory]]

File:Bohr equations.jpg

2022-04-18T02:49:27Z

Erinhorbacz:

File:Bohr equations.jpeg

2022-04-18T02:46:57Z

Erinhorbacz:

Atomic Theory

2022-04-18T02:45:18Z

Erinhorbacz: /* A Mathematical Model */

Claimed by: Erin Horbacz (4/17/2022)

Atomic theory states that matter is composed of discrete units, called atoms. The word "atom" comes from the Greek word for uncuttable, ''atomos'', since it was believed that if one cut a substance into smaller and smaller pieces, one would reach a point where the substance could not be cut any further. Scientists later discovered that atoms were indeed able to be broken into subatomic, or elementary, particles including protons, neutrons, and electrons. Furthermore, protons and neutrons can be broken down yet again into smaller, elementary particles called [https://en.wikipedia.org/wiki/Quark#:~:text=A%20quark%20(%2Fkw%C9%94%CB%90r,the%20components%20of%20atomic%20nuclei./ quarks]. Atomic theory has evolved greatly over time, but the most recent model stems from quantum mechanics[https://en.wikipedia.org/wiki/Atomic_theory].

==The Main Idea==
===A Mathematical Model===
Mathematical models of atomic processes have become more thorough and sophisticated as knowledge of atomic properties has grown. The goal of a mathematical model is to express the underlying rules that govern atomic processes in a formula that can then predict and describe the behavior of atoms [https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf] (such as is seen with the list of Bohr's mathematical models for the atom). Such fundamental formulas are powerful tools for helping scientists understand the interactions within and processes of both microscopic and macroscopic systems. For example, it was [https://en.wikipedia.org/wiki/Charles-Augustin_de_Coulomb/ Charles-Augustin de Coulomb] who first determined the mathematical equation which could accurately describe the electrostatic potential between charged particles that make up an atom:

<math>
V = \frac{1}{4 \pi \epsilon} \frac{q_1 q_2}{r}
</math>

[[bohr.png|thumb|Bohr's mathematical model to describe the atom]]

where V is the [https://en.wikipedia.org/wiki/Electric_potential/ electrostatic potential] (in volts), <math> \frac{1}{4 \pi \epsilon} </math> is the [https://en.wikipedia.org/wiki/Coulomb_constant#:~:text=The%20Coulomb%20constant%2C%20the%20electric,%E2%88%922%E2%8B%85C%E2%88%922./ Coulomb constant], <math>q_1 </math> and <math> q_2 </math> are the charges of two particles, and r is the distance between the two particles.

Additionally, stretching of atomic bonds are known to be affected by force fields around an equilibrium point, and they can be modeled according to the equation:

<math>
\Delta V(l) = \frac{1}{2} k_l (l - l_0)^2
</math>

Where <math>\Delta V(l) </math> is the change in potential energy at <math>l</math>, <math>k_1</math> is the spring constant (a proportionality constant), <math>l</math> is the bond length, and <math>l_0</math> is the equilibrium bond length[http://cmt.dur.ac.uk/sjc/thesis_dlc/node45.html].

The use and creation of these formulas is incredibly prominent in simulation modeling. For example, simulations modeling the motion of multiple atoms can use mathematical models such as [https://en.wikipedia.org/wiki/Leapfrog_integration/ Leapfrog integration] and [https://en.wikipedia.org/wiki/Verlet_integration/ Verlet integration] to update particle positions and velocities respectively[https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf].

Perhaps the most important aspect of these mathematical models are their ability to take difficult, abstract concepts and represent them in a form that can be manipulated for further research. The creation of models to describe quantum phenomena makes the information more digestible and the concepts somewhat clearer. In fact, it is often the case that a mathematical model describing quantum behavior helps others think about concepts in different ways. In this manner, many discoveries have resulted from generalizing these models to extend beyond their initial boundaries. For example, the [https://en.wikipedia.org/wiki/Wave%E2%80%93particle_duality#:~:text=Wave%E2%80%93particle%20duality%20is%20the,behaviour%20of%20quantum%2Dscale%20objects./ wave-particle duality] of electrons became known through experiments such as the [https://en.wikipedia.org/wiki/Double-slit_experiment/ double-slit experiment] and the [https://en.wikipedia.org/wiki/Photoelectric_effect/ photoelectric effect]. However, it was Louis de Broglie who considered extending the wave nature to all particles, not just electrons. He discovered that all matter has wave properties, and he formulated the de Broglie wavelength[https://en.wikipedia.org/wiki/Matter_wave]:

<math>
\lambda = \frac{h}{p}
</math>

This formula tells us the wavelength of any particle with a given momentum. This was a huge breakthrough for atomic theory, and is a great example of the usefulness of atomic mathematical models to represent information and inspire new findings.

===A Computational Model===
Understanding the composition and structure of atoms is essential to the study of both microscopic and macroscopic systems. Researchers have made use of atomic information to create what are called atomistic models. These models are used to predict and analyze the behavior of complex systems through knowledge of their most fundamental parts. By understanding how atomic structure affects characteristic properties of atoms, scientists are able to create computational models based on simple microscopic characteristics that simulate complex macroscopic systems. In doing so, they aim to better understand the connection between these macroscopic systems and the underlying atomic structures that govern them.

Use of simulations in research has broadened both the volume and complexity of analysis that can be done at any one time. The ability to model atoms through simulations has been an integral part of the research done in diverse areas of science, notably materials science. In this field, atomistic models are often used to predict material properties under certain conditions using information about their nucleus and electron density. For example, professor ABFIEJABF of the physics department of Georgia Tech created an atomistic model that simulates the behavior of atoms in ABFIEJABF. Another use of atomistic models is to simulate and analyze important processes such as a nuclear chain reaction; an example of such a simulation can be viewed on [https://javalab.org/en/nuclear_chain_reaction_en/ JavaLab].

Atomistic models use the mathematical models discussed above to computationally represent atomic forces, atomic positions, velocities, and magnetic charges of atoms among other things. The result is an accurate model of quantum processes. Ultimately, the use of such simulations help to understand the collective behavior of atoms and how this behavior affects macroscopic processes (such as deformation and phase change) as well as performance abilities (such as strength of material).

==History==

===John Dalton: The Law of Multiple Proportions and Atomic Mass===
[[File:Daltons_symbols.gif|thumb|Dalton's concept of atoms and molecules]]
Working from the conservation of mass principle, chemist John Dalton determined the law of multiple proportions to understand how different elements combined in compounds. In 1803, he proposed that each element of the periodic table was composed of identical components, atoms, that were unique to each element. He also suggested that these atoms were not created nor destroyed when one element was combined with another. Dalton's empirical, experimentally-based work marked the first scientific theory of the atom.

Dalton proposed a list of atomic weights in 1805. However, Dalton failed to recognize natural tendencies of elements in nature (for example, oxygen typically exists as a diatomic molecule as <math>\text{O}_2</math>). Dalton was unable to distinguish between atoms and molecules (groups of atoms).

===Amedeo Avogadro: Avogadro's Law===
In 1811, [[Amedeo Avogadro]] studied gases and determined that the amount of volume a gas occupies is not determined by the mass of the gas. This allowed Avogadro to take more accurate atomic measurements of gases than Dalton, and differentiate atoms from molecules.

===Robert Brown: Brownian Motion===
A Scottish botanist, Robert Brown, studied the motion of tiny pollen particles in water in 1827. The particles followed complex paths, dubbed Brownian Motion. As early as 1905, [[Albert Einstein]] used Brownian Motion to predict the size of atoms and molecules.

===J.J. Thomson: The Plum-Pudding Model and Electrons===
[[File:Plum_pudding_model.svg|thumb|Tomson's Plum-Pudding Model]]
Through his work with cathode rays, [[J.J. Thomson]] discovered the electron in 1897, and was the first to learn that atoms weren't actually "uncuttable" as initially thought. Thomson knew that atoms had a net neutral charge, but he only knew that negative particles existed. Thus, Thomson developed the "plum-pudding" model of negatively charged electrons floating in a sea of positive charge. (He likened the relationship of electrons to the sea of positive charge to that of plums in plum pudding.)

===Ernest Rutherford: Gold Foil Experiment and the Nucleus===
In 1909, one of Thomson's students, [[Ernest Rutherford]], determined that the positive charge of atoms was located in a central nucleus. He shot small, positively charged alpha particles at thin sheets of gold foil and noted that some particles were sharply deflected. This deflection could only occur if the positive components of atoms were located in a small area, which Rutherford assumed to be the center. He proposed a planetary model of atoms where a cloud of electrons surrounded a central, positively charged nucleus.

===Niels Bohr: Introducing Quantum Physics===
[[File:Bohr_atom_animation_2.gif|thumb|The Bohr model for a Hydrogen atom with its electron moving between energy levels]]
As quantum mechanics progressed through the work of [[Albert Einstein]] and [[Max Planck]], [[Niels Bohr]] updated the atomic model in 1913 to account for quantum phenomena. Bohr, who was also one of Rutherford's students, suggested that electrostatic forces kept electrons in circular orbit around the positively charged central nucleus. In support of his theory, Bohr examined the behavior of electrons in hydrogen molecules and noted that they followed distinct energy levels. When an electron changed energy levels, it gained or lost energy, which could be emitted in the form of light. While the Bohr model holds true for hydrogen, it isn't accurate for multi-electron elements.

===James Chadwick: Neutrons===
James Chadwick won a Nobel Prize in 1935 for his discovery of the neutron. Starting with Rutherford's work, Chadwick continued experimenting to determine the excess mass in the nucleus that wasn't accounted for by protons. He found that neutrally charged particles, dubbed neutrons, were also inside the nucleus.

===The Current Model: Quantum Physics and Electron Orbitals===
Erwin Schrödinger examined the possibility that moving electrons behaved more like waves than particles, and published "Schrödinger's Equation" in 1926. Although this resolved many issues encountered with the Bohr model, it faced opposition from physicist [[Max Born]]. Instead, Born suggested a wave-particle duality of electrons, which stated that electrons could behave both like a wave and a particle.
As electrons were now given properties of waves, it was impossible to simultaneously determine an electron's exact location and momentum around the nucleus. Werner Heisenberg, first described this phenomena in 1927, and it was later named the Heisenberg Uncertainty Principle. This refuted the Bohr model of the atom, and replaced it with a pattern of probabilities as to where electrons are located around the nucleus. These patterns are referred to as atomic orbitals and come in a variety of shapes (basic spheres, rings, dumbbells, etc.) and the nucleus is always at the center.
[[File:Neon_orbitals.JPG|thumb|center|The first five atomic orbitals: 1s, 2s, 2px, 2py, and 2pz.]]

==Connectedness==
While classical physics applies to large objects moving much slower than the speed of light, modern physics deals with special cases of tiny objects, like atoms, subject to relativistic effects. Atomic theory is vital to understanding many quantum physics concepts that are covered in both Physics 2211 and 2212, like the ball-and-spring model of solids, point charges, and conductivity.

Although one can argue physics applies to just about every aspect of life, and atomic theory is critical to understanding physics, atomic theory has directly influenced material science, power generation, electronics, and even food processing, to name a few.

<gallery>
File:Apollo_synthetic_diamond.jpg|'''Material Science:''' Synthetic diamonds are used for both cosmetic retail and in manufacturing cutting tools.
File:Electrical_and_Mechanical_Services_Department_Headquarters_Photovoltaics.jpg|'''Power:''' Solar cells and power rely on the photovoltaic effect and the wave-particle duality of subatomic particles (like photons).
File:Monokristalines_Silizium_f%C3%BCr_die_Waferherstellung.jpg|'''Electronics:''' Silicon, a popular semiconductor used in electronics, is produced industrially in a single-crystal form.
File:Sodium-chloride-3D-ionic.png|'''Food processing:''' An atomic view of table salt. Purple particles are sodium (Na), and green particles are chlorine (Cl).
File:Nagasakibomb.jpg|'''Defense:''' Nuclear weapons were used during World War II.
File:White_Matter_Connections_Obtained_with_MRI_Tractography.png|'''Medicine:''' MRI's provide doctors critical information without the risks of surgery.
File:Plastic_household_items.jpg|'''Manufacturing:''' Many common household items are made with plastic.
</gallery>

== See also ==

*[[Bohr Model]]
*[[Electronic Energy Levels and Photons]]
*[[Rutherford Experiment and Atomic Collisions]]

===Notable Scientists===
*[[Amedeo Avogadro]]
*[[J.J. Thomson]]
*[[Ernest Rutherford]]
*[[Albert Einstein]]
*[[Max Planck]]
*[[Niels Bohr]]
*[[Max Born]]

===Related Theories===
*[[Quantum Theory]]
*[[Einstein's Theory of Special Relativity]]

===Concept Application===
*[[Ball and Spring Model of Matter]], [[Ball and Spring Model]]
*[[Length and Stiffness of an Interatomic Bond]], [[Young's Modulus]]
*[[Density]], [[Charge]], [[Spin]], and [[Conductivity]]
*[[The Photoelectric Effect]], [[Photons]]
*[[Rest Mass Energy]]
*[[Potential Energy of a Pair of Neutral Atoms]]

===External links===
*Physics Portal description of [https://en.wikipedia.org/wiki/History_of_molecular_theory Molecular Theory] and [https://en.wikipedia.org/wiki/Elementary_particle Subatomic Particles]
*HyperPhysics summary of [http://hyperphysics.phy-astr.gsu.edu/hbase/quacon.html#quacon Quantum Physics]
*Demonstration of the [https://phet.colorado.edu/en/simulation/legacy/hydrogen-atom various models] of a hydrogen atom

==References==

1. “Atomic Theory.” Wikipedia, Wikimedia Foundation, 19 Feb. 2022, https://en.wikipedia.org/wiki/Atomic_theory.

2. Introduction to Atomistic Modeling Xxx Techniques. https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf.

3. Clark, S J. “Atomistic Models.” Atomistic Models, http://cmt.dur.ac.uk/sjc/thesis_dlc/node45.html.

4. Introduction to Atomistic Modeling Xxx Techniques. https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf.

5. “Matter Wave.” Wikipedia, Wikimedia Foundation, 3 Apr. 2022, https://en.wikipedia.org/wiki/Matter_wave.

Chapter 30 of [https://openstaxcollege.org/files/textbook_version/hi_res_pdf/9/CollegePhysics-OP.pdf OpenStax Textbook]

Physics Portal page on [https://en.wikipedia.org/wiki/Atomic_theory Atomic Theory]

[[Category: Theory]]

Atomic Theory

2022-04-18T02:37:53Z

Erinhorbacz: /* A Mathematical Model */

Claimed by: Erin Horbacz (4/17/2022)

Atomic theory states that matter is composed of discrete units, called atoms. The word "atom" comes from the Greek word for uncuttable, ''atomos'', since it was believed that if one cut a substance into smaller and smaller pieces, one would reach a point where the substance could not be cut any further. Scientists later discovered that atoms were indeed able to be broken into subatomic, or elementary, particles including protons, neutrons, and electrons. Furthermore, protons and neutrons can be broken down yet again into smaller, elementary particles called [https://en.wikipedia.org/wiki/Quark#:~:text=A%20quark%20(%2Fkw%C9%94%CB%90r,the%20components%20of%20atomic%20nuclei./ quarks]. Atomic theory has evolved greatly over time, but the most recent model stems from quantum mechanics[https://en.wikipedia.org/wiki/Atomic_theory].

==The Main Idea==
===A Mathematical Model===
Mathematical models of atomic processes have become more thorough and sophisticated as knowledge of atomic properties has grown. The goal of a mathematical model is to express the underlying rules that govern atomic processes in a formula that can then predict and describe the behavior of atoms [https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf] (such as is seen with the list of Bohr's mathematical models for the atom). Such fundamental formulas are powerful tools for helping scientists understand the interactions within and processes of both microscopic and macroscopic systems. For example, it was [https://en.wikipedia.org/wiki/Charles-Augustin_de_Coulomb/ Charles-Augustin de Coulomb] who first determined the mathematical equation which could accurately describe the electrostatic potential between charged particles that make up an atom:

<math>
V = \frac{1}{4 \pi \epsilon} \frac{q_1 q_2}{r}
</math>

[[https://qph.cf2.quoracdn.net/main-qimg-4d2482650000cb87178261f65b568536-lq|thumb|Bohr's mathematical model to describe the atom]]

where V is the [https://en.wikipedia.org/wiki/Electric_potential/ electrostatic potential] (in volts), <math> \frac{1}{4 \pi \epsilon} </math> is the [https://en.wikipedia.org/wiki/Coulomb_constant#:~:text=The%20Coulomb%20constant%2C%20the%20electric,%E2%88%922%E2%8B%85C%E2%88%922./ Coulomb constant], <math>q_1 </math> and <math> q_2 </math> are the charges of two particles, and r is the distance between the two particles.

Additionally, stretching of atomic bonds are known to be affected by force fields around an equilibrium point, and they can be modeled according to the equation:

<math>
\Delta V(l) = \frac{1}{2} k_l (l - l_0)^2
</math>

Where <math>\Delta V(l) </math> is the change in potential energy at <math>l</math>, <math>k_1</math> is the spring constant (a proportionality constant), <math>l</math> is the bond length, and <math>l_0</math> is the equilibrium bond length[http://cmt.dur.ac.uk/sjc/thesis_dlc/node45.html].

The use and creation of these formulas is incredibly prominent in simulation modeling. For example, simulations modeling the motion of multiple atoms can use mathematical models such as [https://en.wikipedia.org/wiki/Leapfrog_integration/ Leapfrog integration] and [https://en.wikipedia.org/wiki/Verlet_integration/ Verlet integration] to update particle positions and velocities respectively[https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf].

Perhaps the most important aspect of these mathematical models are their ability to take difficult, abstract concepts and represent them in a form that can be manipulated for further research. The creation of models to describe quantum phenomena makes the information more digestible and the concepts somewhat clearer. In fact, it is often the case that a mathematical model describing quantum behavior helps others think about concepts in different ways. In this manner, many discoveries have resulted from generalizing these models to extend beyond their initial boundaries. For example, the [https://en.wikipedia.org/wiki/Wave%E2%80%93particle_duality#:~:text=Wave%E2%80%93particle%20duality%20is%20the,behaviour%20of%20quantum%2Dscale%20objects./ wave-particle duality] of electrons became known through experiments such as the [https://en.wikipedia.org/wiki/Double-slit_experiment/ double-slit experiment] and the [https://en.wikipedia.org/wiki/Photoelectric_effect/ photoelectric effect]. However, it was Louis de Broglie who considered extending the wave nature to all particles, not just electrons. He discovered that all matter has wave properties, and he formulated the de Broglie wavelength[https://en.wikipedia.org/wiki/Matter_wave]:

<math>
\lambda = \frac{h}{p}
</math>

This formula tells us the wavelength of any particle with a given momentum. This was a huge breakthrough for atomic theory, and is a great example of the usefulness of atomic mathematical models to represent information and inspire new findings.

===A Computational Model===
Understanding the composition and structure of atoms is essential to the study of both microscopic and macroscopic systems. Researchers have made use of atomic information to create what are called atomistic models. These models are used to predict and analyze the behavior of complex systems through knowledge of their most fundamental parts. By understanding how atomic structure affects characteristic properties of atoms, scientists are able to create computational models based on simple microscopic characteristics that simulate complex macroscopic systems. In doing so, they aim to better understand the connection between these macroscopic systems and the underlying atomic structures that govern them.

Use of simulations in research has broadened both the volume and complexity of analysis that can be done at any one time. The ability to model atoms through simulations has been an integral part of the research done in diverse areas of science, notably materials science. In this field, atomistic models are often used to predict material properties under certain conditions using information about their nucleus and electron density. For example, professor ABFIEJABF of the physics department of Georgia Tech created an atomistic model that simulates the behavior of atoms in ABFIEJABF. Another use of atomistic models is to simulate and analyze important processes such as a nuclear chain reaction; an example of such a simulation can be viewed on [https://javalab.org/en/nuclear_chain_reaction_en/ JavaLab].

Atomistic models use the mathematical models discussed above to computationally represent atomic forces, atomic positions, velocities, and magnetic charges of atoms among other things. The result is an accurate model of quantum processes. Ultimately, the use of such simulations help to understand the collective behavior of atoms and how this behavior affects macroscopic processes (such as deformation and phase change) as well as performance abilities (such as strength of material).

==History==

===John Dalton: The Law of Multiple Proportions and Atomic Mass===
[[File:Daltons_symbols.gif|thumb|Dalton's concept of atoms and molecules]]
Working from the conservation of mass principle, chemist John Dalton determined the law of multiple proportions to understand how different elements combined in compounds. In 1803, he proposed that each element of the periodic table was composed of identical components, atoms, that were unique to each element. He also suggested that these atoms were not created nor destroyed when one element was combined with another. Dalton's empirical, experimentally-based work marked the first scientific theory of the atom.

Dalton proposed a list of atomic weights in 1805. However, Dalton failed to recognize natural tendencies of elements in nature (for example, oxygen typically exists as a diatomic molecule as <math>\text{O}_2</math>). Dalton was unable to distinguish between atoms and molecules (groups of atoms).

===Amedeo Avogadro: Avogadro's Law===
In 1811, [[Amedeo Avogadro]] studied gases and determined that the amount of volume a gas occupies is not determined by the mass of the gas. This allowed Avogadro to take more accurate atomic measurements of gases than Dalton, and differentiate atoms from molecules.

===Robert Brown: Brownian Motion===
A Scottish botanist, Robert Brown, studied the motion of tiny pollen particles in water in 1827. The particles followed complex paths, dubbed Brownian Motion. As early as 1905, [[Albert Einstein]] used Brownian Motion to predict the size of atoms and molecules.

===J.J. Thomson: The Plum-Pudding Model and Electrons===
[[File:Plum_pudding_model.svg|thumb|Tomson's Plum-Pudding Model]]
Through his work with cathode rays, [[J.J. Thomson]] discovered the electron in 1897, and was the first to learn that atoms weren't actually "uncuttable" as initially thought. Thomson knew that atoms had a net neutral charge, but he only knew that negative particles existed. Thus, Thomson developed the "plum-pudding" model of negatively charged electrons floating in a sea of positive charge. (He likened the relationship of electrons to the sea of positive charge to that of plums in plum pudding.)

===Ernest Rutherford: Gold Foil Experiment and the Nucleus===
In 1909, one of Thomson's students, [[Ernest Rutherford]], determined that the positive charge of atoms was located in a central nucleus. He shot small, positively charged alpha particles at thin sheets of gold foil and noted that some particles were sharply deflected. This deflection could only occur if the positive components of atoms were located in a small area, which Rutherford assumed to be the center. He proposed a planetary model of atoms where a cloud of electrons surrounded a central, positively charged nucleus.

===Niels Bohr: Introducing Quantum Physics===
[[File:Bohr_atom_animation_2.gif|thumb|The Bohr model for a Hydrogen atom with its electron moving between energy levels]]
As quantum mechanics progressed through the work of [[Albert Einstein]] and [[Max Planck]], [[Niels Bohr]] updated the atomic model in 1913 to account for quantum phenomena. Bohr, who was also one of Rutherford's students, suggested that electrostatic forces kept electrons in circular orbit around the positively charged central nucleus. In support of his theory, Bohr examined the behavior of electrons in hydrogen molecules and noted that they followed distinct energy levels. When an electron changed energy levels, it gained or lost energy, which could be emitted in the form of light. While the Bohr model holds true for hydrogen, it isn't accurate for multi-electron elements.

===James Chadwick: Neutrons===
James Chadwick won a Nobel Prize in 1935 for his discovery of the neutron. Starting with Rutherford's work, Chadwick continued experimenting to determine the excess mass in the nucleus that wasn't accounted for by protons. He found that neutrally charged particles, dubbed neutrons, were also inside the nucleus.

===The Current Model: Quantum Physics and Electron Orbitals===
Erwin Schrödinger examined the possibility that moving electrons behaved more like waves than particles, and published "Schrödinger's Equation" in 1926. Although this resolved many issues encountered with the Bohr model, it faced opposition from physicist [[Max Born]]. Instead, Born suggested a wave-particle duality of electrons, which stated that electrons could behave both like a wave and a particle.
As electrons were now given properties of waves, it was impossible to simultaneously determine an electron's exact location and momentum around the nucleus. Werner Heisenberg, first described this phenomena in 1927, and it was later named the Heisenberg Uncertainty Principle. This refuted the Bohr model of the atom, and replaced it with a pattern of probabilities as to where electrons are located around the nucleus. These patterns are referred to as atomic orbitals and come in a variety of shapes (basic spheres, rings, dumbbells, etc.) and the nucleus is always at the center.
[[File:Neon_orbitals.JPG|thumb|center|The first five atomic orbitals: 1s, 2s, 2px, 2py, and 2pz.]]

==Connectedness==
While classical physics applies to large objects moving much slower than the speed of light, modern physics deals with special cases of tiny objects, like atoms, subject to relativistic effects. Atomic theory is vital to understanding many quantum physics concepts that are covered in both Physics 2211 and 2212, like the ball-and-spring model of solids, point charges, and conductivity.

Although one can argue physics applies to just about every aspect of life, and atomic theory is critical to understanding physics, atomic theory has directly influenced material science, power generation, electronics, and even food processing, to name a few.

<gallery>
File:Apollo_synthetic_diamond.jpg|'''Material Science:''' Synthetic diamonds are used for both cosmetic retail and in manufacturing cutting tools.
File:Electrical_and_Mechanical_Services_Department_Headquarters_Photovoltaics.jpg|'''Power:''' Solar cells and power rely on the photovoltaic effect and the wave-particle duality of subatomic particles (like photons).
File:Monokristalines_Silizium_f%C3%BCr_die_Waferherstellung.jpg|'''Electronics:''' Silicon, a popular semiconductor used in electronics, is produced industrially in a single-crystal form.
File:Sodium-chloride-3D-ionic.png|'''Food processing:''' An atomic view of table salt. Purple particles are sodium (Na), and green particles are chlorine (Cl).
File:Nagasakibomb.jpg|'''Defense:''' Nuclear weapons were used during World War II.
File:White_Matter_Connections_Obtained_with_MRI_Tractography.png|'''Medicine:''' MRI's provide doctors critical information without the risks of surgery.
File:Plastic_household_items.jpg|'''Manufacturing:''' Many common household items are made with plastic.
</gallery>

== See also ==

*[[Bohr Model]]
*[[Electronic Energy Levels and Photons]]
*[[Rutherford Experiment and Atomic Collisions]]

===Notable Scientists===
*[[Amedeo Avogadro]]
*[[J.J. Thomson]]
*[[Ernest Rutherford]]
*[[Albert Einstein]]
*[[Max Planck]]
*[[Niels Bohr]]
*[[Max Born]]

===Related Theories===
*[[Quantum Theory]]
*[[Einstein's Theory of Special Relativity]]

===Concept Application===
*[[Ball and Spring Model of Matter]], [[Ball and Spring Model]]
*[[Length and Stiffness of an Interatomic Bond]], [[Young's Modulus]]
*[[Density]], [[Charge]], [[Spin]], and [[Conductivity]]
*[[The Photoelectric Effect]], [[Photons]]
*[[Rest Mass Energy]]
*[[Potential Energy of a Pair of Neutral Atoms]]

===External links===
*Physics Portal description of [https://en.wikipedia.org/wiki/History_of_molecular_theory Molecular Theory] and [https://en.wikipedia.org/wiki/Elementary_particle Subatomic Particles]
*HyperPhysics summary of [http://hyperphysics.phy-astr.gsu.edu/hbase/quacon.html#quacon Quantum Physics]
*Demonstration of the [https://phet.colorado.edu/en/simulation/legacy/hydrogen-atom various models] of a hydrogen atom

==References==

1. “Atomic Theory.” Wikipedia, Wikimedia Foundation, 19 Feb. 2022, https://en.wikipedia.org/wiki/Atomic_theory.

2. Introduction to Atomistic Modeling Xxx Techniques. https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf.

3. Clark, S J. “Atomistic Models.” Atomistic Models, http://cmt.dur.ac.uk/sjc/thesis_dlc/node45.html.

4. Introduction to Atomistic Modeling Xxx Techniques. https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf.

5. “Matter Wave.” Wikipedia, Wikimedia Foundation, 3 Apr. 2022, https://en.wikipedia.org/wiki/Matter_wave.

Chapter 30 of [https://openstaxcollege.org/files/textbook_version/hi_res_pdf/9/CollegePhysics-OP.pdf OpenStax Textbook]

Physics Portal page on [https://en.wikipedia.org/wiki/Atomic_theory Atomic Theory]

[[Category: Theory]]

Atomic Theory

2022-04-18T02:31:22Z

Erinhorbacz: /* A Mathematical Model */

Claimed by: Erin Horbacz (4/17/2022)

Atomic theory states that matter is composed of discrete units, called atoms. The word "atom" comes from the Greek word for uncuttable, ''atomos'', since it was believed that if one cut a substance into smaller and smaller pieces, one would reach a point where the substance could not be cut any further. Scientists later discovered that atoms were indeed able to be broken into subatomic, or elementary, particles including protons, neutrons, and electrons. Furthermore, protons and neutrons can be broken down yet again into smaller, elementary particles called [https://en.wikipedia.org/wiki/Quark#:~:text=A%20quark%20(%2Fkw%C9%94%CB%90r,the%20components%20of%20atomic%20nuclei./ quarks]. Atomic theory has evolved greatly over time, but the most recent model stems from quantum mechanics[https://en.wikipedia.org/wiki/Atomic_theory].

==The Main Idea==
===A Mathematical Model===
Mathematical models of atomic processes have become more thorough and sophisticated as knowledge of atomic properties has grown. The goal of a mathematical model is to express the underlying rules that govern atomic processes in a formula that can then predict and describe the behavior of atoms [https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf]. Such fundamental formulas are powerful tools for helping scientists understand the interactions within and processes of both microscopic and macroscopic systems. For example, it was [https://en.wikipedia.org/wiki/Charles-Augustin_de_Coulomb/ Charles-Augustin de Coulomb] who first determined the mathematical equation which could accurately describe the electrostatic potential between charged particles that make up an atom:

<math>
V = \frac{1}{4 \pi \epsilon} \frac{q_1 q_2}{r}
</math>

where V is the [https://en.wikipedia.org/wiki/Electric_potential/ electrostatic potential] (in volts), <math> \frac{1}{4 \pi \epsilon} </math> is the [https://en.wikipedia.org/wiki/Coulomb_constant#:~:text=The%20Coulomb%20constant%2C%20the%20electric,%E2%88%922%E2%8B%85C%E2%88%922./ Coulomb constant], <math>q_1 </math> and <math> q_2 </math> are the charges of two particles, and r is the distance between the two particles.

Additionally, stretching of atomic bonds are known to be affected by force fields around an equilibrium point, and they can be modeled according to the equation:

<math>
\Delta V(l) = \frac{1}{2} k_l (l - l_0)^2
</math>

Where <math>\Delta V(l) </math> is the change in potential energy at <math>l</math>, <math>k_1</math> is the spring constant (a proportionality constant), <math>l</math> is the bond length, and <math>l_0</math> is the equilibrium bond length[http://cmt.dur.ac.uk/sjc/thesis_dlc/node45.html].

The use and creation of these formulas is incredibly prominent in simulation modeling. For example, simulations modeling the motion of multiple atoms can use mathematical models such as [https://en.wikipedia.org/wiki/Leapfrog_integration/ Leapfrog integration] and [https://en.wikipedia.org/wiki/Verlet_integration/ Verlet integration] to update particle positions and velocities respectively[https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf].

Perhaps the most important aspect of these mathematical models are their ability to take difficult, abstract concepts and represent them in a form that can be manipulated for further research. The creation of models to describe quantum phenomena makes the information more digestible and the concepts somewhat clearer. In fact, it is often the case that a mathematical model describing quantum behavior helps others think about concepts in different ways. In this manner, many discoveries have resulted from generalizing these models to extend beyond their initial boundaries. For example, the [https://en.wikipedia.org/wiki/Wave%E2%80%93particle_duality#:~:text=Wave%E2%80%93particle%20duality%20is%20the,behaviour%20of%20quantum%2Dscale%20objects./ wave-particle duality] of electrons became known through experiments such as the [https://en.wikipedia.org/wiki/Double-slit_experiment/ double-slit experiment] and the [https://en.wikipedia.org/wiki/Photoelectric_effect/ photoelectric effect]. However, it was Louis de Broglie who considered extending the wave nature to all particles, not just electrons. He discovered that all matter has wave properties, and he formulated the de Broglie wavelength[https://en.wikipedia.org/wiki/Matter_wave]:

<math>
\lambda = \frac{h}{p}
</math>

This formula tells us the wavelength of any particle with a given momentum. This was a huge breakthrough for atomic theory, and is a great example of the usefulness of atomic mathematical models to represent information and inspire new findings.

===A Computational Model===
Understanding the composition and structure of atoms is essential to the study of both microscopic and macroscopic systems. Researchers have made use of atomic information to create what are called atomistic models. These models are used to predict and analyze the behavior of complex systems through knowledge of their most fundamental parts. By understanding how atomic structure affects characteristic properties of atoms, scientists are able to create computational models based on simple microscopic characteristics that simulate complex macroscopic systems. In doing so, they aim to better understand the connection between these macroscopic systems and the underlying atomic structures that govern them.

Use of simulations in research has broadened both the volume and complexity of analysis that can be done at any one time. The ability to model atoms through simulations has been an integral part of the research done in diverse areas of science, notably materials science. In this field, atomistic models are often used to predict material properties under certain conditions using information about their nucleus and electron density. For example, professor ABFIEJABF of the physics department of Georgia Tech created an atomistic model that simulates the behavior of atoms in ABFIEJABF. Another use of atomistic models is to simulate and analyze important processes such as a nuclear chain reaction; an example of such a simulation can be viewed on [https://javalab.org/en/nuclear_chain_reaction_en/ JavaLab].

Atomistic models use the mathematical models discussed above to computationally represent atomic forces, atomic positions, velocities, and magnetic charges of atoms among other things. The result is an accurate model of quantum processes. Ultimately, the use of such simulations help to understand the collective behavior of atoms and how this behavior affects macroscopic processes (such as deformation and phase change) as well as performance abilities (such as strength of material).

==History==

===John Dalton: The Law of Multiple Proportions and Atomic Mass===
[[File:Daltons_symbols.gif|thumb|Dalton's concept of atoms and molecules]]
Working from the conservation of mass principle, chemist John Dalton determined the law of multiple proportions to understand how different elements combined in compounds. In 1803, he proposed that each element of the periodic table was composed of identical components, atoms, that were unique to each element. He also suggested that these atoms were not created nor destroyed when one element was combined with another. Dalton's empirical, experimentally-based work marked the first scientific theory of the atom.

Dalton proposed a list of atomic weights in 1805. However, Dalton failed to recognize natural tendencies of elements in nature (for example, oxygen typically exists as a diatomic molecule as <math>\text{O}_2</math>). Dalton was unable to distinguish between atoms and molecules (groups of atoms).

===Amedeo Avogadro: Avogadro's Law===
In 1811, [[Amedeo Avogadro]] studied gases and determined that the amount of volume a gas occupies is not determined by the mass of the gas. This allowed Avogadro to take more accurate atomic measurements of gases than Dalton, and differentiate atoms from molecules.

===Robert Brown: Brownian Motion===
A Scottish botanist, Robert Brown, studied the motion of tiny pollen particles in water in 1827. The particles followed complex paths, dubbed Brownian Motion. As early as 1905, [[Albert Einstein]] used Brownian Motion to predict the size of atoms and molecules.

===J.J. Thomson: The Plum-Pudding Model and Electrons===
[[File:Plum_pudding_model.svg|thumb|Tomson's Plum-Pudding Model]]
Through his work with cathode rays, [[J.J. Thomson]] discovered the electron in 1897, and was the first to learn that atoms weren't actually "uncuttable" as initially thought. Thomson knew that atoms had a net neutral charge, but he only knew that negative particles existed. Thus, Thomson developed the "plum-pudding" model of negatively charged electrons floating in a sea of positive charge. (He likened the relationship of electrons to the sea of positive charge to that of plums in plum pudding.)

===Ernest Rutherford: Gold Foil Experiment and the Nucleus===
In 1909, one of Thomson's students, [[Ernest Rutherford]], determined that the positive charge of atoms was located in a central nucleus. He shot small, positively charged alpha particles at thin sheets of gold foil and noted that some particles were sharply deflected. This deflection could only occur if the positive components of atoms were located in a small area, which Rutherford assumed to be the center. He proposed a planetary model of atoms where a cloud of electrons surrounded a central, positively charged nucleus.

===Niels Bohr: Introducing Quantum Physics===
[[File:Bohr_atom_animation_2.gif|thumb|The Bohr model for a Hydrogen atom with its electron moving between energy levels]]
As quantum mechanics progressed through the work of [[Albert Einstein]] and [[Max Planck]], [[Niels Bohr]] updated the atomic model in 1913 to account for quantum phenomena. Bohr, who was also one of Rutherford's students, suggested that electrostatic forces kept electrons in circular orbit around the positively charged central nucleus. In support of his theory, Bohr examined the behavior of electrons in hydrogen molecules and noted that they followed distinct energy levels. When an electron changed energy levels, it gained or lost energy, which could be emitted in the form of light. While the Bohr model holds true for hydrogen, it isn't accurate for multi-electron elements.

===James Chadwick: Neutrons===
James Chadwick won a Nobel Prize in 1935 for his discovery of the neutron. Starting with Rutherford's work, Chadwick continued experimenting to determine the excess mass in the nucleus that wasn't accounted for by protons. He found that neutrally charged particles, dubbed neutrons, were also inside the nucleus.

===The Current Model: Quantum Physics and Electron Orbitals===
Erwin Schrödinger examined the possibility that moving electrons behaved more like waves than particles, and published "Schrödinger's Equation" in 1926. Although this resolved many issues encountered with the Bohr model, it faced opposition from physicist [[Max Born]]. Instead, Born suggested a wave-particle duality of electrons, which stated that electrons could behave both like a wave and a particle.
As electrons were now given properties of waves, it was impossible to simultaneously determine an electron's exact location and momentum around the nucleus. Werner Heisenberg, first described this phenomena in 1927, and it was later named the Heisenberg Uncertainty Principle. This refuted the Bohr model of the atom, and replaced it with a pattern of probabilities as to where electrons are located around the nucleus. These patterns are referred to as atomic orbitals and come in a variety of shapes (basic spheres, rings, dumbbells, etc.) and the nucleus is always at the center.
[[File:Neon_orbitals.JPG|thumb|center|The first five atomic orbitals: 1s, 2s, 2px, 2py, and 2pz.]]

==Connectedness==
While classical physics applies to large objects moving much slower than the speed of light, modern physics deals with special cases of tiny objects, like atoms, subject to relativistic effects. Atomic theory is vital to understanding many quantum physics concepts that are covered in both Physics 2211 and 2212, like the ball-and-spring model of solids, point charges, and conductivity.

Although one can argue physics applies to just about every aspect of life, and atomic theory is critical to understanding physics, atomic theory has directly influenced material science, power generation, electronics, and even food processing, to name a few.

<gallery>
File:Apollo_synthetic_diamond.jpg|'''Material Science:''' Synthetic diamonds are used for both cosmetic retail and in manufacturing cutting tools.
File:Electrical_and_Mechanical_Services_Department_Headquarters_Photovoltaics.jpg|'''Power:''' Solar cells and power rely on the photovoltaic effect and the wave-particle duality of subatomic particles (like photons).
File:Monokristalines_Silizium_f%C3%BCr_die_Waferherstellung.jpg|'''Electronics:''' Silicon, a popular semiconductor used in electronics, is produced industrially in a single-crystal form.
File:Sodium-chloride-3D-ionic.png|'''Food processing:''' An atomic view of table salt. Purple particles are sodium (Na), and green particles are chlorine (Cl).
File:Nagasakibomb.jpg|'''Defense:''' Nuclear weapons were used during World War II.
File:White_Matter_Connections_Obtained_with_MRI_Tractography.png|'''Medicine:''' MRI's provide doctors critical information without the risks of surgery.
File:Plastic_household_items.jpg|'''Manufacturing:''' Many common household items are made with plastic.
</gallery>

== See also ==

*[[Bohr Model]]
*[[Electronic Energy Levels and Photons]]
*[[Rutherford Experiment and Atomic Collisions]]

===Notable Scientists===
*[[Amedeo Avogadro]]
*[[J.J. Thomson]]
*[[Ernest Rutherford]]
*[[Albert Einstein]]
*[[Max Planck]]
*[[Niels Bohr]]
*[[Max Born]]

===Related Theories===
*[[Quantum Theory]]
*[[Einstein's Theory of Special Relativity]]

===Concept Application===
*[[Ball and Spring Model of Matter]], [[Ball and Spring Model]]
*[[Length and Stiffness of an Interatomic Bond]], [[Young's Modulus]]
*[[Density]], [[Charge]], [[Spin]], and [[Conductivity]]
*[[The Photoelectric Effect]], [[Photons]]
*[[Rest Mass Energy]]
*[[Potential Energy of a Pair of Neutral Atoms]]

===External links===
*Physics Portal description of [https://en.wikipedia.org/wiki/History_of_molecular_theory Molecular Theory] and [https://en.wikipedia.org/wiki/Elementary_particle Subatomic Particles]
*HyperPhysics summary of [http://hyperphysics.phy-astr.gsu.edu/hbase/quacon.html#quacon Quantum Physics]
*Demonstration of the [https://phet.colorado.edu/en/simulation/legacy/hydrogen-atom various models] of a hydrogen atom

==References==

1. “Atomic Theory.” Wikipedia, Wikimedia Foundation, 19 Feb. 2022, https://en.wikipedia.org/wiki/Atomic_theory.

2. Introduction to Atomistic Modeling Xxx Techniques. https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf.

3. Clark, S J. “Atomistic Models.” Atomistic Models, http://cmt.dur.ac.uk/sjc/thesis_dlc/node45.html.

4. Introduction to Atomistic Modeling Xxx Techniques. https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf.

5. “Matter Wave.” Wikipedia, Wikimedia Foundation, 3 Apr. 2022, https://en.wikipedia.org/wiki/Matter_wave.

Chapter 30 of [https://openstaxcollege.org/files/textbook_version/hi_res_pdf/9/CollegePhysics-OP.pdf OpenStax Textbook]

Physics Portal page on [https://en.wikipedia.org/wiki/Atomic_theory Atomic Theory]

[[Category: Theory]]

Atomic Theory

2022-04-18T02:18:35Z

Erinhorbacz: /* References */

Claimed by: Erin Horbacz (4/17/2022)

Atomic theory states that matter is composed of discrete units, called atoms. The word "atom" comes from the Greek word for uncuttable, ''atomos'', since it was believed that if one cut a substance into smaller and smaller pieces, one would reach a point where the substance could not be cut any further. Scientists later discovered that atoms were indeed able to be broken into subatomic, or elementary, particles including protons, neutrons, and electrons. Furthermore, protons and neutrons can be broken down yet again into smaller, elementary particles called [https://en.wikipedia.org/wiki/Quark#:~:text=A%20quark%20(%2Fkw%C9%94%CB%90r,the%20components%20of%20atomic%20nuclei./ quarks]. Atomic theory has evolved greatly over time, but the most recent model stems from quantum mechanics[https://en.wikipedia.org/wiki/Atomic_theory].

==The Main Idea==
===A Mathematical Model===
Mathematical models of atomic processes have become more thorough and sophisticated as knowledge of atomic properties has grown. The goal of a mathematical model is to express the underlying rules that govern atomic processes in a formula that can then predict and describe the behavior of atoms [https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf]. Such fundamental formulas are powerful tools for helping scientists understand the interactions and processes of both microscopic and macroscopic systems. For example, it was [https://en.wikipedia.org/wiki/Charles-Augustin_de_Coulomb/ Charles-Augustin de Coulomb] who first determined the mathematical equation which could accurately describe the electrostatic potential between charged particles that make up an atom:

<math>
V = \frac{1}{4 \pi \epsilon} \frac{q_1 q_2}{r}
</math>

where V is the [https://en.wikipedia.org/wiki/Electric_potential/ electrostatic potential] (in volts), <math> \frac{1}{4 \pi \epsilon} </math> is the [https://en.wikipedia.org/wiki/Coulomb_constant#:~:text=The%20Coulomb%20constant%2C%20the%20electric,%E2%88%922%E2%8B%85C%E2%88%922./ Coulomb constant], <math>q_1 </math> and <math> q_2 </math> are the charges of two particles, and r is the distance between the two particles.

Additionally, stretching of atomic bonds are known to be affected by force fields around an equilibrium point, and they can be modeled according to the equation:

<math>
\Delta V(l) = \frac{1}{2} k_l (l - l_0)^2
</math>

Where <math>\Delta V(l) </math> is the change in potential energy at <math>l</math>, <math>k_1</math> is the spring constant (a proportionality constant), <math>l</math> is the bond length, and <math>l_0</math> is the equilibrium bond length[http://cmt.dur.ac.uk/sjc/thesis_dlc/node45.html].

The use and creation of these formulas is incredibly prominent in simulation modeling. For example, simulations modeling the motion of multiple atoms can use mathematical models such as [https://en.wikipedia.org/wiki/Leapfrog_integration/ Leapfrog integration] and [https://en.wikipedia.org/wiki/Verlet_integration/ Verlet integration] to update particle positions and velocities respectively[https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf].

Perhaps the most important aspect of these mathematical models are their ability to take difficult, abstract concepts and represent them in a form that can be manipulated for further research. The creation of models to describe quantum phenomena makes the information more digestible and the concepts somewhat clearer. In fact, it is often the case that a mathematical model describing quantum behavior helps others think about concepts in different ways. In this manner, many discoveries have resulted from generalizing these models to extend beyond their initial boundaries. For example, the [https://en.wikipedia.org/wiki/Wave%E2%80%93particle_duality#:~:text=Wave%E2%80%93particle%20duality%20is%20the,behaviour%20of%20quantum%2Dscale%20objects./ wave-particle duality] of electrons became known through experiments such as the [https://en.wikipedia.org/wiki/Double-slit_experiment/ double-slit experiment] and the [https://en.wikipedia.org/wiki/Photoelectric_effect/ photoelectric effect]. However, it was Louis de Broglie who considered extending the wave nature to all particles, not just electrons. He discovered that all matter has wave properties, and he formulated the de Broglie wavelength[https://en.wikipedia.org/wiki/Matter_wave]:

<math>
\lambda = \frac{h}{p}
</math>

This formula tells us the wavelength of any particle with a given momentum. This was a huge breakthrough for atomic theory, and is a great example of the usefulness of atomic mathematical models to represent information and inspire new findings.

===A Computational Model===
Understanding the composition and structure of atoms is essential to the study of both microscopic and macroscopic systems. Researchers have made use of atomic information to create what are called atomistic models. These models are used to predict and analyze the behavior of complex systems through knowledge of their most fundamental parts. By understanding how atomic structure affects characteristic properties of atoms, scientists are able to create computational models based on simple microscopic characteristics that simulate complex macroscopic systems. In doing so, they aim to better understand the connection between these macroscopic systems and the underlying atomic structures that govern them.

Use of simulations in research has broadened both the volume and complexity of analysis that can be done at any one time. The ability to model atoms through simulations has been an integral part of the research done in diverse areas of science, notably materials science. In this field, atomistic models are often used to predict material properties under certain conditions using information about their nucleus and electron density. For example, professor ABFIEJABF of the physics department of Georgia Tech created an atomistic model that simulates the behavior of atoms in ABFIEJABF. Another use of atomistic models is to simulate and analyze important processes such as a nuclear chain reaction; an example of such a simulation can be viewed on [https://javalab.org/en/nuclear_chain_reaction_en/ JavaLab].

Atomistic models use the mathematical models discussed above to computationally represent atomic forces, atomic positions, velocities, and magnetic charges of atoms among other things. The result is an accurate model of quantum processes. Ultimately, the use of such simulations help to understand the collective behavior of atoms and how this behavior affects macroscopic processes (such as deformation and phase change) as well as performance abilities (such as strength of material).

==History==

===John Dalton: The Law of Multiple Proportions and Atomic Mass===
[[File:Daltons_symbols.gif|thumb|Dalton's concept of atoms and molecules]]
Working from the conservation of mass principle, chemist John Dalton determined the law of multiple proportions to understand how different elements combined in compounds. In 1803, he proposed that each element of the periodic table was composed of identical components, atoms, that were unique to each element. He also suggested that these atoms were not created nor destroyed when one element was combined with another. Dalton's empirical, experimentally-based work marked the first scientific theory of the atom.

Dalton proposed a list of atomic weights in 1805. However, Dalton failed to recognize natural tendencies of elements in nature (for example, oxygen typically exists as a diatomic molecule as <math>\text{O}_2</math>). Dalton was unable to distinguish between atoms and molecules (groups of atoms).

===Amedeo Avogadro: Avogadro's Law===
In 1811, [[Amedeo Avogadro]] studied gases and determined that the amount of volume a gas occupies is not determined by the mass of the gas. This allowed Avogadro to take more accurate atomic measurements of gases than Dalton, and differentiate atoms from molecules.

===Robert Brown: Brownian Motion===
A Scottish botanist, Robert Brown, studied the motion of tiny pollen particles in water in 1827. The particles followed complex paths, dubbed Brownian Motion. As early as 1905, [[Albert Einstein]] used Brownian Motion to predict the size of atoms and molecules.

===J.J. Thomson: The Plum-Pudding Model and Electrons===
[[File:Plum_pudding_model.svg|thumb|Tomson's Plum-Pudding Model]]
Through his work with cathode rays, [[J.J. Thomson]] discovered the electron in 1897, and was the first to learn that atoms weren't actually "uncuttable" as initially thought. Thomson knew that atoms had a net neutral charge, but he only knew that negative particles existed. Thus, Thomson developed the "plum-pudding" model of negatively charged electrons floating in a sea of positive charge. (He likened the relationship of electrons to the sea of positive charge to that of plums in plum pudding.)

===Ernest Rutherford: Gold Foil Experiment and the Nucleus===
In 1909, one of Thomson's students, [[Ernest Rutherford]], determined that the positive charge of atoms was located in a central nucleus. He shot small, positively charged alpha particles at thin sheets of gold foil and noted that some particles were sharply deflected. This deflection could only occur if the positive components of atoms were located in a small area, which Rutherford assumed to be the center. He proposed a planetary model of atoms where a cloud of electrons surrounded a central, positively charged nucleus.

===Niels Bohr: Introducing Quantum Physics===
[[File:Bohr_atom_animation_2.gif|thumb|The Bohr model for a Hydrogen atom with its electron moving between energy levels]]
As quantum mechanics progressed through the work of [[Albert Einstein]] and [[Max Planck]], [[Niels Bohr]] updated the atomic model in 1913 to account for quantum phenomena. Bohr, who was also one of Rutherford's students, suggested that electrostatic forces kept electrons in circular orbit around the positively charged central nucleus. In support of his theory, Bohr examined the behavior of electrons in hydrogen molecules and noted that they followed distinct energy levels. When an electron changed energy levels, it gained or lost energy, which could be emitted in the form of light. While the Bohr model holds true for hydrogen, it isn't accurate for multi-electron elements.

===James Chadwick: Neutrons===
James Chadwick won a Nobel Prize in 1935 for his discovery of the neutron. Starting with Rutherford's work, Chadwick continued experimenting to determine the excess mass in the nucleus that wasn't accounted for by protons. He found that neutrally charged particles, dubbed neutrons, were also inside the nucleus.

===The Current Model: Quantum Physics and Electron Orbitals===
Erwin Schrödinger examined the possibility that moving electrons behaved more like waves than particles, and published "Schrödinger's Equation" in 1926. Although this resolved many issues encountered with the Bohr model, it faced opposition from physicist [[Max Born]]. Instead, Born suggested a wave-particle duality of electrons, which stated that electrons could behave both like a wave and a particle.
As electrons were now given properties of waves, it was impossible to simultaneously determine an electron's exact location and momentum around the nucleus. Werner Heisenberg, first described this phenomena in 1927, and it was later named the Heisenberg Uncertainty Principle. This refuted the Bohr model of the atom, and replaced it with a pattern of probabilities as to where electrons are located around the nucleus. These patterns are referred to as atomic orbitals and come in a variety of shapes (basic spheres, rings, dumbbells, etc.) and the nucleus is always at the center.
[[File:Neon_orbitals.JPG|thumb|center|The first five atomic orbitals: 1s, 2s, 2px, 2py, and 2pz.]]

==Connectedness==
While classical physics applies to large objects moving much slower than the speed of light, modern physics deals with special cases of tiny objects, like atoms, subject to relativistic effects. Atomic theory is vital to understanding many quantum physics concepts that are covered in both Physics 2211 and 2212, like the ball-and-spring model of solids, point charges, and conductivity.

Although one can argue physics applies to just about every aspect of life, and atomic theory is critical to understanding physics, atomic theory has directly influenced material science, power generation, electronics, and even food processing, to name a few.

<gallery>
File:Apollo_synthetic_diamond.jpg|'''Material Science:''' Synthetic diamonds are used for both cosmetic retail and in manufacturing cutting tools.
File:Electrical_and_Mechanical_Services_Department_Headquarters_Photovoltaics.jpg|'''Power:''' Solar cells and power rely on the photovoltaic effect and the wave-particle duality of subatomic particles (like photons).
File:Monokristalines_Silizium_f%C3%BCr_die_Waferherstellung.jpg|'''Electronics:''' Silicon, a popular semiconductor used in electronics, is produced industrially in a single-crystal form.
File:Sodium-chloride-3D-ionic.png|'''Food processing:''' An atomic view of table salt. Purple particles are sodium (Na), and green particles are chlorine (Cl).
File:Nagasakibomb.jpg|'''Defense:''' Nuclear weapons were used during World War II.
File:White_Matter_Connections_Obtained_with_MRI_Tractography.png|'''Medicine:''' MRI's provide doctors critical information without the risks of surgery.
File:Plastic_household_items.jpg|'''Manufacturing:''' Many common household items are made with plastic.
</gallery>

== See also ==

*[[Bohr Model]]
*[[Electronic Energy Levels and Photons]]
*[[Rutherford Experiment and Atomic Collisions]]

===Notable Scientists===
*[[Amedeo Avogadro]]
*[[J.J. Thomson]]
*[[Ernest Rutherford]]
*[[Albert Einstein]]
*[[Max Planck]]
*[[Niels Bohr]]
*[[Max Born]]

===Related Theories===
*[[Quantum Theory]]
*[[Einstein's Theory of Special Relativity]]

===Concept Application===
*[[Ball and Spring Model of Matter]], [[Ball and Spring Model]]
*[[Length and Stiffness of an Interatomic Bond]], [[Young's Modulus]]
*[[Density]], [[Charge]], [[Spin]], and [[Conductivity]]
*[[The Photoelectric Effect]], [[Photons]]
*[[Rest Mass Energy]]
*[[Potential Energy of a Pair of Neutral Atoms]]

===External links===
*Physics Portal description of [https://en.wikipedia.org/wiki/History_of_molecular_theory Molecular Theory] and [https://en.wikipedia.org/wiki/Elementary_particle Subatomic Particles]
*HyperPhysics summary of [http://hyperphysics.phy-astr.gsu.edu/hbase/quacon.html#quacon Quantum Physics]
*Demonstration of the [https://phet.colorado.edu/en/simulation/legacy/hydrogen-atom various models] of a hydrogen atom

==References==

1. “Atomic Theory.” Wikipedia, Wikimedia Foundation, 19 Feb. 2022, https://en.wikipedia.org/wiki/Atomic_theory.

2. Introduction to Atomistic Modeling Xxx Techniques. https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf.

3. Clark, S J. “Atomistic Models.” Atomistic Models, http://cmt.dur.ac.uk/sjc/thesis_dlc/node45.html.

4. Introduction to Atomistic Modeling Xxx Techniques. https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf.

5. “Matter Wave.” Wikipedia, Wikimedia Foundation, 3 Apr. 2022, https://en.wikipedia.org/wiki/Matter_wave.

Chapter 30 of [https://openstaxcollege.org/files/textbook_version/hi_res_pdf/9/CollegePhysics-OP.pdf OpenStax Textbook]

Physics Portal page on [https://en.wikipedia.org/wiki/Atomic_theory Atomic Theory]

[[Category: Theory]]

Atomic Theory

2022-04-18T02:17:50Z

Erinhorbacz: /* A Mathematical Model */

Claimed by: Erin Horbacz (4/17/2022)

Atomic theory states that matter is composed of discrete units, called atoms. The word "atom" comes from the Greek word for uncuttable, ''atomos'', since it was believed that if one cut a substance into smaller and smaller pieces, one would reach a point where the substance could not be cut any further. Scientists later discovered that atoms were indeed able to be broken into subatomic, or elementary, particles including protons, neutrons, and electrons. Furthermore, protons and neutrons can be broken down yet again into smaller, elementary particles called [https://en.wikipedia.org/wiki/Quark#:~:text=A%20quark%20(%2Fkw%C9%94%CB%90r,the%20components%20of%20atomic%20nuclei./ quarks]. Atomic theory has evolved greatly over time, but the most recent model stems from quantum mechanics[https://en.wikipedia.org/wiki/Atomic_theory].

==The Main Idea==
===A Mathematical Model===
Mathematical models of atomic processes have become more thorough and sophisticated as knowledge of atomic properties has grown. The goal of a mathematical model is to express the underlying rules that govern atomic processes in a formula that can then predict and describe the behavior of atoms [https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf]. Such fundamental formulas are powerful tools for helping scientists understand the interactions and processes of both microscopic and macroscopic systems. For example, it was [https://en.wikipedia.org/wiki/Charles-Augustin_de_Coulomb/ Charles-Augustin de Coulomb] who first determined the mathematical equation which could accurately describe the electrostatic potential between charged particles that make up an atom:

<math>
V = \frac{1}{4 \pi \epsilon} \frac{q_1 q_2}{r}
</math>

where V is the [https://en.wikipedia.org/wiki/Electric_potential/ electrostatic potential] (in volts), <math> \frac{1}{4 \pi \epsilon} </math> is the [https://en.wikipedia.org/wiki/Coulomb_constant#:~:text=The%20Coulomb%20constant%2C%20the%20electric,%E2%88%922%E2%8B%85C%E2%88%922./ Coulomb constant], <math>q_1 </math> and <math> q_2 </math> are the charges of two particles, and r is the distance between the two particles.

Additionally, stretching of atomic bonds are known to be affected by force fields around an equilibrium point, and they can be modeled according to the equation:

<math>
\Delta V(l) = \frac{1}{2} k_l (l - l_0)^2
</math>

Where <math>\Delta V(l) </math> is the change in potential energy at <math>l</math>, <math>k_1</math> is the spring constant (a proportionality constant), <math>l</math> is the bond length, and <math>l_0</math> is the equilibrium bond length[http://cmt.dur.ac.uk/sjc/thesis_dlc/node45.html].

The use and creation of these formulas is incredibly prominent in simulation modeling. For example, simulations modeling the motion of multiple atoms can use mathematical models such as [https://en.wikipedia.org/wiki/Leapfrog_integration/ Leapfrog integration] and [https://en.wikipedia.org/wiki/Verlet_integration/ Verlet integration] to update particle positions and velocities respectively[https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf].

Perhaps the most important aspect of these mathematical models are their ability to take difficult, abstract concepts and represent them in a form that can be manipulated for further research. The creation of models to describe quantum phenomena makes the information more digestible and the concepts somewhat clearer. In fact, it is often the case that a mathematical model describing quantum behavior helps others think about concepts in different ways. In this manner, many discoveries have resulted from generalizing these models to extend beyond their initial boundaries. For example, the [https://en.wikipedia.org/wiki/Wave%E2%80%93particle_duality#:~:text=Wave%E2%80%93particle%20duality%20is%20the,behaviour%20of%20quantum%2Dscale%20objects./ wave-particle duality] of electrons became known through experiments such as the [https://en.wikipedia.org/wiki/Double-slit_experiment/ double-slit experiment] and the [https://en.wikipedia.org/wiki/Photoelectric_effect/ photoelectric effect]. However, it was Louis de Broglie who considered extending the wave nature to all particles, not just electrons. He discovered that all matter has wave properties, and he formulated the de Broglie wavelength[https://en.wikipedia.org/wiki/Matter_wave]:

<math>
\lambda = \frac{h}{p}
</math>

This formula tells us the wavelength of any particle with a given momentum. This was a huge breakthrough for atomic theory, and is a great example of the usefulness of atomic mathematical models to represent information and inspire new findings.

===A Computational Model===
Understanding the composition and structure of atoms is essential to the study of both microscopic and macroscopic systems. Researchers have made use of atomic information to create what are called atomistic models. These models are used to predict and analyze the behavior of complex systems through knowledge of their most fundamental parts. By understanding how atomic structure affects characteristic properties of atoms, scientists are able to create computational models based on simple microscopic characteristics that simulate complex macroscopic systems. In doing so, they aim to better understand the connection between these macroscopic systems and the underlying atomic structures that govern them.

Use of simulations in research has broadened both the volume and complexity of analysis that can be done at any one time. The ability to model atoms through simulations has been an integral part of the research done in diverse areas of science, notably materials science. In this field, atomistic models are often used to predict material properties under certain conditions using information about their nucleus and electron density. For example, professor ABFIEJABF of the physics department of Georgia Tech created an atomistic model that simulates the behavior of atoms in ABFIEJABF. Another use of atomistic models is to simulate and analyze important processes such as a nuclear chain reaction; an example of such a simulation can be viewed on [https://javalab.org/en/nuclear_chain_reaction_en/ JavaLab].

Atomistic models use the mathematical models discussed above to computationally represent atomic forces, atomic positions, velocities, and magnetic charges of atoms among other things. The result is an accurate model of quantum processes. Ultimately, the use of such simulations help to understand the collective behavior of atoms and how this behavior affects macroscopic processes (such as deformation and phase change) as well as performance abilities (such as strength of material).

==History==

===John Dalton: The Law of Multiple Proportions and Atomic Mass===
[[File:Daltons_symbols.gif|thumb|Dalton's concept of atoms and molecules]]
Working from the conservation of mass principle, chemist John Dalton determined the law of multiple proportions to understand how different elements combined in compounds. In 1803, he proposed that each element of the periodic table was composed of identical components, atoms, that were unique to each element. He also suggested that these atoms were not created nor destroyed when one element was combined with another. Dalton's empirical, experimentally-based work marked the first scientific theory of the atom.

Dalton proposed a list of atomic weights in 1805. However, Dalton failed to recognize natural tendencies of elements in nature (for example, oxygen typically exists as a diatomic molecule as <math>\text{O}_2</math>). Dalton was unable to distinguish between atoms and molecules (groups of atoms).

===Amedeo Avogadro: Avogadro's Law===
In 1811, [[Amedeo Avogadro]] studied gases and determined that the amount of volume a gas occupies is not determined by the mass of the gas. This allowed Avogadro to take more accurate atomic measurements of gases than Dalton, and differentiate atoms from molecules.

===Robert Brown: Brownian Motion===
A Scottish botanist, Robert Brown, studied the motion of tiny pollen particles in water in 1827. The particles followed complex paths, dubbed Brownian Motion. As early as 1905, [[Albert Einstein]] used Brownian Motion to predict the size of atoms and molecules.

===J.J. Thomson: The Plum-Pudding Model and Electrons===
[[File:Plum_pudding_model.svg|thumb|Tomson's Plum-Pudding Model]]
Through his work with cathode rays, [[J.J. Thomson]] discovered the electron in 1897, and was the first to learn that atoms weren't actually "uncuttable" as initially thought. Thomson knew that atoms had a net neutral charge, but he only knew that negative particles existed. Thus, Thomson developed the "plum-pudding" model of negatively charged electrons floating in a sea of positive charge. (He likened the relationship of electrons to the sea of positive charge to that of plums in plum pudding.)

===Ernest Rutherford: Gold Foil Experiment and the Nucleus===
In 1909, one of Thomson's students, [[Ernest Rutherford]], determined that the positive charge of atoms was located in a central nucleus. He shot small, positively charged alpha particles at thin sheets of gold foil and noted that some particles were sharply deflected. This deflection could only occur if the positive components of atoms were located in a small area, which Rutherford assumed to be the center. He proposed a planetary model of atoms where a cloud of electrons surrounded a central, positively charged nucleus.

===Niels Bohr: Introducing Quantum Physics===
[[File:Bohr_atom_animation_2.gif|thumb|The Bohr model for a Hydrogen atom with its electron moving between energy levels]]
As quantum mechanics progressed through the work of [[Albert Einstein]] and [[Max Planck]], [[Niels Bohr]] updated the atomic model in 1913 to account for quantum phenomena. Bohr, who was also one of Rutherford's students, suggested that electrostatic forces kept electrons in circular orbit around the positively charged central nucleus. In support of his theory, Bohr examined the behavior of electrons in hydrogen molecules and noted that they followed distinct energy levels. When an electron changed energy levels, it gained or lost energy, which could be emitted in the form of light. While the Bohr model holds true for hydrogen, it isn't accurate for multi-electron elements.

===James Chadwick: Neutrons===
James Chadwick won a Nobel Prize in 1935 for his discovery of the neutron. Starting with Rutherford's work, Chadwick continued experimenting to determine the excess mass in the nucleus that wasn't accounted for by protons. He found that neutrally charged particles, dubbed neutrons, were also inside the nucleus.

===The Current Model: Quantum Physics and Electron Orbitals===
Erwin Schrödinger examined the possibility that moving electrons behaved more like waves than particles, and published "Schrödinger's Equation" in 1926. Although this resolved many issues encountered with the Bohr model, it faced opposition from physicist [[Max Born]]. Instead, Born suggested a wave-particle duality of electrons, which stated that electrons could behave both like a wave and a particle.
As electrons were now given properties of waves, it was impossible to simultaneously determine an electron's exact location and momentum around the nucleus. Werner Heisenberg, first described this phenomena in 1927, and it was later named the Heisenberg Uncertainty Principle. This refuted the Bohr model of the atom, and replaced it with a pattern of probabilities as to where electrons are located around the nucleus. These patterns are referred to as atomic orbitals and come in a variety of shapes (basic spheres, rings, dumbbells, etc.) and the nucleus is always at the center.
[[File:Neon_orbitals.JPG|thumb|center|The first five atomic orbitals: 1s, 2s, 2px, 2py, and 2pz.]]

==Connectedness==
While classical physics applies to large objects moving much slower than the speed of light, modern physics deals with special cases of tiny objects, like atoms, subject to relativistic effects. Atomic theory is vital to understanding many quantum physics concepts that are covered in both Physics 2211 and 2212, like the ball-and-spring model of solids, point charges, and conductivity.

Although one can argue physics applies to just about every aspect of life, and atomic theory is critical to understanding physics, atomic theory has directly influenced material science, power generation, electronics, and even food processing, to name a few.

<gallery>
File:Apollo_synthetic_diamond.jpg|'''Material Science:''' Synthetic diamonds are used for both cosmetic retail and in manufacturing cutting tools.
File:Electrical_and_Mechanical_Services_Department_Headquarters_Photovoltaics.jpg|'''Power:''' Solar cells and power rely on the photovoltaic effect and the wave-particle duality of subatomic particles (like photons).
File:Monokristalines_Silizium_f%C3%BCr_die_Waferherstellung.jpg|'''Electronics:''' Silicon, a popular semiconductor used in electronics, is produced industrially in a single-crystal form.
File:Sodium-chloride-3D-ionic.png|'''Food processing:''' An atomic view of table salt. Purple particles are sodium (Na), and green particles are chlorine (Cl).
File:Nagasakibomb.jpg|'''Defense:''' Nuclear weapons were used during World War II.
File:White_Matter_Connections_Obtained_with_MRI_Tractography.png|'''Medicine:''' MRI's provide doctors critical information without the risks of surgery.
File:Plastic_household_items.jpg|'''Manufacturing:''' Many common household items are made with plastic.
</gallery>

== See also ==

*[[Bohr Model]]
*[[Electronic Energy Levels and Photons]]
*[[Rutherford Experiment and Atomic Collisions]]

===Notable Scientists===
*[[Amedeo Avogadro]]
*[[J.J. Thomson]]
*[[Ernest Rutherford]]
*[[Albert Einstein]]
*[[Max Planck]]
*[[Niels Bohr]]
*[[Max Born]]

===Related Theories===
*[[Quantum Theory]]
*[[Einstein's Theory of Special Relativity]]

===Concept Application===
*[[Ball and Spring Model of Matter]], [[Ball and Spring Model]]
*[[Length and Stiffness of an Interatomic Bond]], [[Young's Modulus]]
*[[Density]], [[Charge]], [[Spin]], and [[Conductivity]]
*[[The Photoelectric Effect]], [[Photons]]
*[[Rest Mass Energy]]
*[[Potential Energy of a Pair of Neutral Atoms]]

===External links===
*Physics Portal description of [https://en.wikipedia.org/wiki/History_of_molecular_theory Molecular Theory] and [https://en.wikipedia.org/wiki/Elementary_particle Subatomic Particles]
*HyperPhysics summary of [http://hyperphysics.phy-astr.gsu.edu/hbase/quacon.html#quacon Quantum Physics]
*Demonstration of the [https://phet.colorado.edu/en/simulation/legacy/hydrogen-atom various models] of a hydrogen atom

==References==

1. “Atomic Theory.” Wikipedia, Wikimedia Foundation, 19 Feb. 2022, https://en.wikipedia.org/wiki/Atomic_theory.

2. Introduction to Atomistic Modeling Xxx Techniques. https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf.

3. Clark, S J. “Atomistic Models.” Atomistic Models, http://cmt.dur.ac.uk/sjc/thesis_dlc/node45.html.

Chapter 30 of [https://openstaxcollege.org/files/textbook_version/hi_res_pdf/9/CollegePhysics-OP.pdf OpenStax Textbook]

Physics Portal page on [https://en.wikipedia.org/wiki/Atomic_theory Atomic Theory]

[[Category: Theory]]

Atomic Theory

2022-04-18T02:16:59Z

Erinhorbacz: /* A Mathematical Model */

Claimed by: Erin Horbacz (4/17/2022)

Atomic theory states that matter is composed of discrete units, called atoms. The word "atom" comes from the Greek word for uncuttable, ''atomos'', since it was believed that if one cut a substance into smaller and smaller pieces, one would reach a point where the substance could not be cut any further. Scientists later discovered that atoms were indeed able to be broken into subatomic, or elementary, particles including protons, neutrons, and electrons. Furthermore, protons and neutrons can be broken down yet again into smaller, elementary particles called [https://en.wikipedia.org/wiki/Quark#:~:text=A%20quark%20(%2Fkw%C9%94%CB%90r,the%20components%20of%20atomic%20nuclei./ quarks]. Atomic theory has evolved greatly over time, but the most recent model stems from quantum mechanics[https://en.wikipedia.org/wiki/Atomic_theory].

==The Main Idea==
===A Mathematical Model===
Mathematical models of atomic processes have become more thorough and sophisticated as knowledge of atomic properties has grown. The goal of a mathematical model is to express the underlying rules that govern atomic processes in a formula that can then predict and describe the behavior of atoms [https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf]. Such fundamental formulas are powerful tools for helping scientists understand the interactions and processes of both microscopic and macroscopic systems. For example, it was [https://en.wikipedia.org/wiki/Charles-Augustin_de_Coulomb/ Charles-Augustin de Coulomb] who first determined the mathematical equation which could accurately describe the electrostatic potential between charged particles that make up an atom:

<math>
V = \frac{1}{4 \pi \epsilon} \frac{q_1 q_2}{r}
</math>

where V is the [https://en.wikipedia.org/wiki/Electric_potential/ electrostatic potential] (in volts), <math> \frac{1}{4 \pi \epsilon} </math> is the [https://en.wikipedia.org/wiki/Coulomb_constant#:~:text=The%20Coulomb%20constant%2C%20the%20electric,%E2%88%922%E2%8B%85C%E2%88%922./ Coulomb constant], <math>q_1 </math> and <math> q_2 </math> are the charges of two particles, and r is the distance between the two particles.

Additionally, stretching of atomic bonds are known to be affected by force fields around an equilibrium point, and they can be modeled according to the equation:

<math>
\Delta V(l) = \frac{1}{2} k_l (l - l_0)^2
</math>

Where <math>\Delta V(l) </math> is the change in potential energy at <math>l</math>, <math>k_1</math> is the spring constant (a proportionality constant), <math>l</math> is the bond length, and <math>l_0</math> is the equilibrium bond length[http://cmt.dur.ac.uk/sjc/thesis_dlc/node45.html].

The use and creation of these formulas is incredibly prominent in simulation modeling. For example, simulations modeling the motion of multiple atoms can use mathematical models such as [https://en.wikipedia.org/wiki/Leapfrog_integration/ Leapfrog integration] and [https://en.wikipedia.org/wiki/Verlet_integration/ Verlet integration] to update particle positions and velocities respectively[https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf].

Perhaps the most important aspect of these mathematical models are their ability to take difficult, abstract concepts and represent them in a form that can be manipulated for further research. The creation of models to describe quantum phenomena makes the information more digestible and the concepts somewhat clearer. In fact, it is often the case that a mathematical model describing quantum behavior helps others think about concepts in different ways. In this manner, many discoveries have resulted from generalizing these models to extend beyond their initial boundaries. For example, the [https://en.wikipedia.org/wiki/Wave%E2%80%93particle_duality#:~:text=Wave%E2%80%93particle%20duality%20is%20the,behaviour%20of%20quantum%2Dscale%20objects./ wave-particle duality] of electrons became known through experiments such as the [https://en.wikipedia.org/wiki/Double-slit_experiment/ double-slit experiment] and the [https://en.wikipedia.org/wiki/Photoelectric_effect/ photoelectric effect]. However, it was Louis de Broglie who considered extending the wave nature to all particles, not just electrons. He discovered that all matter has wave properties, and he formulated the de Broglie wavelength:

<math>
\lambda = \frac{h}{p}
</math>

This formula tells us the wavelength of any particle with a given momentum. This was a huge breakthrough for atomic theory, and is a great example of the usefulness of atomic mathematical models to represent information and inspire new findings.

===A Computational Model===
Understanding the composition and structure of atoms is essential to the study of both microscopic and macroscopic systems. Researchers have made use of atomic information to create what are called atomistic models. These models are used to predict and analyze the behavior of complex systems through knowledge of their most fundamental parts. By understanding how atomic structure affects characteristic properties of atoms, scientists are able to create computational models based on simple microscopic characteristics that simulate complex macroscopic systems. In doing so, they aim to better understand the connection between these macroscopic systems and the underlying atomic structures that govern them.

Use of simulations in research has broadened both the volume and complexity of analysis that can be done at any one time. The ability to model atoms through simulations has been an integral part of the research done in diverse areas of science, notably materials science. In this field, atomistic models are often used to predict material properties under certain conditions using information about their nucleus and electron density. For example, professor ABFIEJABF of the physics department of Georgia Tech created an atomistic model that simulates the behavior of atoms in ABFIEJABF. Another use of atomistic models is to simulate and analyze important processes such as a nuclear chain reaction; an example of such a simulation can be viewed on [https://javalab.org/en/nuclear_chain_reaction_en/ JavaLab].

Atomistic models use the mathematical models discussed above to computationally represent atomic forces, atomic positions, velocities, and magnetic charges of atoms among other things. The result is an accurate model of quantum processes. Ultimately, the use of such simulations help to understand the collective behavior of atoms and how this behavior affects macroscopic processes (such as deformation and phase change) as well as performance abilities (such as strength of material).

==History==

===John Dalton: The Law of Multiple Proportions and Atomic Mass===
[[File:Daltons_symbols.gif|thumb|Dalton's concept of atoms and molecules]]
Working from the conservation of mass principle, chemist John Dalton determined the law of multiple proportions to understand how different elements combined in compounds. In 1803, he proposed that each element of the periodic table was composed of identical components, atoms, that were unique to each element. He also suggested that these atoms were not created nor destroyed when one element was combined with another. Dalton's empirical, experimentally-based work marked the first scientific theory of the atom.

Dalton proposed a list of atomic weights in 1805. However, Dalton failed to recognize natural tendencies of elements in nature (for example, oxygen typically exists as a diatomic molecule as <math>\text{O}_2</math>). Dalton was unable to distinguish between atoms and molecules (groups of atoms).

===Amedeo Avogadro: Avogadro's Law===
In 1811, [[Amedeo Avogadro]] studied gases and determined that the amount of volume a gas occupies is not determined by the mass of the gas. This allowed Avogadro to take more accurate atomic measurements of gases than Dalton, and differentiate atoms from molecules.

===Robert Brown: Brownian Motion===
A Scottish botanist, Robert Brown, studied the motion of tiny pollen particles in water in 1827. The particles followed complex paths, dubbed Brownian Motion. As early as 1905, [[Albert Einstein]] used Brownian Motion to predict the size of atoms and molecules.

===J.J. Thomson: The Plum-Pudding Model and Electrons===
[[File:Plum_pudding_model.svg|thumb|Tomson's Plum-Pudding Model]]
Through his work with cathode rays, [[J.J. Thomson]] discovered the electron in 1897, and was the first to learn that atoms weren't actually "uncuttable" as initially thought. Thomson knew that atoms had a net neutral charge, but he only knew that negative particles existed. Thus, Thomson developed the "plum-pudding" model of negatively charged electrons floating in a sea of positive charge. (He likened the relationship of electrons to the sea of positive charge to that of plums in plum pudding.)

===Ernest Rutherford: Gold Foil Experiment and the Nucleus===
In 1909, one of Thomson's students, [[Ernest Rutherford]], determined that the positive charge of atoms was located in a central nucleus. He shot small, positively charged alpha particles at thin sheets of gold foil and noted that some particles were sharply deflected. This deflection could only occur if the positive components of atoms were located in a small area, which Rutherford assumed to be the center. He proposed a planetary model of atoms where a cloud of electrons surrounded a central, positively charged nucleus.

===Niels Bohr: Introducing Quantum Physics===
[[File:Bohr_atom_animation_2.gif|thumb|The Bohr model for a Hydrogen atom with its electron moving between energy levels]]
As quantum mechanics progressed through the work of [[Albert Einstein]] and [[Max Planck]], [[Niels Bohr]] updated the atomic model in 1913 to account for quantum phenomena. Bohr, who was also one of Rutherford's students, suggested that electrostatic forces kept electrons in circular orbit around the positively charged central nucleus. In support of his theory, Bohr examined the behavior of electrons in hydrogen molecules and noted that they followed distinct energy levels. When an electron changed energy levels, it gained or lost energy, which could be emitted in the form of light. While the Bohr model holds true for hydrogen, it isn't accurate for multi-electron elements.

===James Chadwick: Neutrons===
James Chadwick won a Nobel Prize in 1935 for his discovery of the neutron. Starting with Rutherford's work, Chadwick continued experimenting to determine the excess mass in the nucleus that wasn't accounted for by protons. He found that neutrally charged particles, dubbed neutrons, were also inside the nucleus.

===The Current Model: Quantum Physics and Electron Orbitals===
Erwin Schrödinger examined the possibility that moving electrons behaved more like waves than particles, and published "Schrödinger's Equation" in 1926. Although this resolved many issues encountered with the Bohr model, it faced opposition from physicist [[Max Born]]. Instead, Born suggested a wave-particle duality of electrons, which stated that electrons could behave both like a wave and a particle.
As electrons were now given properties of waves, it was impossible to simultaneously determine an electron's exact location and momentum around the nucleus. Werner Heisenberg, first described this phenomena in 1927, and it was later named the Heisenberg Uncertainty Principle. This refuted the Bohr model of the atom, and replaced it with a pattern of probabilities as to where electrons are located around the nucleus. These patterns are referred to as atomic orbitals and come in a variety of shapes (basic spheres, rings, dumbbells, etc.) and the nucleus is always at the center.
[[File:Neon_orbitals.JPG|thumb|center|The first five atomic orbitals: 1s, 2s, 2px, 2py, and 2pz.]]

==Connectedness==
While classical physics applies to large objects moving much slower than the speed of light, modern physics deals with special cases of tiny objects, like atoms, subject to relativistic effects. Atomic theory is vital to understanding many quantum physics concepts that are covered in both Physics 2211 and 2212, like the ball-and-spring model of solids, point charges, and conductivity.

Although one can argue physics applies to just about every aspect of life, and atomic theory is critical to understanding physics, atomic theory has directly influenced material science, power generation, electronics, and even food processing, to name a few.

<gallery>
File:Apollo_synthetic_diamond.jpg|'''Material Science:''' Synthetic diamonds are used for both cosmetic retail and in manufacturing cutting tools.
File:Electrical_and_Mechanical_Services_Department_Headquarters_Photovoltaics.jpg|'''Power:''' Solar cells and power rely on the photovoltaic effect and the wave-particle duality of subatomic particles (like photons).
File:Monokristalines_Silizium_f%C3%BCr_die_Waferherstellung.jpg|'''Electronics:''' Silicon, a popular semiconductor used in electronics, is produced industrially in a single-crystal form.
File:Sodium-chloride-3D-ionic.png|'''Food processing:''' An atomic view of table salt. Purple particles are sodium (Na), and green particles are chlorine (Cl).
File:Nagasakibomb.jpg|'''Defense:''' Nuclear weapons were used during World War II.
File:White_Matter_Connections_Obtained_with_MRI_Tractography.png|'''Medicine:''' MRI's provide doctors critical information without the risks of surgery.
File:Plastic_household_items.jpg|'''Manufacturing:''' Many common household items are made with plastic.
</gallery>

== See also ==

*[[Bohr Model]]
*[[Electronic Energy Levels and Photons]]
*[[Rutherford Experiment and Atomic Collisions]]

===Notable Scientists===
*[[Amedeo Avogadro]]
*[[J.J. Thomson]]
*[[Ernest Rutherford]]
*[[Albert Einstein]]
*[[Max Planck]]
*[[Niels Bohr]]
*[[Max Born]]

===Related Theories===
*[[Quantum Theory]]
*[[Einstein's Theory of Special Relativity]]

===Concept Application===
*[[Ball and Spring Model of Matter]], [[Ball and Spring Model]]
*[[Length and Stiffness of an Interatomic Bond]], [[Young's Modulus]]
*[[Density]], [[Charge]], [[Spin]], and [[Conductivity]]
*[[The Photoelectric Effect]], [[Photons]]
*[[Rest Mass Energy]]
*[[Potential Energy of a Pair of Neutral Atoms]]

===External links===
*Physics Portal description of [https://en.wikipedia.org/wiki/History_of_molecular_theory Molecular Theory] and [https://en.wikipedia.org/wiki/Elementary_particle Subatomic Particles]
*HyperPhysics summary of [http://hyperphysics.phy-astr.gsu.edu/hbase/quacon.html#quacon Quantum Physics]
*Demonstration of the [https://phet.colorado.edu/en/simulation/legacy/hydrogen-atom various models] of a hydrogen atom

==References==

1. “Atomic Theory.” Wikipedia, Wikimedia Foundation, 19 Feb. 2022, https://en.wikipedia.org/wiki/Atomic_theory.

2. Introduction to Atomistic Modeling Xxx Techniques. https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf.

3. Clark, S J. “Atomistic Models.” Atomistic Models, http://cmt.dur.ac.uk/sjc/thesis_dlc/node45.html.

Chapter 30 of [https://openstaxcollege.org/files/textbook_version/hi_res_pdf/9/CollegePhysics-OP.pdf OpenStax Textbook]

Physics Portal page on [https://en.wikipedia.org/wiki/Atomic_theory Atomic Theory]

[[Category: Theory]]

Atomic Theory

2022-04-18T01:42:34Z

Erinhorbacz: /* A Mathematical Model */

Claimed by: Erin Horbacz (4/17/2022)

Atomic theory states that matter is composed of discrete units, called atoms. The word "atom" comes from the Greek word for uncuttable, ''atomos'', since it was believed that if one cut a substance into smaller and smaller pieces, one would reach a point where the substance could not be cut any further. Scientists later discovered that atoms were indeed able to be broken into subatomic, or elementary, particles including protons, neutrons, and electrons. Furthermore, protons and neutrons can be broken down yet again into smaller, elementary particles called [https://en.wikipedia.org/wiki/Quark#:~:text=A%20quark%20(%2Fkw%C9%94%CB%90r,the%20components%20of%20atomic%20nuclei./ quarks]. Atomic theory has evolved greatly over time, but the most recent model stems from quantum mechanics[https://en.wikipedia.org/wiki/Atomic_theory].

==The Main Idea==
===A Mathematical Model===
Mathematical models of atomic processes have become more thorough and sophisticated as knowledge of atomic properties has grown. The goal of a mathematical model is to express the underlying rules that govern atomic processes in a formula that can then predict and describe the behavior of atoms [https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf]. Such fundamental formulas are powerful tools for helping scientists understand the interactions and processes of both microscopic and macroscopic systems. For example, it was [https://en.wikipedia.org/wiki/Charles-Augustin_de_Coulomb/ Charles-Augustin de Coulomb] who first determined the mathematical equation which could accurately describe the electrostatic potential between charged particles that make up an atom:

<math>
V = \frac{1}{4 \pi \epsilon} \frac{q_1 q_2}{r}
</math>

where V is the [https://en.wikipedia.org/wiki/Electric_potential/ electrostatic potential] (in volts), <math> \frac{1}{4 \pi \epsilon} </math> is the [https://en.wikipedia.org/wiki/Coulomb_constant#:~:text=The%20Coulomb%20constant%2C%20the%20electric,%E2%88%922%E2%8B%85C%E2%88%922./ Coulomb constant], <math>q_1 </math> and <math> q_2 </math> are the charges of two particles, and r is the distance between the two particles.

Additionally, stretching of atomic bonds are known to be affected by force fields around an equilibrium point, and they can be modeled according to the equation:

<math>
\Delta V(l) = \frac{1}{2} k_l (l - l_0)^2
</math>

Where <math>\Delta V(l) </math> is the change in potential energy at <math>l</math>, <math>k_1</math> is the spring constant (a proportionality constant), <math>l</math> is the bond length, and <math>l_0</math> is the equilibrium bond length[http://cmt.dur.ac.uk/sjc/thesis_dlc/node45.html].

The use and creation of these formulas is incredibly prominent in simulation modeling. For example, simulations modeling the motion of multiple atoms can use mathematical models such as [https://en.wikipedia.org/wiki/Leapfrog_integration/ Leapfrog integration] and [https://en.wikipedia.org/wiki/Verlet_integration/ Verlet integration] to update particle positions and velocities respectively[https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf].

- have been generalized to macroscopic systems (debroglie wavelength)

===A Computational Model===
Understanding the composition and structure of atoms is essential to the study of both microscopic and macroscopic systems. Researchers have made use of atomic information to create what are called atomistic models. These models are used to predict and analyze the behavior of complex systems through knowledge of their most fundamental parts. By understanding how atomic structure affects characteristic properties of atoms, scientists are able to create computational models based on simple microscopic characteristics that simulate complex macroscopic systems. In doing so, they aim to better understand the connection between these macroscopic systems and the underlying atomic structures that govern them.

Use of simulations in research has broadened both the volume and complexity of analysis that can be done at any one time. The ability to model atoms through simulations has been an integral part of the research done in diverse areas of science, notably materials science. In this field, atomistic models are often used to predict material properties under certain conditions using information about their nucleus and electron density. For example, professor ABFIEJABF of the physics department of Georgia Tech created an atomistic model that simulates the behavior of atoms in ABFIEJABF. Another use of atomistic models is to simulate and analyze important processes such as a nuclear chain reaction; an example of such a simulation can be viewed on [https://javalab.org/en/nuclear_chain_reaction_en/ JavaLab].

Atomistic models use the mathematical models discussed above to computationally represent atomic forces, atomic positions, velocities, and magnetic charges of atoms among other things. The result is an accurate model of quantum processes. Ultimately, the use of such simulations help to understand the collective behavior of atoms and how this behavior affects macroscopic processes (such as deformation and phase change) as well as performance abilities (such as strength of material).

==History==

===John Dalton: The Law of Multiple Proportions and Atomic Mass===
[[File:Daltons_symbols.gif|thumb|Dalton's concept of atoms and molecules]]
Working from the conservation of mass principle, chemist John Dalton determined the law of multiple proportions to understand how different elements combined in compounds. In 1803, he proposed that each element of the periodic table was composed of identical components, atoms, that were unique to each element. He also suggested that these atoms were not created nor destroyed when one element was combined with another. Dalton's empirical, experimentally-based work marked the first scientific theory of the atom.

Dalton proposed a list of atomic weights in 1805. However, Dalton failed to recognize natural tendencies of elements in nature (for example, oxygen typically exists as a diatomic molecule as <math>\text{O}_2</math>). Dalton was unable to distinguish between atoms and molecules (groups of atoms).

===Amedeo Avogadro: Avogadro's Law===
In 1811, [[Amedeo Avogadro]] studied gases and determined that the amount of volume a gas occupies is not determined by the mass of the gas. This allowed Avogadro to take more accurate atomic measurements of gases than Dalton, and differentiate atoms from molecules.

===Robert Brown: Brownian Motion===
A Scottish botanist, Robert Brown, studied the motion of tiny pollen particles in water in 1827. The particles followed complex paths, dubbed Brownian Motion. As early as 1905, [[Albert Einstein]] used Brownian Motion to predict the size of atoms and molecules.

===J.J. Thomson: The Plum-Pudding Model and Electrons===
[[File:Plum_pudding_model.svg|thumb|Tomson's Plum-Pudding Model]]
Through his work with cathode rays, [[J.J. Thomson]] discovered the electron in 1897, and was the first to learn that atoms weren't actually "uncuttable" as initially thought. Thomson knew that atoms had a net neutral charge, but he only knew that negative particles existed. Thus, Thomson developed the "plum-pudding" model of negatively charged electrons floating in a sea of positive charge. (He likened the relationship of electrons to the sea of positive charge to that of plums in plum pudding.)

===Ernest Rutherford: Gold Foil Experiment and the Nucleus===
In 1909, one of Thomson's students, [[Ernest Rutherford]], determined that the positive charge of atoms was located in a central nucleus. He shot small, positively charged alpha particles at thin sheets of gold foil and noted that some particles were sharply deflected. This deflection could only occur if the positive components of atoms were located in a small area, which Rutherford assumed to be the center. He proposed a planetary model of atoms where a cloud of electrons surrounded a central, positively charged nucleus.

===Niels Bohr: Introducing Quantum Physics===
[[File:Bohr_atom_animation_2.gif|thumb|The Bohr model for a Hydrogen atom with its electron moving between energy levels]]
As quantum mechanics progressed through the work of [[Albert Einstein]] and [[Max Planck]], [[Niels Bohr]] updated the atomic model in 1913 to account for quantum phenomena. Bohr, who was also one of Rutherford's students, suggested that electrostatic forces kept electrons in circular orbit around the positively charged central nucleus. In support of his theory, Bohr examined the behavior of electrons in hydrogen molecules and noted that they followed distinct energy levels. When an electron changed energy levels, it gained or lost energy, which could be emitted in the form of light. While the Bohr model holds true for hydrogen, it isn't accurate for multi-electron elements.

===James Chadwick: Neutrons===
James Chadwick won a Nobel Prize in 1935 for his discovery of the neutron. Starting with Rutherford's work, Chadwick continued experimenting to determine the excess mass in the nucleus that wasn't accounted for by protons. He found that neutrally charged particles, dubbed neutrons, were also inside the nucleus.

===The Current Model: Quantum Physics and Electron Orbitals===
Erwin Schrödinger examined the possibility that moving electrons behaved more like waves than particles, and published "Schrödinger's Equation" in 1926. Although this resolved many issues encountered with the Bohr model, it faced opposition from physicist [[Max Born]]. Instead, Born suggested a wave-particle duality of electrons, which stated that electrons could behave both like a wave and a particle.
As electrons were now given properties of waves, it was impossible to simultaneously determine an electron's exact location and momentum around the nucleus. Werner Heisenberg, first described this phenomena in 1927, and it was later named the Heisenberg Uncertainty Principle. This refuted the Bohr model of the atom, and replaced it with a pattern of probabilities as to where electrons are located around the nucleus. These patterns are referred to as atomic orbitals and come in a variety of shapes (basic spheres, rings, dumbbells, etc.) and the nucleus is always at the center.
[[File:Neon_orbitals.JPG|thumb|center|The first five atomic orbitals: 1s, 2s, 2px, 2py, and 2pz.]]

==Connectedness==
While classical physics applies to large objects moving much slower than the speed of light, modern physics deals with special cases of tiny objects, like atoms, subject to relativistic effects. Atomic theory is vital to understanding many quantum physics concepts that are covered in both Physics 2211 and 2212, like the ball-and-spring model of solids, point charges, and conductivity.

Although one can argue physics applies to just about every aspect of life, and atomic theory is critical to understanding physics, atomic theory has directly influenced material science, power generation, electronics, and even food processing, to name a few.

<gallery>
File:Apollo_synthetic_diamond.jpg|'''Material Science:''' Synthetic diamonds are used for both cosmetic retail and in manufacturing cutting tools.
File:Electrical_and_Mechanical_Services_Department_Headquarters_Photovoltaics.jpg|'''Power:''' Solar cells and power rely on the photovoltaic effect and the wave-particle duality of subatomic particles (like photons).
File:Monokristalines_Silizium_f%C3%BCr_die_Waferherstellung.jpg|'''Electronics:''' Silicon, a popular semiconductor used in electronics, is produced industrially in a single-crystal form.
File:Sodium-chloride-3D-ionic.png|'''Food processing:''' An atomic view of table salt. Purple particles are sodium (Na), and green particles are chlorine (Cl).
File:Nagasakibomb.jpg|'''Defense:''' Nuclear weapons were used during World War II.
File:White_Matter_Connections_Obtained_with_MRI_Tractography.png|'''Medicine:''' MRI's provide doctors critical information without the risks of surgery.
File:Plastic_household_items.jpg|'''Manufacturing:''' Many common household items are made with plastic.
</gallery>

== See also ==

*[[Bohr Model]]
*[[Electronic Energy Levels and Photons]]
*[[Rutherford Experiment and Atomic Collisions]]

===Notable Scientists===
*[[Amedeo Avogadro]]
*[[J.J. Thomson]]
*[[Ernest Rutherford]]
*[[Albert Einstein]]
*[[Max Planck]]
*[[Niels Bohr]]
*[[Max Born]]

===Related Theories===
*[[Quantum Theory]]
*[[Einstein's Theory of Special Relativity]]

===Concept Application===
*[[Ball and Spring Model of Matter]], [[Ball and Spring Model]]
*[[Length and Stiffness of an Interatomic Bond]], [[Young's Modulus]]
*[[Density]], [[Charge]], [[Spin]], and [[Conductivity]]
*[[The Photoelectric Effect]], [[Photons]]
*[[Rest Mass Energy]]
*[[Potential Energy of a Pair of Neutral Atoms]]

===External links===
*Physics Portal description of [https://en.wikipedia.org/wiki/History_of_molecular_theory Molecular Theory] and [https://en.wikipedia.org/wiki/Elementary_particle Subatomic Particles]
*HyperPhysics summary of [http://hyperphysics.phy-astr.gsu.edu/hbase/quacon.html#quacon Quantum Physics]
*Demonstration of the [https://phet.colorado.edu/en/simulation/legacy/hydrogen-atom various models] of a hydrogen atom

==References==

1. “Atomic Theory.” Wikipedia, Wikimedia Foundation, 19 Feb. 2022, https://en.wikipedia.org/wiki/Atomic_theory.

2. Introduction to Atomistic Modeling Xxx Techniques. https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf.

3. Clark, S J. “Atomistic Models.” Atomistic Models, http://cmt.dur.ac.uk/sjc/thesis_dlc/node45.html.

Chapter 30 of [https://openstaxcollege.org/files/textbook_version/hi_res_pdf/9/CollegePhysics-OP.pdf OpenStax Textbook]

Physics Portal page on [https://en.wikipedia.org/wiki/Atomic_theory Atomic Theory]

[[Category: Theory]]

Atomic Theory

2022-04-18T01:31:42Z

Erinhorbacz: /* References */

Claimed by: Erin Horbacz (4/17/2022)

Atomic theory states that matter is composed of discrete units, called atoms. The word "atom" comes from the Greek word for uncuttable, ''atomos'', since it was believed that if one cut a substance into smaller and smaller pieces, one would reach a point where the substance could not be cut any further. Scientists later discovered that atoms were indeed able to be broken into subatomic, or elementary, particles including protons, neutrons, and electrons. Furthermore, protons and neutrons can be broken down yet again into smaller, elementary particles called [https://en.wikipedia.org/wiki/Quark#:~:text=A%20quark%20(%2Fkw%C9%94%CB%90r,the%20components%20of%20atomic%20nuclei./ quarks]. Atomic theory has evolved greatly over time, but the most recent model stems from quantum mechanics[https://en.wikipedia.org/wiki/Atomic_theory].

==The Main Idea==
===A Mathematical Model===
Mathematical models of atomic processes have become more thorough and sophisticated as knowledge of atomic properties has grown. The goal of a mathematical model is to express the underlying rules that govern atomic processes in a formula that can then predict and describe the behavior of atoms [https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf]. Such fundamental formulas are powerful tools for helping scientists understand the interactions and processes of both microscopic and macroscopic systems. For example, it was [https://en.wikipedia.org/wiki/Charles-Augustin_de_Coulomb/ Charles-Augustin de Coulomb] who first determined the mathematical equation which could accurately describe the electrostatic potential between charged particles that make up an atom:

<math>
V = \frac{1}{4 \pi \epsilon} \frac{q_1 q_2}{r}
</math>

where V is the [https://en.wikipedia.org/wiki/Electric_potential/ electrostatic potential] (in volts), <math> \frac{1}{4 \pi \epsilon} </math> is the [https://en.wikipedia.org/wiki/Coulomb_constant#:~:text=The%20Coulomb%20constant%2C%20the%20electric,%E2%88%922%E2%8B%85C%E2%88%922./ Coulomb constant], <math>q_1 </math> and <math> q_2 </math> are the charges of two particles, and r is the distance between the two particles.

Additionally, stretching of atomic bonds are known to be affected by force fields around an equilibrium point, and they can be modeled according to the equation:

<math>
\Delta V(l) = \frac{1}{2} k_l (l - l_0)^2
</math>

Where <math>\Delta V(l) </math> is the change in potential energy at <math>l</math>, <math>k_1</math> is the spring constant (a proportionality constant), <math>l</math> is the bond length, and <math>l_0</math> is the equilibrium bond length[http://cmt.dur.ac.uk/sjc/thesis_dlc/node45.html].

The use and creation of these formulas is incredibly prominent in simulation modeling. For example, simulations modeling the motion of multiple atoms can update particle positions using [https://en.wikipedia.org/wiki/Leapfrog_integration/ Leapfrog integration] as well as update velocities using [https://en.wikipedia.org/wiki/Verlet_integration/ Verlet integration][https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf].

- have been generalized to macroscopic systems (debroglie wavelength)

===A Computational Model===
Understanding the composition and structure of atoms is essential to the study of both microscopic and macroscopic systems. Researchers have made use of atomic information to create what are called atomistic models. These models are used to predict and analyze the behavior of complex systems through knowledge of their most fundamental parts. By understanding how atomic structure affects characteristic properties of atoms, scientists are able to create computational models based on simple microscopic characteristics that simulate complex macroscopic systems. In doing so, they aim to better understand the connection between these macroscopic systems and the underlying atomic structures that govern them.

Use of simulations in research has broadened both the volume and complexity of analysis that can be done at any one time. The ability to model atoms through simulations has been an integral part of the research done in diverse areas of science, notably materials science. In this field, atomistic models are often used to predict material properties under certain conditions using information about their nucleus and electron density. For example, professor ABFIEJABF of the physics department of Georgia Tech created an atomistic model that simulates the behavior of atoms in ABFIEJABF. Another use of atomistic models is to simulate and analyze important processes such as a nuclear chain reaction; an example of such a simulation can be viewed on [https://javalab.org/en/nuclear_chain_reaction_en/ JavaLab].

Atomistic models use the mathematical models discussed above to computationally represent atomic forces, atomic positions, velocities, and magnetic charges of atoms among other things. The result is an accurate model of quantum processes. Ultimately, the use of such simulations help to understand the collective behavior of atoms and how this behavior affects macroscopic processes (such as deformation and phase change) as well as performance abilities (such as strength of material).

==History==

===John Dalton: The Law of Multiple Proportions and Atomic Mass===
[[File:Daltons_symbols.gif|thumb|Dalton's concept of atoms and molecules]]
Working from the conservation of mass principle, chemist John Dalton determined the law of multiple proportions to understand how different elements combined in compounds. In 1803, he proposed that each element of the periodic table was composed of identical components, atoms, that were unique to each element. He also suggested that these atoms were not created nor destroyed when one element was combined with another. Dalton's empirical, experimentally-based work marked the first scientific theory of the atom.

Dalton proposed a list of atomic weights in 1805. However, Dalton failed to recognize natural tendencies of elements in nature (for example, oxygen typically exists as a diatomic molecule as <math>\text{O}_2</math>). Dalton was unable to distinguish between atoms and molecules (groups of atoms).

===Amedeo Avogadro: Avogadro's Law===
In 1811, [[Amedeo Avogadro]] studied gases and determined that the amount of volume a gas occupies is not determined by the mass of the gas. This allowed Avogadro to take more accurate atomic measurements of gases than Dalton, and differentiate atoms from molecules.

===Robert Brown: Brownian Motion===
A Scottish botanist, Robert Brown, studied the motion of tiny pollen particles in water in 1827. The particles followed complex paths, dubbed Brownian Motion. As early as 1905, [[Albert Einstein]] used Brownian Motion to predict the size of atoms and molecules.

===J.J. Thomson: The Plum-Pudding Model and Electrons===
[[File:Plum_pudding_model.svg|thumb|Tomson's Plum-Pudding Model]]
Through his work with cathode rays, [[J.J. Thomson]] discovered the electron in 1897, and was the first to learn that atoms weren't actually "uncuttable" as initially thought. Thomson knew that atoms had a net neutral charge, but he only knew that negative particles existed. Thus, Thomson developed the "plum-pudding" model of negatively charged electrons floating in a sea of positive charge. (He likened the relationship of electrons to the sea of positive charge to that of plums in plum pudding.)

===Ernest Rutherford: Gold Foil Experiment and the Nucleus===
In 1909, one of Thomson's students, [[Ernest Rutherford]], determined that the positive charge of atoms was located in a central nucleus. He shot small, positively charged alpha particles at thin sheets of gold foil and noted that some particles were sharply deflected. This deflection could only occur if the positive components of atoms were located in a small area, which Rutherford assumed to be the center. He proposed a planetary model of atoms where a cloud of electrons surrounded a central, positively charged nucleus.

===Niels Bohr: Introducing Quantum Physics===
[[File:Bohr_atom_animation_2.gif|thumb|The Bohr model for a Hydrogen atom with its electron moving between energy levels]]
As quantum mechanics progressed through the work of [[Albert Einstein]] and [[Max Planck]], [[Niels Bohr]] updated the atomic model in 1913 to account for quantum phenomena. Bohr, who was also one of Rutherford's students, suggested that electrostatic forces kept electrons in circular orbit around the positively charged central nucleus. In support of his theory, Bohr examined the behavior of electrons in hydrogen molecules and noted that they followed distinct energy levels. When an electron changed energy levels, it gained or lost energy, which could be emitted in the form of light. While the Bohr model holds true for hydrogen, it isn't accurate for multi-electron elements.

===James Chadwick: Neutrons===
James Chadwick won a Nobel Prize in 1935 for his discovery of the neutron. Starting with Rutherford's work, Chadwick continued experimenting to determine the excess mass in the nucleus that wasn't accounted for by protons. He found that neutrally charged particles, dubbed neutrons, were also inside the nucleus.

===The Current Model: Quantum Physics and Electron Orbitals===
Erwin Schrödinger examined the possibility that moving electrons behaved more like waves than particles, and published "Schrödinger's Equation" in 1926. Although this resolved many issues encountered with the Bohr model, it faced opposition from physicist [[Max Born]]. Instead, Born suggested a wave-particle duality of electrons, which stated that electrons could behave both like a wave and a particle.
As electrons were now given properties of waves, it was impossible to simultaneously determine an electron's exact location and momentum around the nucleus. Werner Heisenberg, first described this phenomena in 1927, and it was later named the Heisenberg Uncertainty Principle. This refuted the Bohr model of the atom, and replaced it with a pattern of probabilities as to where electrons are located around the nucleus. These patterns are referred to as atomic orbitals and come in a variety of shapes (basic spheres, rings, dumbbells, etc.) and the nucleus is always at the center.
[[File:Neon_orbitals.JPG|thumb|center|The first five atomic orbitals: 1s, 2s, 2px, 2py, and 2pz.]]

==Connectedness==
While classical physics applies to large objects moving much slower than the speed of light, modern physics deals with special cases of tiny objects, like atoms, subject to relativistic effects. Atomic theory is vital to understanding many quantum physics concepts that are covered in both Physics 2211 and 2212, like the ball-and-spring model of solids, point charges, and conductivity.

Although one can argue physics applies to just about every aspect of life, and atomic theory is critical to understanding physics, atomic theory has directly influenced material science, power generation, electronics, and even food processing, to name a few.

<gallery>
File:Apollo_synthetic_diamond.jpg|'''Material Science:''' Synthetic diamonds are used for both cosmetic retail and in manufacturing cutting tools.
File:Electrical_and_Mechanical_Services_Department_Headquarters_Photovoltaics.jpg|'''Power:''' Solar cells and power rely on the photovoltaic effect and the wave-particle duality of subatomic particles (like photons).
File:Monokristalines_Silizium_f%C3%BCr_die_Waferherstellung.jpg|'''Electronics:''' Silicon, a popular semiconductor used in electronics, is produced industrially in a single-crystal form.
File:Sodium-chloride-3D-ionic.png|'''Food processing:''' An atomic view of table salt. Purple particles are sodium (Na), and green particles are chlorine (Cl).
File:Nagasakibomb.jpg|'''Defense:''' Nuclear weapons were used during World War II.
File:White_Matter_Connections_Obtained_with_MRI_Tractography.png|'''Medicine:''' MRI's provide doctors critical information without the risks of surgery.
File:Plastic_household_items.jpg|'''Manufacturing:''' Many common household items are made with plastic.
</gallery>

== See also ==

*[[Bohr Model]]
*[[Electronic Energy Levels and Photons]]
*[[Rutherford Experiment and Atomic Collisions]]

===Notable Scientists===
*[[Amedeo Avogadro]]
*[[J.J. Thomson]]
*[[Ernest Rutherford]]
*[[Albert Einstein]]
*[[Max Planck]]
*[[Niels Bohr]]
*[[Max Born]]

===Related Theories===
*[[Quantum Theory]]
*[[Einstein's Theory of Special Relativity]]

===Concept Application===
*[[Ball and Spring Model of Matter]], [[Ball and Spring Model]]
*[[Length and Stiffness of an Interatomic Bond]], [[Young's Modulus]]
*[[Density]], [[Charge]], [[Spin]], and [[Conductivity]]
*[[The Photoelectric Effect]], [[Photons]]
*[[Rest Mass Energy]]
*[[Potential Energy of a Pair of Neutral Atoms]]

===External links===
*Physics Portal description of [https://en.wikipedia.org/wiki/History_of_molecular_theory Molecular Theory] and [https://en.wikipedia.org/wiki/Elementary_particle Subatomic Particles]
*HyperPhysics summary of [http://hyperphysics.phy-astr.gsu.edu/hbase/quacon.html#quacon Quantum Physics]
*Demonstration of the [https://phet.colorado.edu/en/simulation/legacy/hydrogen-atom various models] of a hydrogen atom

==References==

1. “Atomic Theory.” Wikipedia, Wikimedia Foundation, 19 Feb. 2022, https://en.wikipedia.org/wiki/Atomic_theory.

2. Introduction to Atomistic Modeling Xxx Techniques. https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf.

3. Clark, S J. “Atomistic Models.” Atomistic Models, http://cmt.dur.ac.uk/sjc/thesis_dlc/node45.html.

Chapter 30 of [https://openstaxcollege.org/files/textbook_version/hi_res_pdf/9/CollegePhysics-OP.pdf OpenStax Textbook]

Physics Portal page on [https://en.wikipedia.org/wiki/Atomic_theory Atomic Theory]

[[Category: Theory]]

Atomic Theory

2022-04-18T01:30:08Z

Erinhorbacz: /* References */

Claimed by: Erin Horbacz (4/17/2022)

Atomic theory states that matter is composed of discrete units, called atoms. The word "atom" comes from the Greek word for uncuttable, ''atomos'', since it was believed that if one cut a substance into smaller and smaller pieces, one would reach a point where the substance could not be cut any further. Scientists later discovered that atoms were indeed able to be broken into subatomic, or elementary, particles including protons, neutrons, and electrons. Furthermore, protons and neutrons can be broken down yet again into smaller, elementary particles called [https://en.wikipedia.org/wiki/Quark#:~:text=A%20quark%20(%2Fkw%C9%94%CB%90r,the%20components%20of%20atomic%20nuclei./ quarks]. Atomic theory has evolved greatly over time, but the most recent model stems from quantum mechanics[https://en.wikipedia.org/wiki/Atomic_theory].

==The Main Idea==
===A Mathematical Model===
Mathematical models of atomic processes have become more thorough and sophisticated as knowledge of atomic properties has grown. The goal of a mathematical model is to express the underlying rules that govern atomic processes in a formula that can then predict and describe the behavior of atoms [https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf]. Such fundamental formulas are powerful tools for helping scientists understand the interactions and processes of both microscopic and macroscopic systems. For example, it was [https://en.wikipedia.org/wiki/Charles-Augustin_de_Coulomb/ Charles-Augustin de Coulomb] who first determined the mathematical equation which could accurately describe the electrostatic potential between charged particles that make up an atom:

<math>
V = \frac{1}{4 \pi \epsilon} \frac{q_1 q_2}{r}
</math>

where V is the [https://en.wikipedia.org/wiki/Electric_potential/ electrostatic potential] (in volts), <math> \frac{1}{4 \pi \epsilon} </math> is the [https://en.wikipedia.org/wiki/Coulomb_constant#:~:text=The%20Coulomb%20constant%2C%20the%20electric,%E2%88%922%E2%8B%85C%E2%88%922./ Coulomb constant], <math>q_1 </math> and <math> q_2 </math> are the charges of two particles, and r is the distance between the two particles.

Additionally, stretching of atomic bonds are known to be affected by force fields around an equilibrium point, and they can be modeled according to the equation:

<math>
\Delta V(l) = \frac{1}{2} k_l (l - l_0)^2
</math>

Where <math>\Delta V(l) </math> is the change in potential energy at <math>l</math>, <math>k_1</math> is the spring constant (a proportionality constant), <math>l</math> is the bond length, and <math>l_0</math> is the equilibrium bond length[http://cmt.dur.ac.uk/sjc/thesis_dlc/node45.html].

The use and creation of these formulas is incredibly prominent in simulation modeling. For example, simulations modeling the motion of multiple atoms can update particle positions using [https://en.wikipedia.org/wiki/Leapfrog_integration/ Leapfrog integration] as well as update velocities using [https://en.wikipedia.org/wiki/Verlet_integration/ Verlet integration][https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf].

- have been generalized to macroscopic systems (debroglie wavelength)

===A Computational Model===
Understanding the composition and structure of atoms is essential to the study of both microscopic and macroscopic systems. Researchers have made use of atomic information to create what are called atomistic models. These models are used to predict and analyze the behavior of complex systems through knowledge of their most fundamental parts. By understanding how atomic structure affects characteristic properties of atoms, scientists are able to create computational models based on simple microscopic characteristics that simulate complex macroscopic systems. In doing so, they aim to better understand the connection between these macroscopic systems and the underlying atomic structures that govern them.

Use of simulations in research has broadened both the volume and complexity of analysis that can be done at any one time. The ability to model atoms through simulations has been an integral part of the research done in diverse areas of science, notably materials science. In this field, atomistic models are often used to predict material properties under certain conditions using information about their nucleus and electron density. For example, professor ABFIEJABF of the physics department of Georgia Tech created an atomistic model that simulates the behavior of atoms in ABFIEJABF. Another use of atomistic models is to simulate and analyze important processes such as a nuclear chain reaction; an example of such a simulation can be viewed on [https://javalab.org/en/nuclear_chain_reaction_en/ JavaLab].

Atomistic models use the mathematical models discussed above to computationally represent atomic forces, atomic positions, velocities, and magnetic charges of atoms among other things. The result is an accurate model of quantum processes. Ultimately, the use of such simulations help to understand the collective behavior of atoms and how this behavior affects macroscopic processes (such as deformation and phase change) as well as performance abilities (such as strength of material).

==History==

===John Dalton: The Law of Multiple Proportions and Atomic Mass===
[[File:Daltons_symbols.gif|thumb|Dalton's concept of atoms and molecules]]
Working from the conservation of mass principle, chemist John Dalton determined the law of multiple proportions to understand how different elements combined in compounds. In 1803, he proposed that each element of the periodic table was composed of identical components, atoms, that were unique to each element. He also suggested that these atoms were not created nor destroyed when one element was combined with another. Dalton's empirical, experimentally-based work marked the first scientific theory of the atom.

Dalton proposed a list of atomic weights in 1805. However, Dalton failed to recognize natural tendencies of elements in nature (for example, oxygen typically exists as a diatomic molecule as <math>\text{O}_2</math>). Dalton was unable to distinguish between atoms and molecules (groups of atoms).

===Amedeo Avogadro: Avogadro's Law===
In 1811, [[Amedeo Avogadro]] studied gases and determined that the amount of volume a gas occupies is not determined by the mass of the gas. This allowed Avogadro to take more accurate atomic measurements of gases than Dalton, and differentiate atoms from molecules.

===Robert Brown: Brownian Motion===
A Scottish botanist, Robert Brown, studied the motion of tiny pollen particles in water in 1827. The particles followed complex paths, dubbed Brownian Motion. As early as 1905, [[Albert Einstein]] used Brownian Motion to predict the size of atoms and molecules.

===J.J. Thomson: The Plum-Pudding Model and Electrons===
[[File:Plum_pudding_model.svg|thumb|Tomson's Plum-Pudding Model]]
Through his work with cathode rays, [[J.J. Thomson]] discovered the electron in 1897, and was the first to learn that atoms weren't actually "uncuttable" as initially thought. Thomson knew that atoms had a net neutral charge, but he only knew that negative particles existed. Thus, Thomson developed the "plum-pudding" model of negatively charged electrons floating in a sea of positive charge. (He likened the relationship of electrons to the sea of positive charge to that of plums in plum pudding.)

===Ernest Rutherford: Gold Foil Experiment and the Nucleus===
In 1909, one of Thomson's students, [[Ernest Rutherford]], determined that the positive charge of atoms was located in a central nucleus. He shot small, positively charged alpha particles at thin sheets of gold foil and noted that some particles were sharply deflected. This deflection could only occur if the positive components of atoms were located in a small area, which Rutherford assumed to be the center. He proposed a planetary model of atoms where a cloud of electrons surrounded a central, positively charged nucleus.

===Niels Bohr: Introducing Quantum Physics===
[[File:Bohr_atom_animation_2.gif|thumb|The Bohr model for a Hydrogen atom with its electron moving between energy levels]]
As quantum mechanics progressed through the work of [[Albert Einstein]] and [[Max Planck]], [[Niels Bohr]] updated the atomic model in 1913 to account for quantum phenomena. Bohr, who was also one of Rutherford's students, suggested that electrostatic forces kept electrons in circular orbit around the positively charged central nucleus. In support of his theory, Bohr examined the behavior of electrons in hydrogen molecules and noted that they followed distinct energy levels. When an electron changed energy levels, it gained or lost energy, which could be emitted in the form of light. While the Bohr model holds true for hydrogen, it isn't accurate for multi-electron elements.

===James Chadwick: Neutrons===
James Chadwick won a Nobel Prize in 1935 for his discovery of the neutron. Starting with Rutherford's work, Chadwick continued experimenting to determine the excess mass in the nucleus that wasn't accounted for by protons. He found that neutrally charged particles, dubbed neutrons, were also inside the nucleus.

===The Current Model: Quantum Physics and Electron Orbitals===
Erwin Schrödinger examined the possibility that moving electrons behaved more like waves than particles, and published "Schrödinger's Equation" in 1926. Although this resolved many issues encountered with the Bohr model, it faced opposition from physicist [[Max Born]]. Instead, Born suggested a wave-particle duality of electrons, which stated that electrons could behave both like a wave and a particle.
As electrons were now given properties of waves, it was impossible to simultaneously determine an electron's exact location and momentum around the nucleus. Werner Heisenberg, first described this phenomena in 1927, and it was later named the Heisenberg Uncertainty Principle. This refuted the Bohr model of the atom, and replaced it with a pattern of probabilities as to where electrons are located around the nucleus. These patterns are referred to as atomic orbitals and come in a variety of shapes (basic spheres, rings, dumbbells, etc.) and the nucleus is always at the center.
[[File:Neon_orbitals.JPG|thumb|center|The first five atomic orbitals: 1s, 2s, 2px, 2py, and 2pz.]]

==Connectedness==
While classical physics applies to large objects moving much slower than the speed of light, modern physics deals with special cases of tiny objects, like atoms, subject to relativistic effects. Atomic theory is vital to understanding many quantum physics concepts that are covered in both Physics 2211 and 2212, like the ball-and-spring model of solids, point charges, and conductivity.

Although one can argue physics applies to just about every aspect of life, and atomic theory is critical to understanding physics, atomic theory has directly influenced material science, power generation, electronics, and even food processing, to name a few.

<gallery>
File:Apollo_synthetic_diamond.jpg|'''Material Science:''' Synthetic diamonds are used for both cosmetic retail and in manufacturing cutting tools.
File:Electrical_and_Mechanical_Services_Department_Headquarters_Photovoltaics.jpg|'''Power:''' Solar cells and power rely on the photovoltaic effect and the wave-particle duality of subatomic particles (like photons).
File:Monokristalines_Silizium_f%C3%BCr_die_Waferherstellung.jpg|'''Electronics:''' Silicon, a popular semiconductor used in electronics, is produced industrially in a single-crystal form.
File:Sodium-chloride-3D-ionic.png|'''Food processing:''' An atomic view of table salt. Purple particles are sodium (Na), and green particles are chlorine (Cl).
File:Nagasakibomb.jpg|'''Defense:''' Nuclear weapons were used during World War II.
File:White_Matter_Connections_Obtained_with_MRI_Tractography.png|'''Medicine:''' MRI's provide doctors critical information without the risks of surgery.
File:Plastic_household_items.jpg|'''Manufacturing:''' Many common household items are made with plastic.
</gallery>

== See also ==

*[[Bohr Model]]
*[[Electronic Energy Levels and Photons]]
*[[Rutherford Experiment and Atomic Collisions]]

===Notable Scientists===
*[[Amedeo Avogadro]]
*[[J.J. Thomson]]
*[[Ernest Rutherford]]
*[[Albert Einstein]]
*[[Max Planck]]
*[[Niels Bohr]]
*[[Max Born]]

===Related Theories===
*[[Quantum Theory]]
*[[Einstein's Theory of Special Relativity]]

===Concept Application===
*[[Ball and Spring Model of Matter]], [[Ball and Spring Model]]
*[[Length and Stiffness of an Interatomic Bond]], [[Young's Modulus]]
*[[Density]], [[Charge]], [[Spin]], and [[Conductivity]]
*[[The Photoelectric Effect]], [[Photons]]
*[[Rest Mass Energy]]
*[[Potential Energy of a Pair of Neutral Atoms]]

===External links===
*Physics Portal description of [https://en.wikipedia.org/wiki/History_of_molecular_theory Molecular Theory] and [https://en.wikipedia.org/wiki/Elementary_particle Subatomic Particles]
*HyperPhysics summary of [http://hyperphysics.phy-astr.gsu.edu/hbase/quacon.html#quacon Quantum Physics]
*Demonstration of the [https://phet.colorado.edu/en/simulation/legacy/hydrogen-atom various models] of a hydrogen atom

==References==

1. “Atomic Theory.” Wikipedia, Wikimedia Foundation, 19 Feb. 2022, https://en.wikipedia.org/wiki/Atomic_theory.
2. Introduction to Atomistic Modeling Xxx Techniques. https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf.

Chapter 30 of [https://openstaxcollege.org/files/textbook_version/hi_res_pdf/9/CollegePhysics-OP.pdf OpenStax Textbook]

Physics Portal page on [https://en.wikipedia.org/wiki/Atomic_theory Atomic Theory]

[[Category: Theory]]

Atomic Theory

2022-04-18T01:28:46Z

Erinhorbacz: /* References */

Claimed by: Erin Horbacz (4/17/2022)

Atomic theory states that matter is composed of discrete units, called atoms. The word "atom" comes from the Greek word for uncuttable, ''atomos'', since it was believed that if one cut a substance into smaller and smaller pieces, one would reach a point where the substance could not be cut any further. Scientists later discovered that atoms were indeed able to be broken into subatomic, or elementary, particles including protons, neutrons, and electrons. Furthermore, protons and neutrons can be broken down yet again into smaller, elementary particles called [https://en.wikipedia.org/wiki/Quark#:~:text=A%20quark%20(%2Fkw%C9%94%CB%90r,the%20components%20of%20atomic%20nuclei./ quarks]. Atomic theory has evolved greatly over time, but the most recent model stems from quantum mechanics[https://en.wikipedia.org/wiki/Atomic_theory].

==The Main Idea==
===A Mathematical Model===
Mathematical models of atomic processes have become more thorough and sophisticated as knowledge of atomic properties has grown. The goal of a mathematical model is to express the underlying rules that govern atomic processes in a formula that can then predict and describe the behavior of atoms [https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf]. Such fundamental formulas are powerful tools for helping scientists understand the interactions and processes of both microscopic and macroscopic systems. For example, it was [https://en.wikipedia.org/wiki/Charles-Augustin_de_Coulomb/ Charles-Augustin de Coulomb] who first determined the mathematical equation which could accurately describe the electrostatic potential between charged particles that make up an atom:

<math>
V = \frac{1}{4 \pi \epsilon} \frac{q_1 q_2}{r}
</math>

where V is the [https://en.wikipedia.org/wiki/Electric_potential/ electrostatic potential] (in volts), <math> \frac{1}{4 \pi \epsilon} </math> is the [https://en.wikipedia.org/wiki/Coulomb_constant#:~:text=The%20Coulomb%20constant%2C%20the%20electric,%E2%88%922%E2%8B%85C%E2%88%922./ Coulomb constant], <math>q_1 </math> and <math> q_2 </math> are the charges of two particles, and r is the distance between the two particles.

Additionally, stretching of atomic bonds are known to be affected by force fields around an equilibrium point, and they can be modeled according to the equation:

<math>
\Delta V(l) = \frac{1}{2} k_l (l - l_0)^2
</math>

Where <math>\Delta V(l) </math> is the change in potential energy at <math>l</math>, <math>k_1</math> is the spring constant (a proportionality constant), <math>l</math> is the bond length, and <math>l_0</math> is the equilibrium bond length[http://cmt.dur.ac.uk/sjc/thesis_dlc/node45.html].

The use and creation of these formulas is incredibly prominent in simulation modeling. For example, simulations modeling the motion of multiple atoms can update particle positions using [https://en.wikipedia.org/wiki/Leapfrog_integration/ Leapfrog integration] as well as update velocities using [https://en.wikipedia.org/wiki/Verlet_integration/ Verlet integration][https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf].

- have been generalized to macroscopic systems (debroglie wavelength)

===A Computational Model===
Understanding the composition and structure of atoms is essential to the study of both microscopic and macroscopic systems. Researchers have made use of atomic information to create what are called atomistic models. These models are used to predict and analyze the behavior of complex systems through knowledge of their most fundamental parts. By understanding how atomic structure affects characteristic properties of atoms, scientists are able to create computational models based on simple microscopic characteristics that simulate complex macroscopic systems. In doing so, they aim to better understand the connection between these macroscopic systems and the underlying atomic structures that govern them.

Use of simulations in research has broadened both the volume and complexity of analysis that can be done at any one time. The ability to model atoms through simulations has been an integral part of the research done in diverse areas of science, notably materials science. In this field, atomistic models are often used to predict material properties under certain conditions using information about their nucleus and electron density. For example, professor ABFIEJABF of the physics department of Georgia Tech created an atomistic model that simulates the behavior of atoms in ABFIEJABF. Another use of atomistic models is to simulate and analyze important processes such as a nuclear chain reaction; an example of such a simulation can be viewed on [https://javalab.org/en/nuclear_chain_reaction_en/ JavaLab].

Atomistic models use the mathematical models discussed above to computationally represent atomic forces, atomic positions, velocities, and magnetic charges of atoms among other things. The result is an accurate model of quantum processes. Ultimately, the use of such simulations help to understand the collective behavior of atoms and how this behavior affects macroscopic processes (such as deformation and phase change) as well as performance abilities (such as strength of material).

==History==

===John Dalton: The Law of Multiple Proportions and Atomic Mass===
[[File:Daltons_symbols.gif|thumb|Dalton's concept of atoms and molecules]]
Working from the conservation of mass principle, chemist John Dalton determined the law of multiple proportions to understand how different elements combined in compounds. In 1803, he proposed that each element of the periodic table was composed of identical components, atoms, that were unique to each element. He also suggested that these atoms were not created nor destroyed when one element was combined with another. Dalton's empirical, experimentally-based work marked the first scientific theory of the atom.

Dalton proposed a list of atomic weights in 1805. However, Dalton failed to recognize natural tendencies of elements in nature (for example, oxygen typically exists as a diatomic molecule as <math>\text{O}_2</math>). Dalton was unable to distinguish between atoms and molecules (groups of atoms).

===Amedeo Avogadro: Avogadro's Law===
In 1811, [[Amedeo Avogadro]] studied gases and determined that the amount of volume a gas occupies is not determined by the mass of the gas. This allowed Avogadro to take more accurate atomic measurements of gases than Dalton, and differentiate atoms from molecules.

===Robert Brown: Brownian Motion===
A Scottish botanist, Robert Brown, studied the motion of tiny pollen particles in water in 1827. The particles followed complex paths, dubbed Brownian Motion. As early as 1905, [[Albert Einstein]] used Brownian Motion to predict the size of atoms and molecules.

===J.J. Thomson: The Plum-Pudding Model and Electrons===
[[File:Plum_pudding_model.svg|thumb|Tomson's Plum-Pudding Model]]
Through his work with cathode rays, [[J.J. Thomson]] discovered the electron in 1897, and was the first to learn that atoms weren't actually "uncuttable" as initially thought. Thomson knew that atoms had a net neutral charge, but he only knew that negative particles existed. Thus, Thomson developed the "plum-pudding" model of negatively charged electrons floating in a sea of positive charge. (He likened the relationship of electrons to the sea of positive charge to that of plums in plum pudding.)

===Ernest Rutherford: Gold Foil Experiment and the Nucleus===
In 1909, one of Thomson's students, [[Ernest Rutherford]], determined that the positive charge of atoms was located in a central nucleus. He shot small, positively charged alpha particles at thin sheets of gold foil and noted that some particles were sharply deflected. This deflection could only occur if the positive components of atoms were located in a small area, which Rutherford assumed to be the center. He proposed a planetary model of atoms where a cloud of electrons surrounded a central, positively charged nucleus.

===Niels Bohr: Introducing Quantum Physics===
[[File:Bohr_atom_animation_2.gif|thumb|The Bohr model for a Hydrogen atom with its electron moving between energy levels]]
As quantum mechanics progressed through the work of [[Albert Einstein]] and [[Max Planck]], [[Niels Bohr]] updated the atomic model in 1913 to account for quantum phenomena. Bohr, who was also one of Rutherford's students, suggested that electrostatic forces kept electrons in circular orbit around the positively charged central nucleus. In support of his theory, Bohr examined the behavior of electrons in hydrogen molecules and noted that they followed distinct energy levels. When an electron changed energy levels, it gained or lost energy, which could be emitted in the form of light. While the Bohr model holds true for hydrogen, it isn't accurate for multi-electron elements.

===James Chadwick: Neutrons===
James Chadwick won a Nobel Prize in 1935 for his discovery of the neutron. Starting with Rutherford's work, Chadwick continued experimenting to determine the excess mass in the nucleus that wasn't accounted for by protons. He found that neutrally charged particles, dubbed neutrons, were also inside the nucleus.

===The Current Model: Quantum Physics and Electron Orbitals===
Erwin Schrödinger examined the possibility that moving electrons behaved more like waves than particles, and published "Schrödinger's Equation" in 1926. Although this resolved many issues encountered with the Bohr model, it faced opposition from physicist [[Max Born]]. Instead, Born suggested a wave-particle duality of electrons, which stated that electrons could behave both like a wave and a particle.
As electrons were now given properties of waves, it was impossible to simultaneously determine an electron's exact location and momentum around the nucleus. Werner Heisenberg, first described this phenomena in 1927, and it was later named the Heisenberg Uncertainty Principle. This refuted the Bohr model of the atom, and replaced it with a pattern of probabilities as to where electrons are located around the nucleus. These patterns are referred to as atomic orbitals and come in a variety of shapes (basic spheres, rings, dumbbells, etc.) and the nucleus is always at the center.
[[File:Neon_orbitals.JPG|thumb|center|The first five atomic orbitals: 1s, 2s, 2px, 2py, and 2pz.]]

==Connectedness==
While classical physics applies to large objects moving much slower than the speed of light, modern physics deals with special cases of tiny objects, like atoms, subject to relativistic effects. Atomic theory is vital to understanding many quantum physics concepts that are covered in both Physics 2211 and 2212, like the ball-and-spring model of solids, point charges, and conductivity.

Although one can argue physics applies to just about every aspect of life, and atomic theory is critical to understanding physics, atomic theory has directly influenced material science, power generation, electronics, and even food processing, to name a few.

<gallery>
File:Apollo_synthetic_diamond.jpg|'''Material Science:''' Synthetic diamonds are used for both cosmetic retail and in manufacturing cutting tools.
File:Electrical_and_Mechanical_Services_Department_Headquarters_Photovoltaics.jpg|'''Power:''' Solar cells and power rely on the photovoltaic effect and the wave-particle duality of subatomic particles (like photons).
File:Monokristalines_Silizium_f%C3%BCr_die_Waferherstellung.jpg|'''Electronics:''' Silicon, a popular semiconductor used in electronics, is produced industrially in a single-crystal form.
File:Sodium-chloride-3D-ionic.png|'''Food processing:''' An atomic view of table salt. Purple particles are sodium (Na), and green particles are chlorine (Cl).
File:Nagasakibomb.jpg|'''Defense:''' Nuclear weapons were used during World War II.
File:White_Matter_Connections_Obtained_with_MRI_Tractography.png|'''Medicine:''' MRI's provide doctors critical information without the risks of surgery.
File:Plastic_household_items.jpg|'''Manufacturing:''' Many common household items are made with plastic.
</gallery>

== See also ==

*[[Bohr Model]]
*[[Electronic Energy Levels and Photons]]
*[[Rutherford Experiment and Atomic Collisions]]

===Notable Scientists===
*[[Amedeo Avogadro]]
*[[J.J. Thomson]]
*[[Ernest Rutherford]]
*[[Albert Einstein]]
*[[Max Planck]]
*[[Niels Bohr]]
*[[Max Born]]

===Related Theories===
*[[Quantum Theory]]
*[[Einstein's Theory of Special Relativity]]

===Concept Application===
*[[Ball and Spring Model of Matter]], [[Ball and Spring Model]]
*[[Length and Stiffness of an Interatomic Bond]], [[Young's Modulus]]
*[[Density]], [[Charge]], [[Spin]], and [[Conductivity]]
*[[The Photoelectric Effect]], [[Photons]]
*[[Rest Mass Energy]]
*[[Potential Energy of a Pair of Neutral Atoms]]

===External links===
*Physics Portal description of [https://en.wikipedia.org/wiki/History_of_molecular_theory Molecular Theory] and [https://en.wikipedia.org/wiki/Elementary_particle Subatomic Particles]
*HyperPhysics summary of [http://hyperphysics.phy-astr.gsu.edu/hbase/quacon.html#quacon Quantum Physics]
*Demonstration of the [https://phet.colorado.edu/en/simulation/legacy/hydrogen-atom various models] of a hydrogen atom

==References==

1. “Atomic Theory.” Wikipedia, Wikimedia Foundation, 19 Feb. 2022, https://en.wikipedia.org/wiki/Atomic_theory.
Chapter 30 of [https://openstaxcollege.org/files/textbook_version/hi_res_pdf/9/CollegePhysics-OP.pdf OpenStax Textbook]

Physics Portal page on [https://en.wikipedia.org/wiki/Atomic_theory Atomic Theory]

[[Category: Theory]]

Atomic Theory

2022-04-18T01:24:40Z

Erinhorbacz:

Claimed by: Erin Horbacz (4/17/2022)

Atomic theory states that matter is composed of discrete units, called atoms. The word "atom" comes from the Greek word for uncuttable, ''atomos'', since it was believed that if one cut a substance into smaller and smaller pieces, one would reach a point where the substance could not be cut any further. Scientists later discovered that atoms were indeed able to be broken into subatomic, or elementary, particles including protons, neutrons, and electrons. Furthermore, protons and neutrons can be broken down yet again into smaller, elementary particles called [https://en.wikipedia.org/wiki/Quark#:~:text=A%20quark%20(%2Fkw%C9%94%CB%90r,the%20components%20of%20atomic%20nuclei./ quarks]. Atomic theory has evolved greatly over time, but the most recent model stems from quantum mechanics[https://en.wikipedia.org/wiki/Atomic_theory].

==The Main Idea==
===A Mathematical Model===
Mathematical models of atomic processes have become more thorough and sophisticated as knowledge of atomic properties has grown. The goal of a mathematical model is to express the underlying rules that govern atomic processes in a formula that can then predict and describe the behavior of atoms [https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf]. Such fundamental formulas are powerful tools for helping scientists understand the interactions and processes of both microscopic and macroscopic systems. For example, it was [https://en.wikipedia.org/wiki/Charles-Augustin_de_Coulomb/ Charles-Augustin de Coulomb] who first determined the mathematical equation which could accurately describe the electrostatic potential between charged particles that make up an atom:

<math>
V = \frac{1}{4 \pi \epsilon} \frac{q_1 q_2}{r}
</math>

where V is the [https://en.wikipedia.org/wiki/Electric_potential/ electrostatic potential] (in volts), <math> \frac{1}{4 \pi \epsilon} </math> is the [https://en.wikipedia.org/wiki/Coulomb_constant#:~:text=The%20Coulomb%20constant%2C%20the%20electric,%E2%88%922%E2%8B%85C%E2%88%922./ Coulomb constant], <math>q_1 </math> and <math> q_2 </math> are the charges of two particles, and r is the distance between the two particles.

Additionally, stretching of atomic bonds are known to be affected by force fields around an equilibrium point, and they can be modeled according to the equation:

<math>
\Delta V(l) = \frac{1}{2} k_l (l - l_0)^2
</math>

Where <math>\Delta V(l) </math> is the change in potential energy at <math>l</math>, <math>k_1</math> is the spring constant (a proportionality constant), <math>l</math> is the bond length, and <math>l_0</math> is the equilibrium bond length[http://cmt.dur.ac.uk/sjc/thesis_dlc/node45.html].

The use and creation of these formulas is incredibly prominent in simulation modeling. For example, simulations modeling the motion of multiple atoms can update particle positions using [https://en.wikipedia.org/wiki/Leapfrog_integration/ Leapfrog integration] as well as update velocities using [https://en.wikipedia.org/wiki/Verlet_integration/ Verlet integration][https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf].

- have been generalized to macroscopic systems (debroglie wavelength)

===A Computational Model===
Understanding the composition and structure of atoms is essential to the study of both microscopic and macroscopic systems. Researchers have made use of atomic information to create what are called atomistic models. These models are used to predict and analyze the behavior of complex systems through knowledge of their most fundamental parts. By understanding how atomic structure affects characteristic properties of atoms, scientists are able to create computational models based on simple microscopic characteristics that simulate complex macroscopic systems. In doing so, they aim to better understand the connection between these macroscopic systems and the underlying atomic structures that govern them.

Use of simulations in research has broadened both the volume and complexity of analysis that can be done at any one time. The ability to model atoms through simulations has been an integral part of the research done in diverse areas of science, notably materials science. In this field, atomistic models are often used to predict material properties under certain conditions using information about their nucleus and electron density. For example, professor ABFIEJABF of the physics department of Georgia Tech created an atomistic model that simulates the behavior of atoms in ABFIEJABF. Another use of atomistic models is to simulate and analyze important processes such as a nuclear chain reaction; an example of such a simulation can be viewed on [https://javalab.org/en/nuclear_chain_reaction_en/ JavaLab].

Atomistic models use the mathematical models discussed above to computationally represent atomic forces, atomic positions, velocities, and magnetic charges of atoms among other things. The result is an accurate model of quantum processes. Ultimately, the use of such simulations help to understand the collective behavior of atoms and how this behavior affects macroscopic processes (such as deformation and phase change) as well as performance abilities (such as strength of material).

==History==

===John Dalton: The Law of Multiple Proportions and Atomic Mass===
[[File:Daltons_symbols.gif|thumb|Dalton's concept of atoms and molecules]]
Working from the conservation of mass principle, chemist John Dalton determined the law of multiple proportions to understand how different elements combined in compounds. In 1803, he proposed that each element of the periodic table was composed of identical components, atoms, that were unique to each element. He also suggested that these atoms were not created nor destroyed when one element was combined with another. Dalton's empirical, experimentally-based work marked the first scientific theory of the atom.

Dalton proposed a list of atomic weights in 1805. However, Dalton failed to recognize natural tendencies of elements in nature (for example, oxygen typically exists as a diatomic molecule as <math>\text{O}_2</math>). Dalton was unable to distinguish between atoms and molecules (groups of atoms).

===Amedeo Avogadro: Avogadro's Law===
In 1811, [[Amedeo Avogadro]] studied gases and determined that the amount of volume a gas occupies is not determined by the mass of the gas. This allowed Avogadro to take more accurate atomic measurements of gases than Dalton, and differentiate atoms from molecules.

===Robert Brown: Brownian Motion===
A Scottish botanist, Robert Brown, studied the motion of tiny pollen particles in water in 1827. The particles followed complex paths, dubbed Brownian Motion. As early as 1905, [[Albert Einstein]] used Brownian Motion to predict the size of atoms and molecules.

===J.J. Thomson: The Plum-Pudding Model and Electrons===
[[File:Plum_pudding_model.svg|thumb|Tomson's Plum-Pudding Model]]
Through his work with cathode rays, [[J.J. Thomson]] discovered the electron in 1897, and was the first to learn that atoms weren't actually "uncuttable" as initially thought. Thomson knew that atoms had a net neutral charge, but he only knew that negative particles existed. Thus, Thomson developed the "plum-pudding" model of negatively charged electrons floating in a sea of positive charge. (He likened the relationship of electrons to the sea of positive charge to that of plums in plum pudding.)

===Ernest Rutherford: Gold Foil Experiment and the Nucleus===
In 1909, one of Thomson's students, [[Ernest Rutherford]], determined that the positive charge of atoms was located in a central nucleus. He shot small, positively charged alpha particles at thin sheets of gold foil and noted that some particles were sharply deflected. This deflection could only occur if the positive components of atoms were located in a small area, which Rutherford assumed to be the center. He proposed a planetary model of atoms where a cloud of electrons surrounded a central, positively charged nucleus.

===Niels Bohr: Introducing Quantum Physics===
[[File:Bohr_atom_animation_2.gif|thumb|The Bohr model for a Hydrogen atom with its electron moving between energy levels]]
As quantum mechanics progressed through the work of [[Albert Einstein]] and [[Max Planck]], [[Niels Bohr]] updated the atomic model in 1913 to account for quantum phenomena. Bohr, who was also one of Rutherford's students, suggested that electrostatic forces kept electrons in circular orbit around the positively charged central nucleus. In support of his theory, Bohr examined the behavior of electrons in hydrogen molecules and noted that they followed distinct energy levels. When an electron changed energy levels, it gained or lost energy, which could be emitted in the form of light. While the Bohr model holds true for hydrogen, it isn't accurate for multi-electron elements.

===James Chadwick: Neutrons===
James Chadwick won a Nobel Prize in 1935 for his discovery of the neutron. Starting with Rutherford's work, Chadwick continued experimenting to determine the excess mass in the nucleus that wasn't accounted for by protons. He found that neutrally charged particles, dubbed neutrons, were also inside the nucleus.

===The Current Model: Quantum Physics and Electron Orbitals===
Erwin Schrödinger examined the possibility that moving electrons behaved more like waves than particles, and published "Schrödinger's Equation" in 1926. Although this resolved many issues encountered with the Bohr model, it faced opposition from physicist [[Max Born]]. Instead, Born suggested a wave-particle duality of electrons, which stated that electrons could behave both like a wave and a particle.
As electrons were now given properties of waves, it was impossible to simultaneously determine an electron's exact location and momentum around the nucleus. Werner Heisenberg, first described this phenomena in 1927, and it was later named the Heisenberg Uncertainty Principle. This refuted the Bohr model of the atom, and replaced it with a pattern of probabilities as to where electrons are located around the nucleus. These patterns are referred to as atomic orbitals and come in a variety of shapes (basic spheres, rings, dumbbells, etc.) and the nucleus is always at the center.
[[File:Neon_orbitals.JPG|thumb|center|The first five atomic orbitals: 1s, 2s, 2px, 2py, and 2pz.]]

==Connectedness==
While classical physics applies to large objects moving much slower than the speed of light, modern physics deals with special cases of tiny objects, like atoms, subject to relativistic effects. Atomic theory is vital to understanding many quantum physics concepts that are covered in both Physics 2211 and 2212, like the ball-and-spring model of solids, point charges, and conductivity.

Although one can argue physics applies to just about every aspect of life, and atomic theory is critical to understanding physics, atomic theory has directly influenced material science, power generation, electronics, and even food processing, to name a few.

<gallery>
File:Apollo_synthetic_diamond.jpg|'''Material Science:''' Synthetic diamonds are used for both cosmetic retail and in manufacturing cutting tools.
File:Electrical_and_Mechanical_Services_Department_Headquarters_Photovoltaics.jpg|'''Power:''' Solar cells and power rely on the photovoltaic effect and the wave-particle duality of subatomic particles (like photons).
File:Monokristalines_Silizium_f%C3%BCr_die_Waferherstellung.jpg|'''Electronics:''' Silicon, a popular semiconductor used in electronics, is produced industrially in a single-crystal form.
File:Sodium-chloride-3D-ionic.png|'''Food processing:''' An atomic view of table salt. Purple particles are sodium (Na), and green particles are chlorine (Cl).
File:Nagasakibomb.jpg|'''Defense:''' Nuclear weapons were used during World War II.
File:White_Matter_Connections_Obtained_with_MRI_Tractography.png|'''Medicine:''' MRI's provide doctors critical information without the risks of surgery.
File:Plastic_household_items.jpg|'''Manufacturing:''' Many common household items are made with plastic.
</gallery>

== See also ==

*[[Bohr Model]]
*[[Electronic Energy Levels and Photons]]
*[[Rutherford Experiment and Atomic Collisions]]

===Notable Scientists===
*[[Amedeo Avogadro]]
*[[J.J. Thomson]]
*[[Ernest Rutherford]]
*[[Albert Einstein]]
*[[Max Planck]]
*[[Niels Bohr]]
*[[Max Born]]

===Related Theories===
*[[Quantum Theory]]
*[[Einstein's Theory of Special Relativity]]

===Concept Application===
*[[Ball and Spring Model of Matter]], [[Ball and Spring Model]]
*[[Length and Stiffness of an Interatomic Bond]], [[Young's Modulus]]
*[[Density]], [[Charge]], [[Spin]], and [[Conductivity]]
*[[The Photoelectric Effect]], [[Photons]]
*[[Rest Mass Energy]]
*[[Potential Energy of a Pair of Neutral Atoms]]

===External links===
*Physics Portal description of [https://en.wikipedia.org/wiki/History_of_molecular_theory Molecular Theory] and [https://en.wikipedia.org/wiki/Elementary_particle Subatomic Particles]
*HyperPhysics summary of [http://hyperphysics.phy-astr.gsu.edu/hbase/quacon.html#quacon Quantum Physics]
*Demonstration of the [https://phet.colorado.edu/en/simulation/legacy/hydrogen-atom various models] of a hydrogen atom

==References==

Chapter 30 of [https://openstaxcollege.org/files/textbook_version/hi_res_pdf/9/CollegePhysics-OP.pdf OpenStax Textbook]

Physics Portal page on [https://en.wikipedia.org/wiki/Atomic_theory Atomic Theory]

[[Category: Theory]]

Atomic Theory

2022-04-18T01:24:08Z

Erinhorbacz:

Claimed by: Erin Horbacz (4/17/2022)

Atomic theory states that matter is composed of discrete units, called atoms. The word "atom" comes from the Greek word for uncuttable, ''atomos'', since it was believed that if one cut a substance into smaller and smaller pieces, one would reach a point where the substance could not be cut any further. Scientists later discovered that atoms were indeed able to be broken into subatomic, or elementary, particles including protons, neutrons, and electrons. Furthermore, protons and neutrons can be broken down yet again into smaller, elementary particles called [https://en.wikipedia.org/wiki/Quark#:~:text=A%20quark%20(%2Fkw%C9%94%CB%90r,the%20components%20of%20atomic%20nuclei./ quarks]. Atomic theory has evolved greatly over time, but the most recent model stems from quantum mechanics.

==The Main Idea==
===A Mathematical Model===
Mathematical models of atomic processes have become more thorough and sophisticated as knowledge of atomic properties has grown. The goal of a mathematical model is to express the underlying rules that govern atomic processes in a formula that can then predict and describe the behavior of atoms [https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf]. Such fundamental formulas are powerful tools for helping scientists understand the interactions and processes of both microscopic and macroscopic systems. For example, it was [https://en.wikipedia.org/wiki/Charles-Augustin_de_Coulomb/ Charles-Augustin de Coulomb] who first determined the mathematical equation which could accurately describe the electrostatic potential between charged particles that make up an atom:

<math>
V = \frac{1}{4 \pi \epsilon} \frac{q_1 q_2}{r}
</math>

where V is the [https://en.wikipedia.org/wiki/Electric_potential/ electrostatic potential] (in volts), <math> \frac{1}{4 \pi \epsilon} </math> is the [https://en.wikipedia.org/wiki/Coulomb_constant#:~:text=The%20Coulomb%20constant%2C%20the%20electric,%E2%88%922%E2%8B%85C%E2%88%922./ Coulomb constant], <math>q_1 </math> and <math> q_2 </math> are the charges of two particles, and r is the distance between the two particles.

Additionally, stretching of atomic bonds are known to be affected by force fields around an equilibrium point, and they can be modeled according to the equation:

<math>
\Delta V(l) = \frac{1}{2} k_l (l - l_0)^2
</math>

Where <math>\Delta V(l) </math> is the change in potential energy at <math>l</math>, <math>k_1</math> is the spring constant (a proportionality constant), <math>l</math> is the bond length, and <math>l_0</math> is the equilibrium bond length[http://cmt.dur.ac.uk/sjc/thesis_dlc/node45.html].

The use and creation of these formulas is incredibly prominent in simulation modeling. For example, simulations modeling the motion of multiple atoms can update particle positions using [https://en.wikipedia.org/wiki/Leapfrog_integration/ Leapfrog integration] as well as update velocities using [https://en.wikipedia.org/wiki/Verlet_integration/ Verlet integration][https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf].

- have been generalized to macroscopic systems (debroglie wavelength)

===A Computational Model===
Understanding the composition and structure of atoms is essential to the study of both microscopic and macroscopic systems. Researchers have made use of atomic information to create what are called atomistic models. These models are used to predict and analyze the behavior of complex systems through knowledge of their most fundamental parts. By understanding how atomic structure affects characteristic properties of atoms, scientists are able to create computational models based on simple microscopic characteristics that simulate complex macroscopic systems. In doing so, they aim to better understand the connection between these macroscopic systems and the underlying atomic structures that govern them.

Use of simulations in research has broadened both the volume and complexity of analysis that can be done at any one time. The ability to model atoms through simulations has been an integral part of the research done in diverse areas of science, notably materials science. In this field, atomistic models are often used to predict material properties under certain conditions using information about their nucleus and electron density. For example, professor ABFIEJABF of the physics department of Georgia Tech created an atomistic model that simulates the behavior of atoms in ABFIEJABF. Another use of atomistic models is to simulate and analyze important processes such as a nuclear chain reaction; an example of such a simulation can be viewed on [https://javalab.org/en/nuclear_chain_reaction_en/ JavaLab].

Atomistic models use the mathematical models discussed above to computationally represent atomic forces, atomic positions, velocities, and magnetic charges of atoms among other things. The result is an accurate model of quantum processes. Ultimately, the use of such simulations help to understand the collective behavior of atoms and how this behavior affects macroscopic processes (such as deformation and phase change) as well as performance abilities (such as strength of material).

==History==

===John Dalton: The Law of Multiple Proportions and Atomic Mass===
[[File:Daltons_symbols.gif|thumb|Dalton's concept of atoms and molecules]]
Working from the conservation of mass principle, chemist John Dalton determined the law of multiple proportions to understand how different elements combined in compounds. In 1803, he proposed that each element of the periodic table was composed of identical components, atoms, that were unique to each element. He also suggested that these atoms were not created nor destroyed when one element was combined with another. Dalton's empirical, experimentally-based work marked the first scientific theory of the atom.

Dalton proposed a list of atomic weights in 1805. However, Dalton failed to recognize natural tendencies of elements in nature (for example, oxygen typically exists as a diatomic molecule as <math>\text{O}_2</math>). Dalton was unable to distinguish between atoms and molecules (groups of atoms).

===Amedeo Avogadro: Avogadro's Law===
In 1811, [[Amedeo Avogadro]] studied gases and determined that the amount of volume a gas occupies is not determined by the mass of the gas. This allowed Avogadro to take more accurate atomic measurements of gases than Dalton, and differentiate atoms from molecules.

===Robert Brown: Brownian Motion===
A Scottish botanist, Robert Brown, studied the motion of tiny pollen particles in water in 1827. The particles followed complex paths, dubbed Brownian Motion. As early as 1905, [[Albert Einstein]] used Brownian Motion to predict the size of atoms and molecules.

===J.J. Thomson: The Plum-Pudding Model and Electrons===
[[File:Plum_pudding_model.svg|thumb|Tomson's Plum-Pudding Model]]
Through his work with cathode rays, [[J.J. Thomson]] discovered the electron in 1897, and was the first to learn that atoms weren't actually "uncuttable" as initially thought. Thomson knew that atoms had a net neutral charge, but he only knew that negative particles existed. Thus, Thomson developed the "plum-pudding" model of negatively charged electrons floating in a sea of positive charge. (He likened the relationship of electrons to the sea of positive charge to that of plums in plum pudding.)

===Ernest Rutherford: Gold Foil Experiment and the Nucleus===
In 1909, one of Thomson's students, [[Ernest Rutherford]], determined that the positive charge of atoms was located in a central nucleus. He shot small, positively charged alpha particles at thin sheets of gold foil and noted that some particles were sharply deflected. This deflection could only occur if the positive components of atoms were located in a small area, which Rutherford assumed to be the center. He proposed a planetary model of atoms where a cloud of electrons surrounded a central, positively charged nucleus.

===Niels Bohr: Introducing Quantum Physics===
[[File:Bohr_atom_animation_2.gif|thumb|The Bohr model for a Hydrogen atom with its electron moving between energy levels]]
As quantum mechanics progressed through the work of [[Albert Einstein]] and [[Max Planck]], [[Niels Bohr]] updated the atomic model in 1913 to account for quantum phenomena. Bohr, who was also one of Rutherford's students, suggested that electrostatic forces kept electrons in circular orbit around the positively charged central nucleus. In support of his theory, Bohr examined the behavior of electrons in hydrogen molecules and noted that they followed distinct energy levels. When an electron changed energy levels, it gained or lost energy, which could be emitted in the form of light. While the Bohr model holds true for hydrogen, it isn't accurate for multi-electron elements.

===James Chadwick: Neutrons===
James Chadwick won a Nobel Prize in 1935 for his discovery of the neutron. Starting with Rutherford's work, Chadwick continued experimenting to determine the excess mass in the nucleus that wasn't accounted for by protons. He found that neutrally charged particles, dubbed neutrons, were also inside the nucleus.

===The Current Model: Quantum Physics and Electron Orbitals===
Erwin Schrödinger examined the possibility that moving electrons behaved more like waves than particles, and published "Schrödinger's Equation" in 1926. Although this resolved many issues encountered with the Bohr model, it faced opposition from physicist [[Max Born]]. Instead, Born suggested a wave-particle duality of electrons, which stated that electrons could behave both like a wave and a particle.
As electrons were now given properties of waves, it was impossible to simultaneously determine an electron's exact location and momentum around the nucleus. Werner Heisenberg, first described this phenomena in 1927, and it was later named the Heisenberg Uncertainty Principle. This refuted the Bohr model of the atom, and replaced it with a pattern of probabilities as to where electrons are located around the nucleus. These patterns are referred to as atomic orbitals and come in a variety of shapes (basic spheres, rings, dumbbells, etc.) and the nucleus is always at the center.
[[File:Neon_orbitals.JPG|thumb|center|The first five atomic orbitals: 1s, 2s, 2px, 2py, and 2pz.]]

==Connectedness==
While classical physics applies to large objects moving much slower than the speed of light, modern physics deals with special cases of tiny objects, like atoms, subject to relativistic effects. Atomic theory is vital to understanding many quantum physics concepts that are covered in both Physics 2211 and 2212, like the ball-and-spring model of solids, point charges, and conductivity.

Although one can argue physics applies to just about every aspect of life, and atomic theory is critical to understanding physics, atomic theory has directly influenced material science, power generation, electronics, and even food processing, to name a few.

<gallery>
File:Apollo_synthetic_diamond.jpg|'''Material Science:''' Synthetic diamonds are used for both cosmetic retail and in manufacturing cutting tools.
File:Electrical_and_Mechanical_Services_Department_Headquarters_Photovoltaics.jpg|'''Power:''' Solar cells and power rely on the photovoltaic effect and the wave-particle duality of subatomic particles (like photons).
File:Monokristalines_Silizium_f%C3%BCr_die_Waferherstellung.jpg|'''Electronics:''' Silicon, a popular semiconductor used in electronics, is produced industrially in a single-crystal form.
File:Sodium-chloride-3D-ionic.png|'''Food processing:''' An atomic view of table salt. Purple particles are sodium (Na), and green particles are chlorine (Cl).
File:Nagasakibomb.jpg|'''Defense:''' Nuclear weapons were used during World War II.
File:White_Matter_Connections_Obtained_with_MRI_Tractography.png|'''Medicine:''' MRI's provide doctors critical information without the risks of surgery.
File:Plastic_household_items.jpg|'''Manufacturing:''' Many common household items are made with plastic.
</gallery>

== See also ==

*[[Bohr Model]]
*[[Electronic Energy Levels and Photons]]
*[[Rutherford Experiment and Atomic Collisions]]

===Notable Scientists===
*[[Amedeo Avogadro]]
*[[J.J. Thomson]]
*[[Ernest Rutherford]]
*[[Albert Einstein]]
*[[Max Planck]]
*[[Niels Bohr]]
*[[Max Born]]

===Related Theories===
*[[Quantum Theory]]
*[[Einstein's Theory of Special Relativity]]

===Concept Application===
*[[Ball and Spring Model of Matter]], [[Ball and Spring Model]]
*[[Length and Stiffness of an Interatomic Bond]], [[Young's Modulus]]
*[[Density]], [[Charge]], [[Spin]], and [[Conductivity]]
*[[The Photoelectric Effect]], [[Photons]]
*[[Rest Mass Energy]]
*[[Potential Energy of a Pair of Neutral Atoms]]

===External links===
*Physics Portal description of [https://en.wikipedia.org/wiki/History_of_molecular_theory Molecular Theory] and [https://en.wikipedia.org/wiki/Elementary_particle Subatomic Particles]
*HyperPhysics summary of [http://hyperphysics.phy-astr.gsu.edu/hbase/quacon.html#quacon Quantum Physics]
*Demonstration of the [https://phet.colorado.edu/en/simulation/legacy/hydrogen-atom various models] of a hydrogen atom

==References==

Chapter 30 of [https://openstaxcollege.org/files/textbook_version/hi_res_pdf/9/CollegePhysics-OP.pdf OpenStax Textbook]

Physics Portal page on [https://en.wikipedia.org/wiki/Atomic_theory Atomic Theory]

[[Category: Theory]]

Atomic Theory

2022-04-17T23:48:35Z

Erinhorbacz: /* A Mathematical Model */

Claimed by: Erin Horbacz (4/17/2022)

Atomic theory states that matter is composed of discrete units, called atoms. The word "atom" comes from the Greek word for uncuttable, ''atomos''. Scientists later discovered that atoms were indeed able to be broken into subatomic, or elementary, particles including protons, neutrons, and electrons. Atomic theory has evolved greatly over time, but the most recent model stems from quantum mechanics.

==The Main Idea==
===A Mathematical Model===
Mathematical models of atomic processes have become more thorough and sophisticated as knowledge of atomic properties has grown. The goal of a mathematical model is to express the underlying rules that govern atomic processes in a formula that can then predict and describe the behavior of atoms [https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf]. Such fundamental formulas are powerful tools for helping scientists understand the interactions and processes of both microscopic and macroscopic systems. For example, it was [https://en.wikipedia.org/wiki/Charles-Augustin_de_Coulomb/ Charles-Augustin de Coulomb] who first determined the mathematical equation which could accurately describe the electrostatic potential between charged particles that make up an atom:

<math>
V = \frac{1}{4 \pi \epsilon} \frac{q_1 q_2}{r}
</math>

where V is the [https://en.wikipedia.org/wiki/Electric_potential/ electrostatic potential] (in volts), <math> \frac{1}{4 \pi \epsilon} </math> is the [https://en.wikipedia.org/wiki/Coulomb_constant#:~:text=The%20Coulomb%20constant%2C%20the%20electric,%E2%88%922%E2%8B%85C%E2%88%922./ Coulomb constant], <math>q_1 </math> and <math> q_2 </math> are the charges of two particles, and r is the distance between the two particles.

Additionally, stretching of atomic bonds are known to be affected by force fields around an equilibrium point, and they can be modeled according to the equation:

<math>
\Delta V(l) = \frac{1}{2} k_l (l - l_0)^2
</math>

Where <math>\Delta V(l) </math> is the change in potential energy at <math>l</math>, <math>k_1</math> is the spring constant (a proportionality constant), <math>l</math> is the bond length, and <math>l_0</math> is the equilibrium bond length[http://cmt.dur.ac.uk/sjc/thesis_dlc/node45.html].

The use and creation of these formulas is incredibly prominent in simulation modeling. For example, simulations modeling the motion of multiple atoms can update particle positions using [https://en.wikipedia.org/wiki/Leapfrog_integration/ Leapfrog integration] as well as update velocities using [https://en.wikipedia.org/wiki/Verlet_integration/ Verlet integration][https://web.mit.edu/mbuehler/www/Teaching/LS/lecture_1_nano-macro-buehler.pdf].

- have been generalized to macroscopic systems (debroglie wavelength)

===A Computational Model===
Understanding the composition and structure of atoms is essential to the study of both microscopic and macroscopic systems. Researchers have made use of atomic information to create what are called atomistic models. These models are used to predict and analyze the behavior of complex systems through knowledge of their most fundamental parts. By understanding how atomic structure affects characteristic properties of atoms, scientists are able to create computational models based on simple microscopic characteristics that simulate complex macroscopic systems. In doing so, they aim to better understand the connection between these macroscopic systems and the underlying atomic structures that govern them.

Use of simulations in research has broadened both the volume and complexity of analysis that can be done at any one time. The ability to model atoms through simulations has been an integral part of the research done in diverse areas of science, notably materials science. In this field, atomistic models are often used to predict material properties under certain conditions using information about their nucleus and electron density. For example, professor ABFIEJABF of the physics department of Georgia Tech created an atomistic model that simulates the behavior of atoms in ABFIEJABF. Another use of atomistic models is to simulate and analyze important processes such as a nuclear chain reaction; an example of such a simulation can be viewed on [https://javalab.org/en/nuclear_chain_reaction_en/ JavaLab].

Atomistic models use the mathematical models discussed above to computationally represent atomic forces, atomic positions, velocities, and magnetic charges of atoms among other things. The result is an accurate model of quantum processes. Ultimately, the use of such simulations help to understand the collective behavior of atoms and how this behavior affects macroscopic processes (such as deformation and phase change) as well as performance abilities (such as strength of material).

==History==

===John Dalton: The Law of Multiple Proportions and Atomic Mass===
[[File:Daltons_symbols.gif|thumb|Dalton's concept of atoms and molecules]]
Working from the conservation of mass principle, chemist John Dalton determined the law of multiple proportions to understand how different elements combined in compounds. In 1803, he proposed that each element of the periodic table was composed of identical components, atoms, that were unique to each element. He also suggested that these atoms were not created nor destroyed when one element was combined with another. Dalton's empirical, experimentally-based work marked the first scientific theory of the atom.

Dalton proposed a list of atomic weights in 1805. However, Dalton failed to recognize natural tendencies of elements in nature (for example, oxygen typically exists as a diatomic molecule as <math>\text{O}_2</math>). Dalton was unable to distinguish between atoms and molecules (groups of atoms).

===Amedeo Avogadro: Avogadro's Law===
In 1811, [[Amedeo Avogadro]] studied gases and determined that the amount of volume a gas occupies is not determined by the mass of the gas. This allowed Avogadro to take more accurate atomic measurements of gases than Dalton, and differentiate atoms from molecules.

===Robert Brown: Brownian Motion===
A Scottish botanist, Robert Brown, studied the motion of tiny pollen particles in water in 1827. The particles followed complex paths, dubbed Brownian Motion. As early as 1905, [[Albert Einstein]] used Brownian Motion to predict the size of atoms and molecules.

===J.J. Thomson: The Plum-Pudding Model and Electrons===
[[File:Plum_pudding_model.svg|thumb|Tomson's Plum-Pudding Model]]
Through his work with cathode rays, [[J.J. Thomson]] discovered the electron in 1897, and was the first to learn that atoms weren't actually "uncuttable" as initially thought. Thomson knew that atoms had a net neutral charge, but he only knew that negative particles existed. Thus, Thomson developed the "plum-pudding" model of negatively charged electrons floating in a sea of positive charge. (He likened the relationship of electrons to the sea of positive charge to that of plums in plum pudding.)

===Ernest Rutherford: Gold Foil Experiment and the Nucleus===
In 1909, one of Thomson's students, [[Ernest Rutherford]], determined that the positive charge of atoms was located in a central nucleus. He shot small, positively charged alpha particles at thin sheets of gold foil and noted that some particles were sharply deflected. This deflection could only occur if the positive components of atoms were located in a small area, which Rutherford assumed to be the center. He proposed a planetary model of atoms where a cloud of electrons surrounded a central, positively charged nucleus.

===Niels Bohr: Introducing Quantum Physics===
[[File:Bohr_atom_animation_2.gif|thumb|The Bohr model for a Hydrogen atom with its electron moving between energy levels]]
As quantum mechanics progressed through the work of [[Albert Einstein]] and [[Max Planck]], [[Niels Bohr]] updated the atomic model in 1913 to account for quantum phenomena. Bohr, who was also one of Rutherford's students, suggested that electrostatic forces kept electrons in circular orbit around the positively charged central nucleus. In support of his theory, Bohr examined the behavior of electrons in hydrogen molecules and noted that they followed distinct energy levels. When an electron changed energy levels, it gained or lost energy, which could be emitted in the form of light. While the Bohr model holds true for hydrogen, it isn't accurate for multi-electron elements.

===James Chadwick: Neutrons===
James Chadwick won a Nobel Prize in 1935 for his discovery of the neutron. Starting with Rutherford's work, Chadwick continued experimenting to determine the excess mass in the nucleus that wasn't accounted for by protons. He found that neutrally charged particles, dubbed neutrons, were also inside the nucleus.

===The Current Model: Quantum Physics and Electron Orbitals===
Erwin Schrödinger examined the possibility that moving electrons behaved more like waves than particles, and published "Schrödinger's Equation" in 1926. Although this resolved many issues encountered with the Bohr model, it faced opposition from physicist [[Max Born]]. Instead, Born suggested a wave-particle duality of electrons, which stated that electrons could behave both like a wave and a particle.
As electrons were now given properties of waves, it was impossible to simultaneously determine an electron's exact location and momentum around the nucleus. Werner Heisenberg, first described this phenomena in 1927, and it was later named the Heisenberg Uncertainty Principle. This refuted the Bohr model of the atom, and replaced it with a pattern of probabilities as to where electrons are located around the nucleus. These patterns are referred to as atomic orbitals and come in a variety of shapes (basic spheres, rings, dumbbells, etc.) and the nucleus is always at the center.
[[File:Neon_orbitals.JPG|thumb|center|The first five atomic orbitals: 1s, 2s, 2px, 2py, and 2pz.]]

==Connectedness==
While classical physics applies to large objects moving much slower than the speed of light, modern physics deals with special cases of tiny objects, like atoms, subject to relativistic effects. Atomic theory is vital to understanding many quantum physics concepts that are covered in both Physics 2211 and 2212, like the ball-and-spring model of solids, point charges, and conductivity.

Although one can argue physics applies to just about every aspect of life, and atomic theory is critical to understanding physics, atomic theory has directly influenced material science, power generation, electronics, and even food processing, to name a few.

<gallery>
File:Apollo_synthetic_diamond.jpg|'''Material Science:''' Synthetic diamonds are used for both cosmetic retail and in manufacturing cutting tools.
File:Electrical_and_Mechanical_Services_Department_Headquarters_Photovoltaics.jpg|'''Power:''' Solar cells and power rely on the photovoltaic effect and the wave-particle duality of subatomic particles (like photons).
File:Monokristalines_Silizium_f%C3%BCr_die_Waferherstellung.jpg|'''Electronics:''' Silicon, a popular semiconductor used in electronics, is produced industrially in a single-crystal form.
File:Sodium-chloride-3D-ionic.png|'''Food processing:''' An atomic view of table salt. Purple particles are sodium (Na), and green particles are chlorine (Cl).
File:Nagasakibomb.jpg|'''Defense:''' Nuclear weapons were used during World War II.
File:White_Matter_Connections_Obtained_with_MRI_Tractography.png|'''Medicine:''' MRI's provide doctors critical information without the risks of surgery.
File:Plastic_household_items.jpg|'''Manufacturing:''' Many common household items are made with plastic.
</gallery>

== See also ==

*[[Bohr Model]]
*[[Electronic Energy Levels and Photons]]
*[[Rutherford Experiment and Atomic Collisions]]

===Notable Scientists===
*[[Amedeo Avogadro]]
*[[J.J. Thomson]]
*[[Ernest Rutherford]]
*[[Albert Einstein]]
*[[Max Planck]]
*[[Niels Bohr]]
*[[Max Born]]

===Related Theories===
*[[Quantum Theory]]
*[[Einstein's Theory of Special Relativity]]

===Concept Application===
*[[Ball and Spring Model of Matter]], [[Ball and Spring Model]]
*[[Length and Stiffness of an Interatomic Bond]], [[Young's Modulus]]
*[[Density]], [[Charge]], [[Spin]], and [[Conductivity]]
*[[The Photoelectric Effect]], [[Photons]]
*[[Rest Mass Energy]]
*[[Potential Energy of a Pair of Neutral Atoms]]

===External links===
*Physics Portal description of [https://en.wikipedia.org/wiki/History_of_molecular_theory Molecular Theory] and [https://en.wikipedia.org/wiki/Elementary_particle Subatomic Particles]
*HyperPhysics summary of [http://hyperphysics.phy-astr.gsu.edu/hbase/quacon.html#quacon Quantum Physics]
*Demonstration of the [https://phet.colorado.edu/en/simulation/legacy/hydrogen-atom various models] of a hydrogen atom

==References==

Chapter 30 of [https://openstaxcollege.org/files/textbook_version/hi_res_pdf/9/CollegePhysics-OP.pdf OpenStax Textbook]

Physics Portal page on [https://en.wikipedia.org/wiki/Atomic_theory Atomic Theory]

[[Category: Theory]]

Atomic Theory

2022-04-17T23:24:33Z

Erinhorbacz: /* A Mathematical Model */

Claimed by: Erin Horbacz (4/17/2022)

Atomic theory states that matter is composed of discrete units, called atoms. The word "atom" comes from the Greek word for uncuttable, ''atomos''. Scientists later discovered that atoms were indeed able to be broken into subatomic, or elementary, particles including protons, neutrons, and electrons. Atomic theory has evolved greatly over time, but the most recent model stems from quantum mechanics.

==The Main Idea==
===A Mathematical Model===
Mathematical models of atomic processes have become more thorough and sophisticated as knowledge of atomic properties has grown. The goal of a mathematical model is to express the underlying rules that govern atomic processes in a formula that can then predict and describe the behavior of atoms. Such fundamental formulas are powerful tools for helping scientists understand the interactions and processes of both microscopic and macroscopic systems. For example, it was [https://en.wikipedia.org/wiki/Charles-Augustin_de_Coulomb/ Charles-Augustin de Coulomb] who first determined the mathematical equation which could accurately describe the electrostatic force between atoms:

<math>
V = \frac{1}{4 \pi \epsilon} \frac{q_1 q_2}{r}
</math>

Additionally, stretching of atomic bonds are known to be affected by force fields around an equilibrium point, and they can be modeled according to the equation:

<math>
\Delta V(l) = \frac{1}{2} k_l (l - l_0)^2
</math>

The use and creation of these formulas is incredibly prominent in simulation modeling. For example,

- have been generalized to macroscopic systems (debroglie wavelength)

===A Computational Model===
Understanding the composition and structure of atoms is essential to the study of both microscopic and macroscopic systems. Researchers have made use of atomic information to create what are called atomistic models. These models are used to predict and analyze the behavior of complex systems through knowledge of their most fundamental parts. By understanding how atomic structure affects characteristic properties of atoms, scientists are able to create computational models based on simple microscopic characteristics that simulate complex macroscopic systems. In doing so, they aim to better understand the connection between these macroscopic systems and the underlying atomic structures that govern them.

Use of simulations in research has broadened both the volume and complexity of analysis that can be done at any one time. The ability to model atoms through simulations has been an integral part of the research done in diverse areas of science, notably materials science. In this field, atomistic models are often used to predict material properties under certain conditions using information about their nucleus and electron density. For example, professor ABFIEJABF of the physics department of Georgia Tech created an atomistic model that simulates the behavior of atoms in ABFIEJABF. Another use of atomistic models is to simulate and analyze important processes such as a nuclear chain reaction; an example of such a simulation can be viewed on [https://javalab.org/en/nuclear_chain_reaction_en/ JavaLab].

Atomistic models use the mathematical models discussed above to computationally represent atomic forces, atomic positions, velocities, and magnetic charges of atoms among other things. The result is an accurate model of quantum processes. Ultimately, the use of such simulations help to understand the collective behavior of atoms and how this behavior affects macroscopic processes (such as deformation and phase change) as well as performance abilities (such as strength of material).

==History==

===John Dalton: The Law of Multiple Proportions and Atomic Mass===
[[File:Daltons_symbols.gif|thumb|Dalton's concept of atoms and molecules]]
Working from the conservation of mass principle, chemist John Dalton determined the law of multiple proportions to understand how different elements combined in compounds. In 1803, he proposed that each element of the periodic table was composed of identical components, atoms, that were unique to each element. He also suggested that these atoms were not created nor destroyed when one element was combined with another. Dalton's empirical, experimentally-based work marked the first scientific theory of the atom.

Dalton proposed a list of atomic weights in 1805. However, Dalton failed to recognize natural tendencies of elements in nature (for example, oxygen typically exists as a diatomic molecule as <math>\text{O}_2</math>). Dalton was unable to distinguish between atoms and molecules (groups of atoms).

===Amedeo Avogadro: Avogadro's Law===
In 1811, [[Amedeo Avogadro]] studied gases and determined that the amount of volume a gas occupies is not determined by the mass of the gas. This allowed Avogadro to take more accurate atomic measurements of gases than Dalton, and differentiate atoms from molecules.

===Robert Brown: Brownian Motion===
A Scottish botanist, Robert Brown, studied the motion of tiny pollen particles in water in 1827. The particles followed complex paths, dubbed Brownian Motion. As early as 1905, [[Albert Einstein]] used Brownian Motion to predict the size of atoms and molecules.

===J.J. Thomson: The Plum-Pudding Model and Electrons===
[[File:Plum_pudding_model.svg|thumb|Tomson's Plum-Pudding Model]]
Through his work with cathode rays, [[J.J. Thomson]] discovered the electron in 1897, and was the first to learn that atoms weren't actually "uncuttable" as initially thought. Thomson knew that atoms had a net neutral charge, but he only knew that negative particles existed. Thus, Thomson developed the "plum-pudding" model of negatively charged electrons floating in a sea of positive charge. (He likened the relationship of electrons to the sea of positive charge to that of plums in plum pudding.)

===Ernest Rutherford: Gold Foil Experiment and the Nucleus===
In 1909, one of Thomson's students, [[Ernest Rutherford]], determined that the positive charge of atoms was located in a central nucleus. He shot small, positively charged alpha particles at thin sheets of gold foil and noted that some particles were sharply deflected. This deflection could only occur if the positive components of atoms were located in a small area, which Rutherford assumed to be the center. He proposed a planetary model of atoms where a cloud of electrons surrounded a central, positively charged nucleus.

===Niels Bohr: Introducing Quantum Physics===
[[File:Bohr_atom_animation_2.gif|thumb|The Bohr model for a Hydrogen atom with its electron moving between energy levels]]
As quantum mechanics progressed through the work of [[Albert Einstein]] and [[Max Planck]], [[Niels Bohr]] updated the atomic model in 1913 to account for quantum phenomena. Bohr, who was also one of Rutherford's students, suggested that electrostatic forces kept electrons in circular orbit around the positively charged central nucleus. In support of his theory, Bohr examined the behavior of electrons in hydrogen molecules and noted that they followed distinct energy levels. When an electron changed energy levels, it gained or lost energy, which could be emitted in the form of light. While the Bohr model holds true for hydrogen, it isn't accurate for multi-electron elements.

===James Chadwick: Neutrons===
James Chadwick won a Nobel Prize in 1935 for his discovery of the neutron. Starting with Rutherford's work, Chadwick continued experimenting to determine the excess mass in the nucleus that wasn't accounted for by protons. He found that neutrally charged particles, dubbed neutrons, were also inside the nucleus.

===The Current Model: Quantum Physics and Electron Orbitals===
Erwin Schrödinger examined the possibility that moving electrons behaved more like waves than particles, and published "Schrödinger's Equation" in 1926. Although this resolved many issues encountered with the Bohr model, it faced opposition from physicist [[Max Born]]. Instead, Born suggested a wave-particle duality of electrons, which stated that electrons could behave both like a wave and a particle.
As electrons were now given properties of waves, it was impossible to simultaneously determine an electron's exact location and momentum around the nucleus. Werner Heisenberg, first described this phenomena in 1927, and it was later named the Heisenberg Uncertainty Principle. This refuted the Bohr model of the atom, and replaced it with a pattern of probabilities as to where electrons are located around the nucleus. These patterns are referred to as atomic orbitals and come in a variety of shapes (basic spheres, rings, dumbbells, etc.) and the nucleus is always at the center.
[[File:Neon_orbitals.JPG|thumb|center|The first five atomic orbitals: 1s, 2s, 2px, 2py, and 2pz.]]

==Connectedness==
While classical physics applies to large objects moving much slower than the speed of light, modern physics deals with special cases of tiny objects, like atoms, subject to relativistic effects. Atomic theory is vital to understanding many quantum physics concepts that are covered in both Physics 2211 and 2212, like the ball-and-spring model of solids, point charges, and conductivity.

Although one can argue physics applies to just about every aspect of life, and atomic theory is critical to understanding physics, atomic theory has directly influenced material science, power generation, electronics, and even food processing, to name a few.

<gallery>
File:Apollo_synthetic_diamond.jpg|'''Material Science:''' Synthetic diamonds are used for both cosmetic retail and in manufacturing cutting tools.
File:Electrical_and_Mechanical_Services_Department_Headquarters_Photovoltaics.jpg|'''Power:''' Solar cells and power rely on the photovoltaic effect and the wave-particle duality of subatomic particles (like photons).
File:Monokristalines_Silizium_f%C3%BCr_die_Waferherstellung.jpg|'''Electronics:''' Silicon, a popular semiconductor used in electronics, is produced industrially in a single-crystal form.
File:Sodium-chloride-3D-ionic.png|'''Food processing:''' An atomic view of table salt. Purple particles are sodium (Na), and green particles are chlorine (Cl).
File:Nagasakibomb.jpg|'''Defense:''' Nuclear weapons were used during World War II.
File:White_Matter_Connections_Obtained_with_MRI_Tractography.png|'''Medicine:''' MRI's provide doctors critical information without the risks of surgery.
File:Plastic_household_items.jpg|'''Manufacturing:''' Many common household items are made with plastic.
</gallery>

== See also ==

*[[Bohr Model]]
*[[Electronic Energy Levels and Photons]]
*[[Rutherford Experiment and Atomic Collisions]]

===Notable Scientists===
*[[Amedeo Avogadro]]
*[[J.J. Thomson]]
*[[Ernest Rutherford]]
*[[Albert Einstein]]
*[[Max Planck]]
*[[Niels Bohr]]
*[[Max Born]]

===Related Theories===
*[[Quantum Theory]]
*[[Einstein's Theory of Special Relativity]]

===Concept Application===
*[[Ball and Spring Model of Matter]], [[Ball and Spring Model]]
*[[Length and Stiffness of an Interatomic Bond]], [[Young's Modulus]]
*[[Density]], [[Charge]], [[Spin]], and [[Conductivity]]
*[[The Photoelectric Effect]], [[Photons]]
*[[Rest Mass Energy]]
*[[Potential Energy of a Pair of Neutral Atoms]]

===External links===
*Physics Portal description of [https://en.wikipedia.org/wiki/History_of_molecular_theory Molecular Theory] and [https://en.wikipedia.org/wiki/Elementary_particle Subatomic Particles]
*HyperPhysics summary of [http://hyperphysics.phy-astr.gsu.edu/hbase/quacon.html#quacon Quantum Physics]
*Demonstration of the [https://phet.colorado.edu/en/simulation/legacy/hydrogen-atom various models] of a hydrogen atom

==References==

Chapter 30 of [https://openstaxcollege.org/files/textbook_version/hi_res_pdf/9/CollegePhysics-OP.pdf OpenStax Textbook]

Physics Portal page on [https://en.wikipedia.org/wiki/Atomic_theory Atomic Theory]

[[Category: Theory]]

Atomic Theory

2022-04-17T23:07:28Z

Erinhorbacz: /* A Mathematical Model */

Claimed by: Erin Horbacz (4/17/2022)

Atomic theory states that matter is composed of discrete units, called atoms. The word "atom" comes from the Greek word for uncuttable, ''atomos''. Scientists later discovered that atoms were indeed able to be broken into subatomic, or elementary, particles including protons, neutrons, and electrons. Atomic theory has evolved greatly over time, but the most recent model stems from quantum mechanics.

==The Main Idea==
===A Mathematical Model===
Mathematical models of atomic processes have become more thorough and sophisticated as knowledge of atomic properties has grown. The goal of a mathematical model is to express the underlying rules that govern atomic processes in a formula that can then predict and describe the behavior of atoms. Such fundamental formulas are powerful tools for helping scientists understand the interactions and processes of both microscopic and macroscopic systems. For example, it was [File:https://en.wikipedia.org/wiki/Charles-Augustin_de_Coulomb/ Charles-Augustin de Coulomb] who first determined the mathematical equation which could accurately describe the electrostatic force between atoms:

<math>
V = \frac{1}{4 \pi\ \epsilon\}
</math>

The use and creation of these formulas is incredibly prominent in simulation modeling. For example,

- have been generalized to macroscopic systems (debroglie wavelength)

===A Computational Model===
Understanding the composition and structure of atoms is essential to the study of both microscopic and macroscopic systems. Researchers have made use of atomic information to create what are called atomistic models. These models are used to predict and analyze the behavior of complex systems through knowledge of their most fundamental parts. By understanding how atomic structure affects characteristic properties of atoms, scientists are able to create computational models based on simple microscopic characteristics that simulate complex macroscopic systems. In doing so, they aim to better understand the connection between these macroscopic systems and the underlying atomic structures that govern them.

Use of simulations in research has broadened both the volume and complexity of analysis that can be done at any one time. The ability to model atoms through simulations has been an integral part of the research done in diverse areas of science, notably materials science. In this field, atomistic models are often used to predict material properties under certain conditions using information about their nucleus and electron density. For example, professor ABFIEJABF of the physics department of Georgia Tech created an atomistic model that simulates the behavior of atoms in ABFIEJABF. Another use of atomistic models is to simulate and analyze important processes such as a nuclear chain reaction; an example of such a simulation can be viewed on [https://javalab.org/en/nuclear_chain_reaction_en/ JavaLab].

Atomistic models use the mathematical models discussed above to computationally represent atomic forces, atomic positions, velocities, and magnetic charges of atoms among other things. The result is an accurate model of quantum processes. Ultimately, the use of such simulations help to understand the collective behavior of atoms and how this behavior affects macroscopic processes (such as deformation and phase change) as well as performance abilities (such as strength of material).

==History==

===John Dalton: The Law of Multiple Proportions and Atomic Mass===
[[File:Daltons_symbols.gif|thumb|Dalton's concept of atoms and molecules]]
Working from the conservation of mass principle, chemist John Dalton determined the law of multiple proportions to understand how different elements combined in compounds. In 1803, he proposed that each element of the periodic table was composed of identical components, atoms, that were unique to each element. He also suggested that these atoms were not created nor destroyed when one element was combined with another. Dalton's empirical, experimentally-based work marked the first scientific theory of the atom.

Dalton proposed a list of atomic weights in 1805. However, Dalton failed to recognize natural tendencies of elements in nature (for example, oxygen typically exists as a diatomic molecule as <math>\text{O}_2</math>). Dalton was unable to distinguish between atoms and molecules (groups of atoms).

===Amedeo Avogadro: Avogadro's Law===
In 1811, [[Amedeo Avogadro]] studied gases and determined that the amount of volume a gas occupies is not determined by the mass of the gas. This allowed Avogadro to take more accurate atomic measurements of gases than Dalton, and differentiate atoms from molecules.

===Robert Brown: Brownian Motion===
A Scottish botanist, Robert Brown, studied the motion of tiny pollen particles in water in 1827. The particles followed complex paths, dubbed Brownian Motion. As early as 1905, [[Albert Einstein]] used Brownian Motion to predict the size of atoms and molecules.

===J.J. Thomson: The Plum-Pudding Model and Electrons===
[[File:Plum_pudding_model.svg|thumb|Tomson's Plum-Pudding Model]]
Through his work with cathode rays, [[J.J. Thomson]] discovered the electron in 1897, and was the first to learn that atoms weren't actually "uncuttable" as initially thought. Thomson knew that atoms had a net neutral charge, but he only knew that negative particles existed. Thus, Thomson developed the "plum-pudding" model of negatively charged electrons floating in a sea of positive charge. (He likened the relationship of electrons to the sea of positive charge to that of plums in plum pudding.)

===Ernest Rutherford: Gold Foil Experiment and the Nucleus===
In 1909, one of Thomson's students, [[Ernest Rutherford]], determined that the positive charge of atoms was located in a central nucleus. He shot small, positively charged alpha particles at thin sheets of gold foil and noted that some particles were sharply deflected. This deflection could only occur if the positive components of atoms were located in a small area, which Rutherford assumed to be the center. He proposed a planetary model of atoms where a cloud of electrons surrounded a central, positively charged nucleus.

===Niels Bohr: Introducing Quantum Physics===
[[File:Bohr_atom_animation_2.gif|thumb|The Bohr model for a Hydrogen atom with its electron moving between energy levels]]
As quantum mechanics progressed through the work of [[Albert Einstein]] and [[Max Planck]], [[Niels Bohr]] updated the atomic model in 1913 to account for quantum phenomena. Bohr, who was also one of Rutherford's students, suggested that electrostatic forces kept electrons in circular orbit around the positively charged central nucleus. In support of his theory, Bohr examined the behavior of electrons in hydrogen molecules and noted that they followed distinct energy levels. When an electron changed energy levels, it gained or lost energy, which could be emitted in the form of light. While the Bohr model holds true for hydrogen, it isn't accurate for multi-electron elements.

===James Chadwick: Neutrons===
James Chadwick won a Nobel Prize in 1935 for his discovery of the neutron. Starting with Rutherford's work, Chadwick continued experimenting to determine the excess mass in the nucleus that wasn't accounted for by protons. He found that neutrally charged particles, dubbed neutrons, were also inside the nucleus.

===The Current Model: Quantum Physics and Electron Orbitals===
Erwin Schrödinger examined the possibility that moving electrons behaved more like waves than particles, and published "Schrödinger's Equation" in 1926. Although this resolved many issues encountered with the Bohr model, it faced opposition from physicist [[Max Born]]. Instead, Born suggested a wave-particle duality of electrons, which stated that electrons could behave both like a wave and a particle.
As electrons were now given properties of waves, it was impossible to simultaneously determine an electron's exact location and momentum around the nucleus. Werner Heisenberg, first described this phenomena in 1927, and it was later named the Heisenberg Uncertainty Principle. This refuted the Bohr model of the atom, and replaced it with a pattern of probabilities as to where electrons are located around the nucleus. These patterns are referred to as atomic orbitals and come in a variety of shapes (basic spheres, rings, dumbbells, etc.) and the nucleus is always at the center.
[[File:Neon_orbitals.JPG|thumb|center|The first five atomic orbitals: 1s, 2s, 2px, 2py, and 2pz.]]

==Connectedness==
While classical physics applies to large objects moving much slower than the speed of light, modern physics deals with special cases of tiny objects, like atoms, subject to relativistic effects. Atomic theory is vital to understanding many quantum physics concepts that are covered in both Physics 2211 and 2212, like the ball-and-spring model of solids, point charges, and conductivity.

Although one can argue physics applies to just about every aspect of life, and atomic theory is critical to understanding physics, atomic theory has directly influenced material science, power generation, electronics, and even food processing, to name a few.

<gallery>
File:Apollo_synthetic_diamond.jpg|'''Material Science:''' Synthetic diamonds are used for both cosmetic retail and in manufacturing cutting tools.
File:Electrical_and_Mechanical_Services_Department_Headquarters_Photovoltaics.jpg|'''Power:''' Solar cells and power rely on the photovoltaic effect and the wave-particle duality of subatomic particles (like photons).
File:Monokristalines_Silizium_f%C3%BCr_die_Waferherstellung.jpg|'''Electronics:''' Silicon, a popular semiconductor used in electronics, is produced industrially in a single-crystal form.
File:Sodium-chloride-3D-ionic.png|'''Food processing:''' An atomic view of table salt. Purple particles are sodium (Na), and green particles are chlorine (Cl).
File:Nagasakibomb.jpg|'''Defense:''' Nuclear weapons were used during World War II.
File:White_Matter_Connections_Obtained_with_MRI_Tractography.png|'''Medicine:''' MRI's provide doctors critical information without the risks of surgery.
File:Plastic_household_items.jpg|'''Manufacturing:''' Many common household items are made with plastic.
</gallery>

== See also ==

*[[Bohr Model]]
*[[Electronic Energy Levels and Photons]]
*[[Rutherford Experiment and Atomic Collisions]]

===Notable Scientists===
*[[Amedeo Avogadro]]
*[[J.J. Thomson]]
*[[Ernest Rutherford]]
*[[Albert Einstein]]
*[[Max Planck]]
*[[Niels Bohr]]
*[[Max Born]]

===Related Theories===
*[[Quantum Theory]]
*[[Einstein's Theory of Special Relativity]]

===Concept Application===
*[[Ball and Spring Model of Matter]], [[Ball and Spring Model]]
*[[Length and Stiffness of an Interatomic Bond]], [[Young's Modulus]]
*[[Density]], [[Charge]], [[Spin]], and [[Conductivity]]
*[[The Photoelectric Effect]], [[Photons]]
*[[Rest Mass Energy]]
*[[Potential Energy of a Pair of Neutral Atoms]]

===External links===
*Physics Portal description of [https://en.wikipedia.org/wiki/History_of_molecular_theory Molecular Theory] and [https://en.wikipedia.org/wiki/Elementary_particle Subatomic Particles]
*HyperPhysics summary of [http://hyperphysics.phy-astr.gsu.edu/hbase/quacon.html#quacon Quantum Physics]
*Demonstration of the [https://phet.colorado.edu/en/simulation/legacy/hydrogen-atom various models] of a hydrogen atom

==References==

Chapter 30 of [https://openstaxcollege.org/files/textbook_version/hi_res_pdf/9/CollegePhysics-OP.pdf OpenStax Textbook]

Physics Portal page on [https://en.wikipedia.org/wiki/Atomic_theory Atomic Theory]

[[Category: Theory]]

Atomic Theory

2022-04-17T23:00:18Z

Erinhorbacz: /* A Mathematical Model */

Claimed by: Erin Horbacz (4/17/2022)

Atomic theory states that matter is composed of discrete units, called atoms. The word "atom" comes from the Greek word for uncuttable, ''atomos''. Scientists later discovered that atoms were indeed able to be broken into subatomic, or elementary, particles including protons, neutrons, and electrons. Atomic theory has evolved greatly over time, but the most recent model stems from quantum mechanics.

==The Main Idea==
===A Mathematical Model===
Mathematical models of atomic processes have become more thorough and sophisticated as knowledge of atomic properties has grown. The goal of a mathematical model is to express the underlying rules that govern atomic processes in a formula that can then predict and describe the behavior of atoms. Such fundamental formulas are powerful tools for helping scientists understand the interactions and processes of both microscopic and macroscopic systems. For example, it was [File:https://en.wikipedia.org/wiki/Charles-Augustin_de_Coulomb/ Charles-Augustin de Coulomb] who first determined the mathematical equation which could accurately describe the electrostatic force between atoms: <math>V=\textstyle\frac{1}{4\pi\\&epsilon\}</math>

The use and creation of these formulas is incredibly prominent in simulation modeling. For example,

- have been generalized to macroscopic systems (debroglie wavelength)

===A Computational Model===
Understanding the composition and structure of atoms is essential to the study of both microscopic and macroscopic systems. Researchers have made use of atomic information to create what are called atomistic models. These models are used to predict and analyze the behavior of complex systems through knowledge of their most fundamental parts. By understanding how atomic structure affects characteristic properties of atoms, scientists are able to create computational models based on simple microscopic characteristics that simulate complex macroscopic systems. In doing so, they aim to better understand the connection between these macroscopic systems and the underlying atomic structures that govern them.

Use of simulations in research has broadened both the volume and complexity of analysis that can be done at any one time. The ability to model atoms through simulations has been an integral part of the research done in diverse areas of science, notably materials science. In this field, atomistic models are often used to predict material properties under certain conditions using information about their nucleus and electron density. For example, professor ABFIEJABF of the physics department of Georgia Tech created an atomistic model that simulates the behavior of atoms in ABFIEJABF. Another use of atomistic models is to simulate and analyze important processes such as a nuclear chain reaction; an example of such a simulation can be viewed on [https://javalab.org/en/nuclear_chain_reaction_en/ JavaLab].

Atomistic models use the mathematical models discussed above to computationally represent atomic forces, atomic positions, velocities, and magnetic charges of atoms among other things. The result is an accurate model of quantum processes. Ultimately, the use of such simulations help to understand the collective behavior of atoms and how this behavior affects macroscopic processes (such as deformation and phase change) as well as performance abilities (such as strength of material).

==History==

===John Dalton: The Law of Multiple Proportions and Atomic Mass===
[[File:Daltons_symbols.gif|thumb|Dalton's concept of atoms and molecules]]
Working from the conservation of mass principle, chemist John Dalton determined the law of multiple proportions to understand how different elements combined in compounds. In 1803, he proposed that each element of the periodic table was composed of identical components, atoms, that were unique to each element. He also suggested that these atoms were not created nor destroyed when one element was combined with another. Dalton's empirical, experimentally-based work marked the first scientific theory of the atom.

Dalton proposed a list of atomic weights in 1805. However, Dalton failed to recognize natural tendencies of elements in nature (for example, oxygen typically exists as a diatomic molecule as <math>\text{O}_2</math>). Dalton was unable to distinguish between atoms and molecules (groups of atoms).

===Amedeo Avogadro: Avogadro's Law===
In 1811, [[Amedeo Avogadro]] studied gases and determined that the amount of volume a gas occupies is not determined by the mass of the gas. This allowed Avogadro to take more accurate atomic measurements of gases than Dalton, and differentiate atoms from molecules.

===Robert Brown: Brownian Motion===
A Scottish botanist, Robert Brown, studied the motion of tiny pollen particles in water in 1827. The particles followed complex paths, dubbed Brownian Motion. As early as 1905, [[Albert Einstein]] used Brownian Motion to predict the size of atoms and molecules.

===J.J. Thomson: The Plum-Pudding Model and Electrons===
[[File:Plum_pudding_model.svg|thumb|Tomson's Plum-Pudding Model]]
Through his work with cathode rays, [[J.J. Thomson]] discovered the electron in 1897, and was the first to learn that atoms weren't actually "uncuttable" as initially thought. Thomson knew that atoms had a net neutral charge, but he only knew that negative particles existed. Thus, Thomson developed the "plum-pudding" model of negatively charged electrons floating in a sea of positive charge. (He likened the relationship of electrons to the sea of positive charge to that of plums in plum pudding.)

===Ernest Rutherford: Gold Foil Experiment and the Nucleus===
In 1909, one of Thomson's students, [[Ernest Rutherford]], determined that the positive charge of atoms was located in a central nucleus. He shot small, positively charged alpha particles at thin sheets of gold foil and noted that some particles were sharply deflected. This deflection could only occur if the positive components of atoms were located in a small area, which Rutherford assumed to be the center. He proposed a planetary model of atoms where a cloud of electrons surrounded a central, positively charged nucleus.

===Niels Bohr: Introducing Quantum Physics===
[[File:Bohr_atom_animation_2.gif|thumb|The Bohr model for a Hydrogen atom with its electron moving between energy levels]]
As quantum mechanics progressed through the work of [[Albert Einstein]] and [[Max Planck]], [[Niels Bohr]] updated the atomic model in 1913 to account for quantum phenomena. Bohr, who was also one of Rutherford's students, suggested that electrostatic forces kept electrons in circular orbit around the positively charged central nucleus. In support of his theory, Bohr examined the behavior of electrons in hydrogen molecules and noted that they followed distinct energy levels. When an electron changed energy levels, it gained or lost energy, which could be emitted in the form of light. While the Bohr model holds true for hydrogen, it isn't accurate for multi-electron elements.

===James Chadwick: Neutrons===
James Chadwick won a Nobel Prize in 1935 for his discovery of the neutron. Starting with Rutherford's work, Chadwick continued experimenting to determine the excess mass in the nucleus that wasn't accounted for by protons. He found that neutrally charged particles, dubbed neutrons, were also inside the nucleus.

===The Current Model: Quantum Physics and Electron Orbitals===
Erwin Schrödinger examined the possibility that moving electrons behaved more like waves than particles, and published "Schrödinger's Equation" in 1926. Although this resolved many issues encountered with the Bohr model, it faced opposition from physicist [[Max Born]]. Instead, Born suggested a wave-particle duality of electrons, which stated that electrons could behave both like a wave and a particle.
As electrons were now given properties of waves, it was impossible to simultaneously determine an electron's exact location and momentum around the nucleus. Werner Heisenberg, first described this phenomena in 1927, and it was later named the Heisenberg Uncertainty Principle. This refuted the Bohr model of the atom, and replaced it with a pattern of probabilities as to where electrons are located around the nucleus. These patterns are referred to as atomic orbitals and come in a variety of shapes (basic spheres, rings, dumbbells, etc.) and the nucleus is always at the center.
[[File:Neon_orbitals.JPG|thumb|center|The first five atomic orbitals: 1s, 2s, 2px, 2py, and 2pz.]]

==Connectedness==
While classical physics applies to large objects moving much slower than the speed of light, modern physics deals with special cases of tiny objects, like atoms, subject to relativistic effects. Atomic theory is vital to understanding many quantum physics concepts that are covered in both Physics 2211 and 2212, like the ball-and-spring model of solids, point charges, and conductivity.

Although one can argue physics applies to just about every aspect of life, and atomic theory is critical to understanding physics, atomic theory has directly influenced material science, power generation, electronics, and even food processing, to name a few.

<gallery>
File:Apollo_synthetic_diamond.jpg|'''Material Science:''' Synthetic diamonds are used for both cosmetic retail and in manufacturing cutting tools.
File:Electrical_and_Mechanical_Services_Department_Headquarters_Photovoltaics.jpg|'''Power:''' Solar cells and power rely on the photovoltaic effect and the wave-particle duality of subatomic particles (like photons).
File:Monokristalines_Silizium_f%C3%BCr_die_Waferherstellung.jpg|'''Electronics:''' Silicon, a popular semiconductor used in electronics, is produced industrially in a single-crystal form.
File:Sodium-chloride-3D-ionic.png|'''Food processing:''' An atomic view of table salt. Purple particles are sodium (Na), and green particles are chlorine (Cl).
File:Nagasakibomb.jpg|'''Defense:''' Nuclear weapons were used during World War II.
File:White_Matter_Connections_Obtained_with_MRI_Tractography.png|'''Medicine:''' MRI's provide doctors critical information without the risks of surgery.
File:Plastic_household_items.jpg|'''Manufacturing:''' Many common household items are made with plastic.
</gallery>

== See also ==

*[[Bohr Model]]
*[[Electronic Energy Levels and Photons]]
*[[Rutherford Experiment and Atomic Collisions]]

===Notable Scientists===
*[[Amedeo Avogadro]]
*[[J.J. Thomson]]
*[[Ernest Rutherford]]
*[[Albert Einstein]]
*[[Max Planck]]
*[[Niels Bohr]]
*[[Max Born]]

===Related Theories===
*[[Quantum Theory]]
*[[Einstein's Theory of Special Relativity]]

===Concept Application===
*[[Ball and Spring Model of Matter]], [[Ball and Spring Model]]
*[[Length and Stiffness of an Interatomic Bond]], [[Young's Modulus]]
*[[Density]], [[Charge]], [[Spin]], and [[Conductivity]]
*[[The Photoelectric Effect]], [[Photons]]
*[[Rest Mass Energy]]
*[[Potential Energy of a Pair of Neutral Atoms]]

===External links===
*Physics Portal description of [https://en.wikipedia.org/wiki/History_of_molecular_theory Molecular Theory] and [https://en.wikipedia.org/wiki/Elementary_particle Subatomic Particles]
*HyperPhysics summary of [http://hyperphysics.phy-astr.gsu.edu/hbase/quacon.html#quacon Quantum Physics]
*Demonstration of the [https://phet.colorado.edu/en/simulation/legacy/hydrogen-atom various models] of a hydrogen atom

==References==

Chapter 30 of [https://openstaxcollege.org/files/textbook_version/hi_res_pdf/9/CollegePhysics-OP.pdf OpenStax Textbook]

Physics Portal page on [https://en.wikipedia.org/wiki/Atomic_theory Atomic Theory]

[[Category: Theory]]

Atomic Theory

2022-04-17T22:58:13Z

Erinhorbacz: /* A Mathematical Model */

Claimed by: Erin Horbacz (4/17/2022)

Atomic theory states that matter is composed of discrete units, called atoms. The word "atom" comes from the Greek word for uncuttable, ''atomos''. Scientists later discovered that atoms were indeed able to be broken into subatomic, or elementary, particles including protons, neutrons, and electrons. Atomic theory has evolved greatly over time, but the most recent model stems from quantum mechanics.

==The Main Idea==
===A Mathematical Model===
Mathematical models of atomic processes have become more thorough and sophisticated as knowledge of atomic properties has grown. The goal of a mathematical model is to express the underlying rules that govern atomic processes in a formula that can then predict and describe the behavior of atoms. Such fundamental formulas are powerful tools for helping scientists understand the interactions and processes of both microscopic and macroscopic systems. For example, it was [File:https://en.wikipedia.org/wiki/Charles-Augustin_de_Coulomb/ Charles-Augustin de Coulomb] who first determined the mathematical equation which could accurately describe the electrostatic force between atoms: <math>V=1/4\pi\\epsilon\</math>

The use and creation of these formulas is incredibly prominent in simulation modeling. For example,

- have been generalized to macroscopic systems (debroglie wavelength)

===A Computational Model===
Understanding the composition and structure of atoms is essential to the study of both microscopic and macroscopic systems. Researchers have made use of atomic information to create what are called atomistic models. These models are used to predict and analyze the behavior of complex systems through knowledge of their most fundamental parts. By understanding how atomic structure affects characteristic properties of atoms, scientists are able to create computational models based on simple microscopic characteristics that simulate complex macroscopic systems. In doing so, they aim to better understand the connection between these macroscopic systems and the underlying atomic structures that govern them.

Use of simulations in research has broadened both the volume and complexity of analysis that can be done at any one time. The ability to model atoms through simulations has been an integral part of the research done in diverse areas of science, notably materials science. In this field, atomistic models are often used to predict material properties under certain conditions using information about their nucleus and electron density. For example, professor ABFIEJABF of the physics department of Georgia Tech created an atomistic model that simulates the behavior of atoms in ABFIEJABF. Another use of atomistic models is to simulate and analyze important processes such as a nuclear chain reaction; an example of such a simulation can be viewed on [https://javalab.org/en/nuclear_chain_reaction_en/ JavaLab].

Atomistic models use the mathematical models discussed above to computationally represent atomic forces, atomic positions, velocities, and magnetic charges of atoms among other things. The result is an accurate model of quantum processes. Ultimately, the use of such simulations help to understand the collective behavior of atoms and how this behavior affects macroscopic processes (such as deformation and phase change) as well as performance abilities (such as strength of material).

==History==

===John Dalton: The Law of Multiple Proportions and Atomic Mass===
[[File:Daltons_symbols.gif|thumb|Dalton's concept of atoms and molecules]]
Working from the conservation of mass principle, chemist John Dalton determined the law of multiple proportions to understand how different elements combined in compounds. In 1803, he proposed that each element of the periodic table was composed of identical components, atoms, that were unique to each element. He also suggested that these atoms were not created nor destroyed when one element was combined with another. Dalton's empirical, experimentally-based work marked the first scientific theory of the atom.

Dalton proposed a list of atomic weights in 1805. However, Dalton failed to recognize natural tendencies of elements in nature (for example, oxygen typically exists as a diatomic molecule as <math>\text{O}_2</math>). Dalton was unable to distinguish between atoms and molecules (groups of atoms).

===Amedeo Avogadro: Avogadro's Law===
In 1811, [[Amedeo Avogadro]] studied gases and determined that the amount of volume a gas occupies is not determined by the mass of the gas. This allowed Avogadro to take more accurate atomic measurements of gases than Dalton, and differentiate atoms from molecules.

===Robert Brown: Brownian Motion===
A Scottish botanist, Robert Brown, studied the motion of tiny pollen particles in water in 1827. The particles followed complex paths, dubbed Brownian Motion. As early as 1905, [[Albert Einstein]] used Brownian Motion to predict the size of atoms and molecules.

===J.J. Thomson: The Plum-Pudding Model and Electrons===
[[File:Plum_pudding_model.svg|thumb|Tomson's Plum-Pudding Model]]
Through his work with cathode rays, [[J.J. Thomson]] discovered the electron in 1897, and was the first to learn that atoms weren't actually "uncuttable" as initially thought. Thomson knew that atoms had a net neutral charge, but he only knew that negative particles existed. Thus, Thomson developed the "plum-pudding" model of negatively charged electrons floating in a sea of positive charge. (He likened the relationship of electrons to the sea of positive charge to that of plums in plum pudding.)

===Ernest Rutherford: Gold Foil Experiment and the Nucleus===
In 1909, one of Thomson's students, [[Ernest Rutherford]], determined that the positive charge of atoms was located in a central nucleus. He shot small, positively charged alpha particles at thin sheets of gold foil and noted that some particles were sharply deflected. This deflection could only occur if the positive components of atoms were located in a small area, which Rutherford assumed to be the center. He proposed a planetary model of atoms where a cloud of electrons surrounded a central, positively charged nucleus.

===Niels Bohr: Introducing Quantum Physics===
[[File:Bohr_atom_animation_2.gif|thumb|The Bohr model for a Hydrogen atom with its electron moving between energy levels]]
As quantum mechanics progressed through the work of [[Albert Einstein]] and [[Max Planck]], [[Niels Bohr]] updated the atomic model in 1913 to account for quantum phenomena. Bohr, who was also one of Rutherford's students, suggested that electrostatic forces kept electrons in circular orbit around the positively charged central nucleus. In support of his theory, Bohr examined the behavior of electrons in hydrogen molecules and noted that they followed distinct energy levels. When an electron changed energy levels, it gained or lost energy, which could be emitted in the form of light. While the Bohr model holds true for hydrogen, it isn't accurate for multi-electron elements.

===James Chadwick: Neutrons===
James Chadwick won a Nobel Prize in 1935 for his discovery of the neutron. Starting with Rutherford's work, Chadwick continued experimenting to determine the excess mass in the nucleus that wasn't accounted for by protons. He found that neutrally charged particles, dubbed neutrons, were also inside the nucleus.

===The Current Model: Quantum Physics and Electron Orbitals===
Erwin Schrödinger examined the possibility that moving electrons behaved more like waves than particles, and published "Schrödinger's Equation" in 1926. Although this resolved many issues encountered with the Bohr model, it faced opposition from physicist [[Max Born]]. Instead, Born suggested a wave-particle duality of electrons, which stated that electrons could behave both like a wave and a particle.
As electrons were now given properties of waves, it was impossible to simultaneously determine an electron's exact location and momentum around the nucleus. Werner Heisenberg, first described this phenomena in 1927, and it was later named the Heisenberg Uncertainty Principle. This refuted the Bohr model of the atom, and replaced it with a pattern of probabilities as to where electrons are located around the nucleus. These patterns are referred to as atomic orbitals and come in a variety of shapes (basic spheres, rings, dumbbells, etc.) and the nucleus is always at the center.
[[File:Neon_orbitals.JPG|thumb|center|The first five atomic orbitals: 1s, 2s, 2px, 2py, and 2pz.]]

==Connectedness==
While classical physics applies to large objects moving much slower than the speed of light, modern physics deals with special cases of tiny objects, like atoms, subject to relativistic effects. Atomic theory is vital to understanding many quantum physics concepts that are covered in both Physics 2211 and 2212, like the ball-and-spring model of solids, point charges, and conductivity.

Although one can argue physics applies to just about every aspect of life, and atomic theory is critical to understanding physics, atomic theory has directly influenced material science, power generation, electronics, and even food processing, to name a few.

<gallery>
File:Apollo_synthetic_diamond.jpg|'''Material Science:''' Synthetic diamonds are used for both cosmetic retail and in manufacturing cutting tools.
File:Electrical_and_Mechanical_Services_Department_Headquarters_Photovoltaics.jpg|'''Power:''' Solar cells and power rely on the photovoltaic effect and the wave-particle duality of subatomic particles (like photons).
File:Monokristalines_Silizium_f%C3%BCr_die_Waferherstellung.jpg|'''Electronics:''' Silicon, a popular semiconductor used in electronics, is produced industrially in a single-crystal form.
File:Sodium-chloride-3D-ionic.png|'''Food processing:''' An atomic view of table salt. Purple particles are sodium (Na), and green particles are chlorine (Cl).
File:Nagasakibomb.jpg|'''Defense:''' Nuclear weapons were used during World War II.
File:White_Matter_Connections_Obtained_with_MRI_Tractography.png|'''Medicine:''' MRI's provide doctors critical information without the risks of surgery.
File:Plastic_household_items.jpg|'''Manufacturing:''' Many common household items are made with plastic.
</gallery>

== See also ==

*[[Bohr Model]]
*[[Electronic Energy Levels and Photons]]
*[[Rutherford Experiment and Atomic Collisions]]

===Notable Scientists===
*[[Amedeo Avogadro]]
*[[J.J. Thomson]]
*[[Ernest Rutherford]]
*[[Albert Einstein]]
*[[Max Planck]]
*[[Niels Bohr]]
*[[Max Born]]

===Related Theories===
*[[Quantum Theory]]
*[[Einstein's Theory of Special Relativity]]

===Concept Application===
*[[Ball and Spring Model of Matter]], [[Ball and Spring Model]]
*[[Length and Stiffness of an Interatomic Bond]], [[Young's Modulus]]
*[[Density]], [[Charge]], [[Spin]], and [[Conductivity]]
*[[The Photoelectric Effect]], [[Photons]]
*[[Rest Mass Energy]]
*[[Potential Energy of a Pair of Neutral Atoms]]

===External links===
*Physics Portal description of [https://en.wikipedia.org/wiki/History_of_molecular_theory Molecular Theory] and [https://en.wikipedia.org/wiki/Elementary_particle Subatomic Particles]
*HyperPhysics summary of [http://hyperphysics.phy-astr.gsu.edu/hbase/quacon.html#quacon Quantum Physics]
*Demonstration of the [https://phet.colorado.edu/en/simulation/legacy/hydrogen-atom various models] of a hydrogen atom

==References==

Chapter 30 of [https://openstaxcollege.org/files/textbook_version/hi_res_pdf/9/CollegePhysics-OP.pdf OpenStax Textbook]

Physics Portal page on [https://en.wikipedia.org/wiki/Atomic_theory Atomic Theory]

[[Category: Theory]]

Atomic Theory

2022-04-17T22:55:54Z

Erinhorbacz: /* A Mathematical Model */

Claimed by: Erin Horbacz (4/17/2022)

Atomic theory states that matter is composed of discrete units, called atoms. The word "atom" comes from the Greek word for uncuttable, ''atomos''. Scientists later discovered that atoms were indeed able to be broken into subatomic, or elementary, particles including protons, neutrons, and electrons. Atomic theory has evolved greatly over time, but the most recent model stems from quantum mechanics.

==The Main Idea==
===A Mathematical Model===
Mathematical models of atomic processes have become more thorough and sophisticated as knowledge of atomic properties has grown. The goal of a mathematical model is to express the underlying rules that govern atomic processes in a formula that can then predict and describe the behavior of atoms. Such fundamental formulas are powerful tools for helping scientists understand the interactions and processes of both microscopic and macroscopic systems. For example, it was [File:https://en.wikipedia.org/wiki/Charles-Augustin_de_Coulomb/ Charles-Augustin de Coulomb] who first determined the mathematical equation which could accurately describe the electrostatic force between atoms: <math>V=1/4\pi\\epsilon\<math>

The use and creation of these formulas is incredibly prominent in simulation modeling. For example,

- have been generalized to macroscopic systems (debroglie wavelength)

===A Computational Model===
Understanding the composition and structure of atoms is essential to the study of both microscopic and macroscopic systems. Researchers have made use of atomic information to create what are called atomistic models. These models are used to predict and analyze the behavior of complex systems through knowledge of their most fundamental parts. By understanding how atomic structure affects characteristic properties of atoms, scientists are able to create computational models based on simple microscopic characteristics that simulate complex macroscopic systems. In doing so, they aim to better understand the connection between these macroscopic systems and the underlying atomic structures that govern them.

Use of simulations in research has broadened both the volume and complexity of analysis that can be done at any one time. The ability to model atoms through simulations has been an integral part of the research done in diverse areas of science, notably materials science. In this field, atomistic models are often used to predict material properties under certain conditions using information about their nucleus and electron density. For example, professor ABFIEJABF of the physics department of Georgia Tech created an atomistic model that simulates the behavior of atoms in ABFIEJABF. Another use of atomistic models is to simulate and analyze important processes such as a nuclear chain reaction; an example of such a simulation can be viewed on [https://javalab.org/en/nuclear_chain_reaction_en/ JavaLab].

Atomistic models use the mathematical models discussed above to computationally represent atomic forces, atomic positions, velocities, and magnetic charges of atoms among other things. The result is an accurate model of quantum processes. Ultimately, the use of such simulations help to understand the collective behavior of atoms and how this behavior affects macroscopic processes (such as deformation and phase change) as well as performance abilities (such as strength of material).

==History==

===John Dalton: The Law of Multiple Proportions and Atomic Mass===
[[File:Daltons_symbols.gif|thumb|Dalton's concept of atoms and molecules]]
Working from the conservation of mass principle, chemist John Dalton determined the law of multiple proportions to understand how different elements combined in compounds. In 1803, he proposed that each element of the periodic table was composed of identical components, atoms, that were unique to each element. He also suggested that these atoms were not created nor destroyed when one element was combined with another. Dalton's empirical, experimentally-based work marked the first scientific theory of the atom.

Dalton proposed a list of atomic weights in 1805. However, Dalton failed to recognize natural tendencies of elements in nature (for example, oxygen typically exists as a diatomic molecule as <math>\text{O}_2</math>). Dalton was unable to distinguish between atoms and molecules (groups of atoms).

===Amedeo Avogadro: Avogadro's Law===
In 1811, [[Amedeo Avogadro]] studied gases and determined that the amount of volume a gas occupies is not determined by the mass of the gas. This allowed Avogadro to take more accurate atomic measurements of gases than Dalton, and differentiate atoms from molecules.

===Robert Brown: Brownian Motion===
A Scottish botanist, Robert Brown, studied the motion of tiny pollen particles in water in 1827. The particles followed complex paths, dubbed Brownian Motion. As early as 1905, [[Albert Einstein]] used Brownian Motion to predict the size of atoms and molecules.

===J.J. Thomson: The Plum-Pudding Model and Electrons===
[[File:Plum_pudding_model.svg|thumb|Tomson's Plum-Pudding Model]]
Through his work with cathode rays, [[J.J. Thomson]] discovered the electron in 1897, and was the first to learn that atoms weren't actually "uncuttable" as initially thought. Thomson knew that atoms had a net neutral charge, but he only knew that negative particles existed. Thus, Thomson developed the "plum-pudding" model of negatively charged electrons floating in a sea of positive charge. (He likened the relationship of electrons to the sea of positive charge to that of plums in plum pudding.)

===Ernest Rutherford: Gold Foil Experiment and the Nucleus===
In 1909, one of Thomson's students, [[Ernest Rutherford]], determined that the positive charge of atoms was located in a central nucleus. He shot small, positively charged alpha particles at thin sheets of gold foil and noted that some particles were sharply deflected. This deflection could only occur if the positive components of atoms were located in a small area, which Rutherford assumed to be the center. He proposed a planetary model of atoms where a cloud of electrons surrounded a central, positively charged nucleus.

===Niels Bohr: Introducing Quantum Physics===
[[File:Bohr_atom_animation_2.gif|thumb|The Bohr model for a Hydrogen atom with its electron moving between energy levels]]
As quantum mechanics progressed through the work of [[Albert Einstein]] and [[Max Planck]], [[Niels Bohr]] updated the atomic model in 1913 to account for quantum phenomena. Bohr, who was also one of Rutherford's students, suggested that electrostatic forces kept electrons in circular orbit around the positively charged central nucleus. In support of his theory, Bohr examined the behavior of electrons in hydrogen molecules and noted that they followed distinct energy levels. When an electron changed energy levels, it gained or lost energy, which could be emitted in the form of light. While the Bohr model holds true for hydrogen, it isn't accurate for multi-electron elements.

===James Chadwick: Neutrons===
James Chadwick won a Nobel Prize in 1935 for his discovery of the neutron. Starting with Rutherford's work, Chadwick continued experimenting to determine the excess mass in the nucleus that wasn't accounted for by protons. He found that neutrally charged particles, dubbed neutrons, were also inside the nucleus.

===The Current Model: Quantum Physics and Electron Orbitals===
Erwin Schrödinger examined the possibility that moving electrons behaved more like waves than particles, and published "Schrödinger's Equation" in 1926. Although this resolved many issues encountered with the Bohr model, it faced opposition from physicist [[Max Born]]. Instead, Born suggested a wave-particle duality of electrons, which stated that electrons could behave both like a wave and a particle.
As electrons were now given properties of waves, it was impossible to simultaneously determine an electron's exact location and momentum around the nucleus. Werner Heisenberg, first described this phenomena in 1927, and it was later named the Heisenberg Uncertainty Principle. This refuted the Bohr model of the atom, and replaced it with a pattern of probabilities as to where electrons are located around the nucleus. These patterns are referred to as atomic orbitals and come in a variety of shapes (basic spheres, rings, dumbbells, etc.) and the nucleus is always at the center.
[[File:Neon_orbitals.JPG|thumb|center|The first five atomic orbitals: 1s, 2s, 2px, 2py, and 2pz.]]

==Connectedness==
While classical physics applies to large objects moving much slower than the speed of light, modern physics deals with special cases of tiny objects, like atoms, subject to relativistic effects. Atomic theory is vital to understanding many quantum physics concepts that are covered in both Physics 2211 and 2212, like the ball-and-spring model of solids, point charges, and conductivity.

Although one can argue physics applies to just about every aspect of life, and atomic theory is critical to understanding physics, atomic theory has directly influenced material science, power generation, electronics, and even food processing, to name a few.

<gallery>
File:Apollo_synthetic_diamond.jpg|'''Material Science:''' Synthetic diamonds are used for both cosmetic retail and in manufacturing cutting tools.
File:Electrical_and_Mechanical_Services_Department_Headquarters_Photovoltaics.jpg|'''Power:''' Solar cells and power rely on the photovoltaic effect and the wave-particle duality of subatomic particles (like photons).
File:Monokristalines_Silizium_f%C3%BCr_die_Waferherstellung.jpg|'''Electronics:''' Silicon, a popular semiconductor used in electronics, is produced industrially in a single-crystal form.
File:Sodium-chloride-3D-ionic.png|'''Food processing:''' An atomic view of table salt. Purple particles are sodium (Na), and green particles are chlorine (Cl).
File:Nagasakibomb.jpg|'''Defense:''' Nuclear weapons were used during World War II.
File:White_Matter_Connections_Obtained_with_MRI_Tractography.png|'''Medicine:''' MRI's provide doctors critical information without the risks of surgery.
File:Plastic_household_items.jpg|'''Manufacturing:''' Many common household items are made with plastic.
</gallery>

== See also ==

*[[Bohr Model]]
*[[Electronic Energy Levels and Photons]]
*[[Rutherford Experiment and Atomic Collisions]]

===Notable Scientists===
*[[Amedeo Avogadro]]
*[[J.J. Thomson]]
*[[Ernest Rutherford]]
*[[Albert Einstein]]
*[[Max Planck]]
*[[Niels Bohr]]
*[[Max Born]]

===Related Theories===
*[[Quantum Theory]]
*[[Einstein's Theory of Special Relativity]]

===Concept Application===
*[[Ball and Spring Model of Matter]], [[Ball and Spring Model]]
*[[Length and Stiffness of an Interatomic Bond]], [[Young's Modulus]]
*[[Density]], [[Charge]], [[Spin]], and [[Conductivity]]
*[[The Photoelectric Effect]], [[Photons]]
*[[Rest Mass Energy]]
*[[Potential Energy of a Pair of Neutral Atoms]]

===External links===
*Physics Portal description of [https://en.wikipedia.org/wiki/History_of_molecular_theory Molecular Theory] and [https://en.wikipedia.org/wiki/Elementary_particle Subatomic Particles]
*HyperPhysics summary of [http://hyperphysics.phy-astr.gsu.edu/hbase/quacon.html#quacon Quantum Physics]
*Demonstration of the [https://phet.colorado.edu/en/simulation/legacy/hydrogen-atom various models] of a hydrogen atom

==References==

Chapter 30 of [https://openstaxcollege.org/files/textbook_version/hi_res_pdf/9/CollegePhysics-OP.pdf OpenStax Textbook]

Physics Portal page on [https://en.wikipedia.org/wiki/Atomic_theory Atomic Theory]

[[Category: Theory]]

Atomic Theory

2022-04-17T22:28:31Z

Erinhorbacz: /* A Computational Model */

Claimed by: Erin Horbacz (4/17/2022)

Atomic theory states that matter is composed of discrete units, called atoms. The word "atom" comes from the Greek word for uncuttable, ''atomos''. Scientists later discovered that atoms were indeed able to be broken into subatomic, or elementary, particles including protons, neutrons, and electrons. Atomic theory has evolved greatly over time, but the most recent model stems from quantum mechanics.

==The Main Idea==
===A Mathematical Model===
===A Computational Model===
Understanding the composition and structure of atoms is essential to the study of both microscopic and macroscopic systems. Researchers have made use of atomic information to create what are called atomistic models. These models are used to predict and analyze the behavior of complex systems through knowledge of their most fundamental parts. By understanding how atomic structure affects characteristic properties of atoms, scientists are able to create computational models based on simple microscopic characteristics that simulate complex macroscopic systems. In doing so, they aim to better understand the connection between these macroscopic systems and the underlying atomic structures that govern them.

Use of simulations in research has broadened both the volume and complexity of analysis that can be done at any one time. The ability to model atoms through simulations has been an integral part of the research done in diverse areas of science, notably materials science. In this field, atomistic models are often used to predict material properties under certain conditions using information about their nucleus and electron density. For example, professor ABFIEJABF of the physics department of Georgia Tech created an atomistic model that simulates the behavior of atoms in ABFIEJABF. Another use of atomistic models is to simulate and analyze important processes such as a nuclear chain reaction; an example of such a simulation can be viewed on [https://javalab.org/en/nuclear_chain_reaction_en/ JavaLab].

Atomistic models use the mathematical models discussed above to computationally represent atomic forces, atomic positions, velocities, and magnetic charges of atoms among other things. The result is an accurate model of quantum processes. Ultimately, the use of such simulations help to understand the collective behavior of atoms and how this behavior affects macroscopic processes (such as deformation and phase change) as well as performance abilities (such as strength of material).

==History==

===John Dalton: The Law of Multiple Proportions and Atomic Mass===
[[File:Daltons_symbols.gif|thumb|Dalton's concept of atoms and molecules]]
Working from the conservation of mass principle, chemist John Dalton determined the law of multiple proportions to understand how different elements combined in compounds. In 1803, he proposed that each element of the periodic table was composed of identical components, atoms, that were unique to each element. He also suggested that these atoms were not created nor destroyed when one element was combined with another. Dalton's empirical, experimentally-based work marked the first scientific theory of the atom.

Dalton proposed a list of atomic weights in 1805. However, Dalton failed to recognize natural tendencies of elements in nature (for example, oxygen typically exists as a diatomic molecule as <math>\text{O}_2</math>). Dalton was unable to distinguish between atoms and molecules (groups of atoms).

===Amedeo Avogadro: Avogadro's Law===
In 1811, [[Amedeo Avogadro]] studied gases and determined that the amount of volume a gas occupies is not determined by the mass of the gas. This allowed Avogadro to take more accurate atomic measurements of gases than Dalton, and differentiate atoms from molecules.

===Robert Brown: Brownian Motion===
A Scottish botanist, Robert Brown, studied the motion of tiny pollen particles in water in 1827. The particles followed complex paths, dubbed Brownian Motion. As early as 1905, [[Albert Einstein]] used Brownian Motion to predict the size of atoms and molecules.

===J.J. Thomson: The Plum-Pudding Model and Electrons===
[[File:Plum_pudding_model.svg|thumb|Tomson's Plum-Pudding Model]]
Through his work with cathode rays, [[J.J. Thomson]] discovered the electron in 1897, and was the first to learn that atoms weren't actually "uncuttable" as initially thought. Thomson knew that atoms had a net neutral charge, but he only knew that negative particles existed. Thus, Thomson developed the "plum-pudding" model of negatively charged electrons floating in a sea of positive charge. (He likened the relationship of electrons to the sea of positive charge to that of plums in plum pudding.)

===Ernest Rutherford: Gold Foil Experiment and the Nucleus===
In 1909, one of Thomson's students, [[Ernest Rutherford]], determined that the positive charge of atoms was located in a central nucleus. He shot small, positively charged alpha particles at thin sheets of gold foil and noted that some particles were sharply deflected. This deflection could only occur if the positive components of atoms were located in a small area, which Rutherford assumed to be the center. He proposed a planetary model of atoms where a cloud of electrons surrounded a central, positively charged nucleus.

===Niels Bohr: Introducing Quantum Physics===
[[File:Bohr_atom_animation_2.gif|thumb|The Bohr model for a Hydrogen atom with its electron moving between energy levels]]
As quantum mechanics progressed through the work of [[Albert Einstein]] and [[Max Planck]], [[Niels Bohr]] updated the atomic model in 1913 to account for quantum phenomena. Bohr, who was also one of Rutherford's students, suggested that electrostatic forces kept electrons in circular orbit around the positively charged central nucleus. In support of his theory, Bohr examined the behavior of electrons in hydrogen molecules and noted that they followed distinct energy levels. When an electron changed energy levels, it gained or lost energy, which could be emitted in the form of light. While the Bohr model holds true for hydrogen, it isn't accurate for multi-electron elements.

===James Chadwick: Neutrons===
James Chadwick won a Nobel Prize in 1935 for his discovery of the neutron. Starting with Rutherford's work, Chadwick continued experimenting to determine the excess mass in the nucleus that wasn't accounted for by protons. He found that neutrally charged particles, dubbed neutrons, were also inside the nucleus.

===The Current Model: Quantum Physics and Electron Orbitals===
Erwin Schrödinger examined the possibility that moving electrons behaved more like waves than particles, and published "Schrödinger's Equation" in 1926. Although this resolved many issues encountered with the Bohr model, it faced opposition from physicist [[Max Born]]. Instead, Born suggested a wave-particle duality of electrons, which stated that electrons could behave both like a wave and a particle.
As electrons were now given properties of waves, it was impossible to simultaneously determine an electron's exact location and momentum around the nucleus. Werner Heisenberg, first described this phenomena in 1927, and it was later named the Heisenberg Uncertainty Principle. This refuted the Bohr model of the atom, and replaced it with a pattern of probabilities as to where electrons are located around the nucleus. These patterns are referred to as atomic orbitals and come in a variety of shapes (basic spheres, rings, dumbbells, etc.) and the nucleus is always at the center.
[[File:Neon_orbitals.JPG|thumb|center|The first five atomic orbitals: 1s, 2s, 2px, 2py, and 2pz.]]

==Connectedness==
While classical physics applies to large objects moving much slower than the speed of light, modern physics deals with special cases of tiny objects, like atoms, subject to relativistic effects. Atomic theory is vital to understanding many quantum physics concepts that are covered in both Physics 2211 and 2212, like the ball-and-spring model of solids, point charges, and conductivity.

Although one can argue physics applies to just about every aspect of life, and atomic theory is critical to understanding physics, atomic theory has directly influenced material science, power generation, electronics, and even food processing, to name a few.

<gallery>
File:Apollo_synthetic_diamond.jpg|'''Material Science:''' Synthetic diamonds are used for both cosmetic retail and in manufacturing cutting tools.
File:Electrical_and_Mechanical_Services_Department_Headquarters_Photovoltaics.jpg|'''Power:''' Solar cells and power rely on the photovoltaic effect and the wave-particle duality of subatomic particles (like photons).
File:Monokristalines_Silizium_f%C3%BCr_die_Waferherstellung.jpg|'''Electronics:''' Silicon, a popular semiconductor used in electronics, is produced industrially in a single-crystal form.
File:Sodium-chloride-3D-ionic.png|'''Food processing:''' An atomic view of table salt. Purple particles are sodium (Na), and green particles are chlorine (Cl).
File:Nagasakibomb.jpg|'''Defense:''' Nuclear weapons were used during World War II.
File:White_Matter_Connections_Obtained_with_MRI_Tractography.png|'''Medicine:''' MRI's provide doctors critical information without the risks of surgery.
File:Plastic_household_items.jpg|'''Manufacturing:''' Many common household items are made with plastic.
</gallery>

== See also ==

*[[Bohr Model]]
*[[Electronic Energy Levels and Photons]]
*[[Rutherford Experiment and Atomic Collisions]]

===Notable Scientists===
*[[Amedeo Avogadro]]
*[[J.J. Thomson]]
*[[Ernest Rutherford]]
*[[Albert Einstein]]
*[[Max Planck]]
*[[Niels Bohr]]
*[[Max Born]]

===Related Theories===
*[[Quantum Theory]]
*[[Einstein's Theory of Special Relativity]]

===Concept Application===
*[[Ball and Spring Model of Matter]], [[Ball and Spring Model]]
*[[Length and Stiffness of an Interatomic Bond]], [[Young's Modulus]]
*[[Density]], [[Charge]], [[Spin]], and [[Conductivity]]
*[[The Photoelectric Effect]], [[Photons]]
*[[Rest Mass Energy]]
*[[Potential Energy of a Pair of Neutral Atoms]]

===External links===
*Physics Portal description of [https://en.wikipedia.org/wiki/History_of_molecular_theory Molecular Theory] and [https://en.wikipedia.org/wiki/Elementary_particle Subatomic Particles]
*HyperPhysics summary of [http://hyperphysics.phy-astr.gsu.edu/hbase/quacon.html#quacon Quantum Physics]
*Demonstration of the [https://phet.colorado.edu/en/simulation/legacy/hydrogen-atom various models] of a hydrogen atom

==References==

Chapter 30 of [https://openstaxcollege.org/files/textbook_version/hi_res_pdf/9/CollegePhysics-OP.pdf OpenStax Textbook]

Physics Portal page on [https://en.wikipedia.org/wiki/Atomic_theory Atomic Theory]

[[Category: Theory]]

Atomic Theory

2022-04-17T22:24:23Z

Erinhorbacz: /* A Computational Model */

Claimed by: Erin Horbacz (4/17/2022)

Atomic theory states that matter is composed of discrete units, called atoms. The word "atom" comes from the Greek word for uncuttable, ''atomos''. Scientists later discovered that atoms were indeed able to be broken into subatomic, or elementary, particles including protons, neutrons, and electrons. Atomic theory has evolved greatly over time, but the most recent model stems from quantum mechanics.

==The Main Idea==
===A Mathematical Model===
===A Computational Model===
Understanding the composition and structure of atoms is essential to the study of both microscopic and macroscopic systems. Researchers have made use of atomic information to create what are called atomistic models. These models are used to predict and analyze the behavior of complex systems through knowledge of their most fundamental parts. By understanding how atomic structure affects characteristic properties of atoms, scientists are able to create computational models based on simple microscopic characteristics that simulate complex macroscopic systems. In doing so, they aim to better understand the connection between these macroscopic systems and the underlying atomic structures that govern them.

Use of simulations in research has broadened both the volume and complexity of analysis that can be done at any one time. The ability to model atoms through simulations has been an integral part of the research done in diverse areas of science, notably materials science. In this field, atomistic models are often used to predict material properties under certain conditions using information about their nucleus and electron density. For example, professor ABFIEJABF of the physics department of Georgia Tech created an atomistic model that simulates the behavior of atoms in ABFIEJABF. Another use of atomistic models is to simulate and analyze important processes such as a nuclear chain reaction; an example of such a simulation can be viewed on [https://javalab.org/en/nuclear_chain_reaction_en/ JavaLab].

Atomistic models computationally represent atomic forces, atomic positions, velocities, and magnetic charges of atoms in order to accurately model quantum processes. Ultimately, the use of such simulations help to understand the collective behavior of atoms and how this behavior affects macroscopic processes (such as deformation and phase change) as well as performance abilities (such as strength of material).

==History==

===John Dalton: The Law of Multiple Proportions and Atomic Mass===
[[File:Daltons_symbols.gif|thumb|Dalton's concept of atoms and molecules]]
Working from the conservation of mass principle, chemist John Dalton determined the law of multiple proportions to understand how different elements combined in compounds. In 1803, he proposed that each element of the periodic table was composed of identical components, atoms, that were unique to each element. He also suggested that these atoms were not created nor destroyed when one element was combined with another. Dalton's empirical, experimentally-based work marked the first scientific theory of the atom.

Dalton proposed a list of atomic weights in 1805. However, Dalton failed to recognize natural tendencies of elements in nature (for example, oxygen typically exists as a diatomic molecule as <math>\text{O}_2</math>). Dalton was unable to distinguish between atoms and molecules (groups of atoms).

===Amedeo Avogadro: Avogadro's Law===
In 1811, [[Amedeo Avogadro]] studied gases and determined that the amount of volume a gas occupies is not determined by the mass of the gas. This allowed Avogadro to take more accurate atomic measurements of gases than Dalton, and differentiate atoms from molecules.

===Robert Brown: Brownian Motion===
A Scottish botanist, Robert Brown, studied the motion of tiny pollen particles in water in 1827. The particles followed complex paths, dubbed Brownian Motion. As early as 1905, [[Albert Einstein]] used Brownian Motion to predict the size of atoms and molecules.

===J.J. Thomson: The Plum-Pudding Model and Electrons===
[[File:Plum_pudding_model.svg|thumb|Tomson's Plum-Pudding Model]]
Through his work with cathode rays, [[J.J. Thomson]] discovered the electron in 1897, and was the first to learn that atoms weren't actually "uncuttable" as initially thought. Thomson knew that atoms had a net neutral charge, but he only knew that negative particles existed. Thus, Thomson developed the "plum-pudding" model of negatively charged electrons floating in a sea of positive charge. (He likened the relationship of electrons to the sea of positive charge to that of plums in plum pudding.)

===Ernest Rutherford: Gold Foil Experiment and the Nucleus===
In 1909, one of Thomson's students, [[Ernest Rutherford]], determined that the positive charge of atoms was located in a central nucleus. He shot small, positively charged alpha particles at thin sheets of gold foil and noted that some particles were sharply deflected. This deflection could only occur if the positive components of atoms were located in a small area, which Rutherford assumed to be the center. He proposed a planetary model of atoms where a cloud of electrons surrounded a central, positively charged nucleus.

===Niels Bohr: Introducing Quantum Physics===
[[File:Bohr_atom_animation_2.gif|thumb|The Bohr model for a Hydrogen atom with its electron moving between energy levels]]
As quantum mechanics progressed through the work of [[Albert Einstein]] and [[Max Planck]], [[Niels Bohr]] updated the atomic model in 1913 to account for quantum phenomena. Bohr, who was also one of Rutherford's students, suggested that electrostatic forces kept electrons in circular orbit around the positively charged central nucleus. In support of his theory, Bohr examined the behavior of electrons in hydrogen molecules and noted that they followed distinct energy levels. When an electron changed energy levels, it gained or lost energy, which could be emitted in the form of light. While the Bohr model holds true for hydrogen, it isn't accurate for multi-electron elements.

===James Chadwick: Neutrons===
James Chadwick won a Nobel Prize in 1935 for his discovery of the neutron. Starting with Rutherford's work, Chadwick continued experimenting to determine the excess mass in the nucleus that wasn't accounted for by protons. He found that neutrally charged particles, dubbed neutrons, were also inside the nucleus.

===The Current Model: Quantum Physics and Electron Orbitals===
Erwin Schrödinger examined the possibility that moving electrons behaved more like waves than particles, and published "Schrödinger's Equation" in 1926. Although this resolved many issues encountered with the Bohr model, it faced opposition from physicist [[Max Born]]. Instead, Born suggested a wave-particle duality of electrons, which stated that electrons could behave both like a wave and a particle.
As electrons were now given properties of waves, it was impossible to simultaneously determine an electron's exact location and momentum around the nucleus. Werner Heisenberg, first described this phenomena in 1927, and it was later named the Heisenberg Uncertainty Principle. This refuted the Bohr model of the atom, and replaced it with a pattern of probabilities as to where electrons are located around the nucleus. These patterns are referred to as atomic orbitals and come in a variety of shapes (basic spheres, rings, dumbbells, etc.) and the nucleus is always at the center.
[[File:Neon_orbitals.JPG|thumb|center|The first five atomic orbitals: 1s, 2s, 2px, 2py, and 2pz.]]

==Connectedness==
While classical physics applies to large objects moving much slower than the speed of light, modern physics deals with special cases of tiny objects, like atoms, subject to relativistic effects. Atomic theory is vital to understanding many quantum physics concepts that are covered in both Physics 2211 and 2212, like the ball-and-spring model of solids, point charges, and conductivity.

Although one can argue physics applies to just about every aspect of life, and atomic theory is critical to understanding physics, atomic theory has directly influenced material science, power generation, electronics, and even food processing, to name a few.

<gallery>
File:Apollo_synthetic_diamond.jpg|'''Material Science:''' Synthetic diamonds are used for both cosmetic retail and in manufacturing cutting tools.
File:Electrical_and_Mechanical_Services_Department_Headquarters_Photovoltaics.jpg|'''Power:''' Solar cells and power rely on the photovoltaic effect and the wave-particle duality of subatomic particles (like photons).
File:Monokristalines_Silizium_f%C3%BCr_die_Waferherstellung.jpg|'''Electronics:''' Silicon, a popular semiconductor used in electronics, is produced industrially in a single-crystal form.
File:Sodium-chloride-3D-ionic.png|'''Food processing:''' An atomic view of table salt. Purple particles are sodium (Na), and green particles are chlorine (Cl).
File:Nagasakibomb.jpg|'''Defense:''' Nuclear weapons were used during World War II.
File:White_Matter_Connections_Obtained_with_MRI_Tractography.png|'''Medicine:''' MRI's provide doctors critical information without the risks of surgery.
File:Plastic_household_items.jpg|'''Manufacturing:''' Many common household items are made with plastic.
</gallery>

== See also ==

*[[Bohr Model]]
*[[Electronic Energy Levels and Photons]]
*[[Rutherford Experiment and Atomic Collisions]]

===Notable Scientists===
*[[Amedeo Avogadro]]
*[[J.J. Thomson]]
*[[Ernest Rutherford]]
*[[Albert Einstein]]
*[[Max Planck]]
*[[Niels Bohr]]
*[[Max Born]]

===Related Theories===
*[[Quantum Theory]]
*[[Einstein's Theory of Special Relativity]]

===Concept Application===
*[[Ball and Spring Model of Matter]], [[Ball and Spring Model]]
*[[Length and Stiffness of an Interatomic Bond]], [[Young's Modulus]]
*[[Density]], [[Charge]], [[Spin]], and [[Conductivity]]
*[[The Photoelectric Effect]], [[Photons]]
*[[Rest Mass Energy]]
*[[Potential Energy of a Pair of Neutral Atoms]]

===External links===
*Physics Portal description of [https://en.wikipedia.org/wiki/History_of_molecular_theory Molecular Theory] and [https://en.wikipedia.org/wiki/Elementary_particle Subatomic Particles]
*HyperPhysics summary of [http://hyperphysics.phy-astr.gsu.edu/hbase/quacon.html#quacon Quantum Physics]
*Demonstration of the [https://phet.colorado.edu/en/simulation/legacy/hydrogen-atom various models] of a hydrogen atom

==References==

Chapter 30 of [https://openstaxcollege.org/files/textbook_version/hi_res_pdf/9/CollegePhysics-OP.pdf OpenStax Textbook]

Physics Portal page on [https://en.wikipedia.org/wiki/Atomic_theory Atomic Theory]

[[Category: Theory]]

Atomic Theory

2022-04-17T22:17:47Z

Erinhorbacz: /* A Computational Model */

Claimed by: Erin Horbacz (4/17/2022)

Atomic theory states that matter is composed of discrete units, called atoms. The word "atom" comes from the Greek word for uncuttable, ''atomos''. Scientists later discovered that atoms were indeed able to be broken into subatomic, or elementary, particles including protons, neutrons, and electrons. Atomic theory has evolved greatly over time, but the most recent model stems from quantum mechanics.

==The Main Idea==
===A Mathematical Model===
===A Computational Model===
Understanding the composition and structure of atoms is essential to the study of both microscopic and macroscopic systems. Researchers have made use of atomic information to create what are called atomistic models. These models are used to predict and analyze the behavior of complex systems through knowledge of their most fundamental parts. By understanding how atomic structure affects characteristic properties of atoms, scientists are able to create computational models based on simple microscopic characteristics that simulate complex macroscopic systems. In doing so, they aim to better understand the connection between these macroscopic systems and the underlying atomic structures that govern them.
Use of simulations in research has broadened both the volume and complexity of analysis that can be done at any one time. The ability to model atoms through simulations has been an integral part of the research done in diverse areas of science, notably materials science. In this field, atomistic models are often used to predict material properties under certain conditions using information about their nucleus and electron density. For example, professor ABFIEJABF of the physics department of Georgia Tech created an atomistic model that simulates the behavior of atoms in ABFIEJABF. Another use of atomistic models is to simulate and analyze important processes such as a nuclear chain reaction; an example of such a simulation can be viewed on [https://javalab.org/en/nuclear_chain_reaction_en/ JavaLab].

Ultimately, the use of such simulations help to understand the collective behavior of atoms and how this behavior affects macroscopic processes (such as deformation and phase change) as well as performance abilities (such as strength of material).

==History==

===John Dalton: The Law of Multiple Proportions and Atomic Mass===
[[File:Daltons_symbols.gif|thumb|Dalton's concept of atoms and molecules]]
Working from the conservation of mass principle, chemist John Dalton determined the law of multiple proportions to understand how different elements combined in compounds. In 1803, he proposed that each element of the periodic table was composed of identical components, atoms, that were unique to each element. He also suggested that these atoms were not created nor destroyed when one element was combined with another. Dalton's empirical, experimentally-based work marked the first scientific theory of the atom.

Dalton proposed a list of atomic weights in 1805. However, Dalton failed to recognize natural tendencies of elements in nature (for example, oxygen typically exists as a diatomic molecule as <math>\text{O}_2</math>). Dalton was unable to distinguish between atoms and molecules (groups of atoms).

===Amedeo Avogadro: Avogadro's Law===
In 1811, [[Amedeo Avogadro]] studied gases and determined that the amount of volume a gas occupies is not determined by the mass of the gas. This allowed Avogadro to take more accurate atomic measurements of gases than Dalton, and differentiate atoms from molecules.

===Robert Brown: Brownian Motion===
A Scottish botanist, Robert Brown, studied the motion of tiny pollen particles in water in 1827. The particles followed complex paths, dubbed Brownian Motion. As early as 1905, [[Albert Einstein]] used Brownian Motion to predict the size of atoms and molecules.

===J.J. Thomson: The Plum-Pudding Model and Electrons===
[[File:Plum_pudding_model.svg|thumb|Tomson's Plum-Pudding Model]]
Through his work with cathode rays, [[J.J. Thomson]] discovered the electron in 1897, and was the first to learn that atoms weren't actually "uncuttable" as initially thought. Thomson knew that atoms had a net neutral charge, but he only knew that negative particles existed. Thus, Thomson developed the "plum-pudding" model of negatively charged electrons floating in a sea of positive charge. (He likened the relationship of electrons to the sea of positive charge to that of plums in plum pudding.)

===Ernest Rutherford: Gold Foil Experiment and the Nucleus===
In 1909, one of Thomson's students, [[Ernest Rutherford]], determined that the positive charge of atoms was located in a central nucleus. He shot small, positively charged alpha particles at thin sheets of gold foil and noted that some particles were sharply deflected. This deflection could only occur if the positive components of atoms were located in a small area, which Rutherford assumed to be the center. He proposed a planetary model of atoms where a cloud of electrons surrounded a central, positively charged nucleus.

===Niels Bohr: Introducing Quantum Physics===
[[File:Bohr_atom_animation_2.gif|thumb|The Bohr model for a Hydrogen atom with its electron moving between energy levels]]
As quantum mechanics progressed through the work of [[Albert Einstein]] and [[Max Planck]], [[Niels Bohr]] updated the atomic model in 1913 to account for quantum phenomena. Bohr, who was also one of Rutherford's students, suggested that electrostatic forces kept electrons in circular orbit around the positively charged central nucleus. In support of his theory, Bohr examined the behavior of electrons in hydrogen molecules and noted that they followed distinct energy levels. When an electron changed energy levels, it gained or lost energy, which could be emitted in the form of light. While the Bohr model holds true for hydrogen, it isn't accurate for multi-electron elements.

===James Chadwick: Neutrons===
James Chadwick won a Nobel Prize in 1935 for his discovery of the neutron. Starting with Rutherford's work, Chadwick continued experimenting to determine the excess mass in the nucleus that wasn't accounted for by protons. He found that neutrally charged particles, dubbed neutrons, were also inside the nucleus.

===The Current Model: Quantum Physics and Electron Orbitals===
Erwin Schrödinger examined the possibility that moving electrons behaved more like waves than particles, and published "Schrödinger's Equation" in 1926. Although this resolved many issues encountered with the Bohr model, it faced opposition from physicist [[Max Born]]. Instead, Born suggested a wave-particle duality of electrons, which stated that electrons could behave both like a wave and a particle.
As electrons were now given properties of waves, it was impossible to simultaneously determine an electron's exact location and momentum around the nucleus. Werner Heisenberg, first described this phenomena in 1927, and it was later named the Heisenberg Uncertainty Principle. This refuted the Bohr model of the atom, and replaced it with a pattern of probabilities as to where electrons are located around the nucleus. These patterns are referred to as atomic orbitals and come in a variety of shapes (basic spheres, rings, dumbbells, etc.) and the nucleus is always at the center.
[[File:Neon_orbitals.JPG|thumb|center|The first five atomic orbitals: 1s, 2s, 2px, 2py, and 2pz.]]

==Connectedness==
While classical physics applies to large objects moving much slower than the speed of light, modern physics deals with special cases of tiny objects, like atoms, subject to relativistic effects. Atomic theory is vital to understanding many quantum physics concepts that are covered in both Physics 2211 and 2212, like the ball-and-spring model of solids, point charges, and conductivity.

Although one can argue physics applies to just about every aspect of life, and atomic theory is critical to understanding physics, atomic theory has directly influenced material science, power generation, electronics, and even food processing, to name a few.

<gallery>
File:Apollo_synthetic_diamond.jpg|'''Material Science:''' Synthetic diamonds are used for both cosmetic retail and in manufacturing cutting tools.
File:Electrical_and_Mechanical_Services_Department_Headquarters_Photovoltaics.jpg|'''Power:''' Solar cells and power rely on the photovoltaic effect and the wave-particle duality of subatomic particles (like photons).
File:Monokristalines_Silizium_f%C3%BCr_die_Waferherstellung.jpg|'''Electronics:''' Silicon, a popular semiconductor used in electronics, is produced industrially in a single-crystal form.
File:Sodium-chloride-3D-ionic.png|'''Food processing:''' An atomic view of table salt. Purple particles are sodium (Na), and green particles are chlorine (Cl).
File:Nagasakibomb.jpg|'''Defense:''' Nuclear weapons were used during World War II.
File:White_Matter_Connections_Obtained_with_MRI_Tractography.png|'''Medicine:''' MRI's provide doctors critical information without the risks of surgery.
File:Plastic_household_items.jpg|'''Manufacturing:''' Many common household items are made with plastic.
</gallery>

== See also ==

*[[Bohr Model]]
*[[Electronic Energy Levels and Photons]]
*[[Rutherford Experiment and Atomic Collisions]]

===Notable Scientists===
*[[Amedeo Avogadro]]
*[[J.J. Thomson]]
*[[Ernest Rutherford]]
*[[Albert Einstein]]
*[[Max Planck]]
*[[Niels Bohr]]
*[[Max Born]]

===Related Theories===
*[[Quantum Theory]]
*[[Einstein's Theory of Special Relativity]]

===Concept Application===
*[[Ball and Spring Model of Matter]], [[Ball and Spring Model]]
*[[Length and Stiffness of an Interatomic Bond]], [[Young's Modulus]]
*[[Density]], [[Charge]], [[Spin]], and [[Conductivity]]
*[[The Photoelectric Effect]], [[Photons]]
*[[Rest Mass Energy]]
*[[Potential Energy of a Pair of Neutral Atoms]]

===External links===
*Physics Portal description of [https://en.wikipedia.org/wiki/History_of_molecular_theory Molecular Theory] and [https://en.wikipedia.org/wiki/Elementary_particle Subatomic Particles]
*HyperPhysics summary of [http://hyperphysics.phy-astr.gsu.edu/hbase/quacon.html#quacon Quantum Physics]
*Demonstration of the [https://phet.colorado.edu/en/simulation/legacy/hydrogen-atom various models] of a hydrogen atom

==References==

Chapter 30 of [https://openstaxcollege.org/files/textbook_version/hi_res_pdf/9/CollegePhysics-OP.pdf OpenStax Textbook]

Physics Portal page on [https://en.wikipedia.org/wiki/Atomic_theory Atomic Theory]

[[Category: Theory]]

Atomic Theory

2022-04-17T22:03:31Z

Erinhorbacz: /* A Computational Model */

Claimed by: Erin Horbacz (4/17/2022)

Atomic theory states that matter is composed of discrete units, called atoms. The word "atom" comes from the Greek word for uncuttable, ''atomos''. Scientists later discovered that atoms were indeed able to be broken into subatomic, or elementary, particles including protons, neutrons, and electrons. Atomic theory has evolved greatly over time, but the most recent model stems from quantum mechanics.

==The Main Idea==
===A Mathematical Model===
===A Computational Model===
Understanding the composition and structure of atoms is essential to the study of both microscopic and macroscopic systems. Researchers have made use of atomic information to create what are called atomistic models. These models are used to predict and analyze the behavior of complex systems through knowledge of their most fundamental parts. By understanding how atomic structure affects characteristic properties of atoms, scientists are able to create computational models based on simple microscopic characteristics that simulate complex macroscopic systems. In doing so, they aim to better understand the connection between these macroscopic systems and the underlying atomic structures that govern them.
Use of simulations in research has broadened both the volume and complexity of analysis that can be done at any one time. The ability to model atoms through simulations has been an integral part of the research done in diverse areas of science, notably materials science. In this field, atomistic models are often used to predict material properties under certain conditions using information about their nucleus and electron density. For example, professor ABFIEJABF of the physics department of Georgia Tech created an atomistic model that simulates the behavior of atoms in ABFIEJABF. Another use of atomistic models is to simulate and analyze important processes such as a nuclear chain reaction.

[[File:https://javalab.org/en/nuclear_chain_reaction_en/|thumb|Caption]]

Ultimately, the use of such simulations help to understand the collective behavior of atoms and how this behavior affects macroscopic processes (such as deformation and phase change) as well as performance abilities (such as strength of material).

==History==

===John Dalton: The Law of Multiple Proportions and Atomic Mass===
[[File:Daltons_symbols.gif|thumb|Dalton's concept of atoms and molecules]]
Working from the conservation of mass principle, chemist John Dalton determined the law of multiple proportions to understand how different elements combined in compounds. In 1803, he proposed that each element of the periodic table was composed of identical components, atoms, that were unique to each element. He also suggested that these atoms were not created nor destroyed when one element was combined with another. Dalton's empirical, experimentally-based work marked the first scientific theory of the atom.

Dalton proposed a list of atomic weights in 1805. However, Dalton failed to recognize natural tendencies of elements in nature (for example, oxygen typically exists as a diatomic molecule as <math>\text{O}_2</math>). Dalton was unable to distinguish between atoms and molecules (groups of atoms).

===Amedeo Avogadro: Avogadro's Law===
In 1811, [[Amedeo Avogadro]] studied gases and determined that the amount of volume a gas occupies is not determined by the mass of the gas. This allowed Avogadro to take more accurate atomic measurements of gases than Dalton, and differentiate atoms from molecules.

===Robert Brown: Brownian Motion===
A Scottish botanist, Robert Brown, studied the motion of tiny pollen particles in water in 1827. The particles followed complex paths, dubbed Brownian Motion. As early as 1905, [[Albert Einstein]] used Brownian Motion to predict the size of atoms and molecules.

===J.J. Thomson: The Plum-Pudding Model and Electrons===
[[File:Plum_pudding_model.svg|thumb|Tomson's Plum-Pudding Model]]
Through his work with cathode rays, [[J.J. Thomson]] discovered the electron in 1897, and was the first to learn that atoms weren't actually "uncuttable" as initially thought. Thomson knew that atoms had a net neutral charge, but he only knew that negative particles existed. Thus, Thomson developed the "plum-pudding" model of negatively charged electrons floating in a sea of positive charge. (He likened the relationship of electrons to the sea of positive charge to that of plums in plum pudding.)

===Ernest Rutherford: Gold Foil Experiment and the Nucleus===
In 1909, one of Thomson's students, [[Ernest Rutherford]], determined that the positive charge of atoms was located in a central nucleus. He shot small, positively charged alpha particles at thin sheets of gold foil and noted that some particles were sharply deflected. This deflection could only occur if the positive components of atoms were located in a small area, which Rutherford assumed to be the center. He proposed a planetary model of atoms where a cloud of electrons surrounded a central, positively charged nucleus.

===Niels Bohr: Introducing Quantum Physics===
[[File:Bohr_atom_animation_2.gif|thumb|The Bohr model for a Hydrogen atom with its electron moving between energy levels]]
As quantum mechanics progressed through the work of [[Albert Einstein]] and [[Max Planck]], [[Niels Bohr]] updated the atomic model in 1913 to account for quantum phenomena. Bohr, who was also one of Rutherford's students, suggested that electrostatic forces kept electrons in circular orbit around the positively charged central nucleus. In support of his theory, Bohr examined the behavior of electrons in hydrogen molecules and noted that they followed distinct energy levels. When an electron changed energy levels, it gained or lost energy, which could be emitted in the form of light. While the Bohr model holds true for hydrogen, it isn't accurate for multi-electron elements.

===James Chadwick: Neutrons===
James Chadwick won a Nobel Prize in 1935 for his discovery of the neutron. Starting with Rutherford's work, Chadwick continued experimenting to determine the excess mass in the nucleus that wasn't accounted for by protons. He found that neutrally charged particles, dubbed neutrons, were also inside the nucleus.

===The Current Model: Quantum Physics and Electron Orbitals===
Erwin Schrödinger examined the possibility that moving electrons behaved more like waves than particles, and published "Schrödinger's Equation" in 1926. Although this resolved many issues encountered with the Bohr model, it faced opposition from physicist [[Max Born]]. Instead, Born suggested a wave-particle duality of electrons, which stated that electrons could behave both like a wave and a particle.
As electrons were now given properties of waves, it was impossible to simultaneously determine an electron's exact location and momentum around the nucleus. Werner Heisenberg, first described this phenomena in 1927, and it was later named the Heisenberg Uncertainty Principle. This refuted the Bohr model of the atom, and replaced it with a pattern of probabilities as to where electrons are located around the nucleus. These patterns are referred to as atomic orbitals and come in a variety of shapes (basic spheres, rings, dumbbells, etc.) and the nucleus is always at the center.
[[File:Neon_orbitals.JPG|thumb|center|The first five atomic orbitals: 1s, 2s, 2px, 2py, and 2pz.]]

==Connectedness==
While classical physics applies to large objects moving much slower than the speed of light, modern physics deals with special cases of tiny objects, like atoms, subject to relativistic effects. Atomic theory is vital to understanding many quantum physics concepts that are covered in both Physics 2211 and 2212, like the ball-and-spring model of solids, point charges, and conductivity.

Although one can argue physics applies to just about every aspect of life, and atomic theory is critical to understanding physics, atomic theory has directly influenced material science, power generation, electronics, and even food processing, to name a few.

<gallery>
File:Apollo_synthetic_diamond.jpg|'''Material Science:''' Synthetic diamonds are used for both cosmetic retail and in manufacturing cutting tools.
File:Electrical_and_Mechanical_Services_Department_Headquarters_Photovoltaics.jpg|'''Power:''' Solar cells and power rely on the photovoltaic effect and the wave-particle duality of subatomic particles (like photons).
File:Monokristalines_Silizium_f%C3%BCr_die_Waferherstellung.jpg|'''Electronics:''' Silicon, a popular semiconductor used in electronics, is produced industrially in a single-crystal form.
File:Sodium-chloride-3D-ionic.png|'''Food processing:''' An atomic view of table salt. Purple particles are sodium (Na), and green particles are chlorine (Cl).
File:Nagasakibomb.jpg|'''Defense:''' Nuclear weapons were used during World War II.
File:White_Matter_Connections_Obtained_with_MRI_Tractography.png|'''Medicine:''' MRI's provide doctors critical information without the risks of surgery.
File:Plastic_household_items.jpg|'''Manufacturing:''' Many common household items are made with plastic.
</gallery>

== See also ==

*[[Bohr Model]]
*[[Electronic Energy Levels and Photons]]
*[[Rutherford Experiment and Atomic Collisions]]

===Notable Scientists===
*[[Amedeo Avogadro]]
*[[J.J. Thomson]]
*[[Ernest Rutherford]]
*[[Albert Einstein]]
*[[Max Planck]]
*[[Niels Bohr]]
*[[Max Born]]

===Related Theories===
*[[Quantum Theory]]
*[[Einstein's Theory of Special Relativity]]

===Concept Application===
*[[Ball and Spring Model of Matter]], [[Ball and Spring Model]]
*[[Length and Stiffness of an Interatomic Bond]], [[Young's Modulus]]
*[[Density]], [[Charge]], [[Spin]], and [[Conductivity]]
*[[The Photoelectric Effect]], [[Photons]]
*[[Rest Mass Energy]]
*[[Potential Energy of a Pair of Neutral Atoms]]

===External links===
*Physics Portal description of [https://en.wikipedia.org/wiki/History_of_molecular_theory Molecular Theory] and [https://en.wikipedia.org/wiki/Elementary_particle Subatomic Particles]
*HyperPhysics summary of [http://hyperphysics.phy-astr.gsu.edu/hbase/quacon.html#quacon Quantum Physics]
*Demonstration of the [https://phet.colorado.edu/en/simulation/legacy/hydrogen-atom various models] of a hydrogen atom

==References==

Chapter 30 of [https://openstaxcollege.org/files/textbook_version/hi_res_pdf/9/CollegePhysics-OP.pdf OpenStax Textbook]

Physics Portal page on [https://en.wikipedia.org/wiki/Atomic_theory Atomic Theory]

[[Category: Theory]]

Atomic Theory

2022-04-17T21:59:44Z

Erinhorbacz: /* A Computational Model */

Claimed by: Erin Horbacz (4/17/2022)

Atomic theory states that matter is composed of discrete units, called atoms. The word "atom" comes from the Greek word for uncuttable, ''atomos''. Scientists later discovered that atoms were indeed able to be broken into subatomic, or elementary, particles including protons, neutrons, and electrons. Atomic theory has evolved greatly over time, but the most recent model stems from quantum mechanics.

==The Main Idea==
===A Mathematical Model===
===A Computational Model===
Understanding the composition and structure of atoms is essential to the study of both microscopic and macroscopic systems. Researchers have made use of atomic information to create what are called atomistic models. These models are used to predict and analyze the behavior of complex systems through knowledge of their most fundamental parts. By understanding how atomic structure affects characteristic properties of atoms, scientists are able to create computational models based on simple microscopic characteristics that simulate complex macroscopic systems. In doing so, they aim to better understand the connection between these macroscopic systems and the underlying atomic structures that govern them.
Use of simulations in research has broadened both the volume and complexity of analysis that can be done at any one time. The ability to model atoms through simulations has been an integral part of the research done in diverse areas of science, notably materials science. In this field, atomistic models are often used to predict material properties under certain conditions using information about their nucleus and electron density. For example, professor ABFIEJABF of the physics department of Georgia Tech created an atomistic model that simulates the behavior of atoms in ABFIEJABF. Another use of atomistic models is to simulate and analyze important processes such as a nuclear chain reaction.

[[File:https://javalab.org/en/nuclear_chain_reaction_en/]]

Ultimately, the use of such simulations help to understand the collective behavior of atoms and how this behavior affects macroscopic processes (such as deformation and phase change) as well as performance abilities (such as strength of material).

==History==

===John Dalton: The Law of Multiple Proportions and Atomic Mass===
[[File:Daltons_symbols.gif|thumb|Dalton's concept of atoms and molecules]]
Working from the conservation of mass principle, chemist John Dalton determined the law of multiple proportions to understand how different elements combined in compounds. In 1803, he proposed that each element of the periodic table was composed of identical components, atoms, that were unique to each element. He also suggested that these atoms were not created nor destroyed when one element was combined with another. Dalton's empirical, experimentally-based work marked the first scientific theory of the atom.

Dalton proposed a list of atomic weights in 1805. However, Dalton failed to recognize natural tendencies of elements in nature (for example, oxygen typically exists as a diatomic molecule as <math>\text{O}_2</math>). Dalton was unable to distinguish between atoms and molecules (groups of atoms).

===Amedeo Avogadro: Avogadro's Law===
In 1811, [[Amedeo Avogadro]] studied gases and determined that the amount of volume a gas occupies is not determined by the mass of the gas. This allowed Avogadro to take more accurate atomic measurements of gases than Dalton, and differentiate atoms from molecules.

===Robert Brown: Brownian Motion===
A Scottish botanist, Robert Brown, studied the motion of tiny pollen particles in water in 1827. The particles followed complex paths, dubbed Brownian Motion. As early as 1905, [[Albert Einstein]] used Brownian Motion to predict the size of atoms and molecules.

===J.J. Thomson: The Plum-Pudding Model and Electrons===
[[File:Plum_pudding_model.svg|thumb|Tomson's Plum-Pudding Model]]
Through his work with cathode rays, [[J.J. Thomson]] discovered the electron in 1897, and was the first to learn that atoms weren't actually "uncuttable" as initially thought. Thomson knew that atoms had a net neutral charge, but he only knew that negative particles existed. Thus, Thomson developed the "plum-pudding" model of negatively charged electrons floating in a sea of positive charge. (He likened the relationship of electrons to the sea of positive charge to that of plums in plum pudding.)

===Ernest Rutherford: Gold Foil Experiment and the Nucleus===
In 1909, one of Thomson's students, [[Ernest Rutherford]], determined that the positive charge of atoms was located in a central nucleus. He shot small, positively charged alpha particles at thin sheets of gold foil and noted that some particles were sharply deflected. This deflection could only occur if the positive components of atoms were located in a small area, which Rutherford assumed to be the center. He proposed a planetary model of atoms where a cloud of electrons surrounded a central, positively charged nucleus.

===Niels Bohr: Introducing Quantum Physics===
[[File:Bohr_atom_animation_2.gif|thumb|The Bohr model for a Hydrogen atom with its electron moving between energy levels]]
As quantum mechanics progressed through the work of [[Albert Einstein]] and [[Max Planck]], [[Niels Bohr]] updated the atomic model in 1913 to account for quantum phenomena. Bohr, who was also one of Rutherford's students, suggested that electrostatic forces kept electrons in circular orbit around the positively charged central nucleus. In support of his theory, Bohr examined the behavior of electrons in hydrogen molecules and noted that they followed distinct energy levels. When an electron changed energy levels, it gained or lost energy, which could be emitted in the form of light. While the Bohr model holds true for hydrogen, it isn't accurate for multi-electron elements.

===James Chadwick: Neutrons===
James Chadwick won a Nobel Prize in 1935 for his discovery of the neutron. Starting with Rutherford's work, Chadwick continued experimenting to determine the excess mass in the nucleus that wasn't accounted for by protons. He found that neutrally charged particles, dubbed neutrons, were also inside the nucleus.

===The Current Model: Quantum Physics and Electron Orbitals===
Erwin Schrödinger examined the possibility that moving electrons behaved more like waves than particles, and published "Schrödinger's Equation" in 1926. Although this resolved many issues encountered with the Bohr model, it faced opposition from physicist [[Max Born]]. Instead, Born suggested a wave-particle duality of electrons, which stated that electrons could behave both like a wave and a particle.
As electrons were now given properties of waves, it was impossible to simultaneously determine an electron's exact location and momentum around the nucleus. Werner Heisenberg, first described this phenomena in 1927, and it was later named the Heisenberg Uncertainty Principle. This refuted the Bohr model of the atom, and replaced it with a pattern of probabilities as to where electrons are located around the nucleus. These patterns are referred to as atomic orbitals and come in a variety of shapes (basic spheres, rings, dumbbells, etc.) and the nucleus is always at the center.
[[File:Neon_orbitals.JPG|thumb|center|The first five atomic orbitals: 1s, 2s, 2px, 2py, and 2pz.]]

==Connectedness==
While classical physics applies to large objects moving much slower than the speed of light, modern physics deals with special cases of tiny objects, like atoms, subject to relativistic effects. Atomic theory is vital to understanding many quantum physics concepts that are covered in both Physics 2211 and 2212, like the ball-and-spring model of solids, point charges, and conductivity.

Although one can argue physics applies to just about every aspect of life, and atomic theory is critical to understanding physics, atomic theory has directly influenced material science, power generation, electronics, and even food processing, to name a few.

<gallery>
File:Apollo_synthetic_diamond.jpg|'''Material Science:''' Synthetic diamonds are used for both cosmetic retail and in manufacturing cutting tools.
File:Electrical_and_Mechanical_Services_Department_Headquarters_Photovoltaics.jpg|'''Power:''' Solar cells and power rely on the photovoltaic effect and the wave-particle duality of subatomic particles (like photons).
File:Monokristalines_Silizium_f%C3%BCr_die_Waferherstellung.jpg|'''Electronics:''' Silicon, a popular semiconductor used in electronics, is produced industrially in a single-crystal form.
File:Sodium-chloride-3D-ionic.png|'''Food processing:''' An atomic view of table salt. Purple particles are sodium (Na), and green particles are chlorine (Cl).
File:Nagasakibomb.jpg|'''Defense:''' Nuclear weapons were used during World War II.
File:White_Matter_Connections_Obtained_with_MRI_Tractography.png|'''Medicine:''' MRI's provide doctors critical information without the risks of surgery.
File:Plastic_household_items.jpg|'''Manufacturing:''' Many common household items are made with plastic.
</gallery>

== See also ==

*[[Bohr Model]]
*[[Electronic Energy Levels and Photons]]
*[[Rutherford Experiment and Atomic Collisions]]

===Notable Scientists===
*[[Amedeo Avogadro]]
*[[J.J. Thomson]]
*[[Ernest Rutherford]]
*[[Albert Einstein]]
*[[Max Planck]]
*[[Niels Bohr]]
*[[Max Born]]

===Related Theories===
*[[Quantum Theory]]
*[[Einstein's Theory of Special Relativity]]

===Concept Application===
*[[Ball and Spring Model of Matter]], [[Ball and Spring Model]]
*[[Length and Stiffness of an Interatomic Bond]], [[Young's Modulus]]
*[[Density]], [[Charge]], [[Spin]], and [[Conductivity]]
*[[The Photoelectric Effect]], [[Photons]]
*[[Rest Mass Energy]]
*[[Potential Energy of a Pair of Neutral Atoms]]

===External links===
*Physics Portal description of [https://en.wikipedia.org/wiki/History_of_molecular_theory Molecular Theory] and [https://en.wikipedia.org/wiki/Elementary_particle Subatomic Particles]
*HyperPhysics summary of [http://hyperphysics.phy-astr.gsu.edu/hbase/quacon.html#quacon Quantum Physics]
*Demonstration of the [https://phet.colorado.edu/en/simulation/legacy/hydrogen-atom various models] of a hydrogen atom

==References==

Chapter 30 of [https://openstaxcollege.org/files/textbook_version/hi_res_pdf/9/CollegePhysics-OP.pdf OpenStax Textbook]

Physics Portal page on [https://en.wikipedia.org/wiki/Atomic_theory Atomic Theory]

[[Category: Theory]]

Atomic Theory

2022-04-17T21:58:16Z

Erinhorbacz: /* A Computational Model */

Claimed by: Erin Horbacz (4/17/2022)

Atomic theory states that matter is composed of discrete units, called atoms. The word "atom" comes from the Greek word for uncuttable, ''atomos''. Scientists later discovered that atoms were indeed able to be broken into subatomic, or elementary, particles including protons, neutrons, and electrons. Atomic theory has evolved greatly over time, but the most recent model stems from quantum mechanics.

==The Main Idea==
===A Mathematical Model===
===A Computational Model===
Understanding the composition and structure of atoms is essential to the study of both microscopic and macroscopic systems. Researchers have made use of atomic information to create what are called atomistic models. These models are used to predict and analyze the behavior of complex systems through knowledge of their most fundamental parts. By understanding how atomic structure affects characteristic properties of atoms, scientists are able to create computational models based on simple microscopic characteristics that simulate complex macroscopic systems. In doing so, they aim to better understand the connection between these macroscopic systems and the underlying atomic structures that govern them.
Use of simulations in research has broadened both the volume and complexity of analysis that can be done at any one time. The ability to model atoms through simulations has been an integral part of the research done in diverse areas of science, notably materials science. In this field, atomistic models are often used to predict material properties under certain conditions using information about their nucleus and electron density. For example, professor ABFIEJABF of the physics department of Georgia Tech created an atomistic model that simulates the behavior of atoms in ABFIEJABF. Another use of atomistic models is to simulate and analyze important processes such as a nuclear chain reaction.
https://javalab.org/en/nuclear_chain_reaction_en/

Ultimately, the use of such simulations help to understand the collective behavior of atoms and how this behavior affects macroscopic processes (such as deformation and phase change) as well as performance abilities (such as strength of material).

==History==

===John Dalton: The Law of Multiple Proportions and Atomic Mass===
[[File:Daltons_symbols.gif|thumb|Dalton's concept of atoms and molecules]]
Working from the conservation of mass principle, chemist John Dalton determined the law of multiple proportions to understand how different elements combined in compounds. In 1803, he proposed that each element of the periodic table was composed of identical components, atoms, that were unique to each element. He also suggested that these atoms were not created nor destroyed when one element was combined with another. Dalton's empirical, experimentally-based work marked the first scientific theory of the atom.

Dalton proposed a list of atomic weights in 1805. However, Dalton failed to recognize natural tendencies of elements in nature (for example, oxygen typically exists as a diatomic molecule as <math>\text{O}_2</math>). Dalton was unable to distinguish between atoms and molecules (groups of atoms).

===Amedeo Avogadro: Avogadro's Law===
In 1811, [[Amedeo Avogadro]] studied gases and determined that the amount of volume a gas occupies is not determined by the mass of the gas. This allowed Avogadro to take more accurate atomic measurements of gases than Dalton, and differentiate atoms from molecules.

===Robert Brown: Brownian Motion===
A Scottish botanist, Robert Brown, studied the motion of tiny pollen particles in water in 1827. The particles followed complex paths, dubbed Brownian Motion. As early as 1905, [[Albert Einstein]] used Brownian Motion to predict the size of atoms and molecules.

===J.J. Thomson: The Plum-Pudding Model and Electrons===
[[File:Plum_pudding_model.svg|thumb|Tomson's Plum-Pudding Model]]
Through his work with cathode rays, [[J.J. Thomson]] discovered the electron in 1897, and was the first to learn that atoms weren't actually "uncuttable" as initially thought. Thomson knew that atoms had a net neutral charge, but he only knew that negative particles existed. Thus, Thomson developed the "plum-pudding" model of negatively charged electrons floating in a sea of positive charge. (He likened the relationship of electrons to the sea of positive charge to that of plums in plum pudding.)

===Ernest Rutherford: Gold Foil Experiment and the Nucleus===
In 1909, one of Thomson's students, [[Ernest Rutherford]], determined that the positive charge of atoms was located in a central nucleus. He shot small, positively charged alpha particles at thin sheets of gold foil and noted that some particles were sharply deflected. This deflection could only occur if the positive components of atoms were located in a small area, which Rutherford assumed to be the center. He proposed a planetary model of atoms where a cloud of electrons surrounded a central, positively charged nucleus.

===Niels Bohr: Introducing Quantum Physics===
[[File:Bohr_atom_animation_2.gif|thumb|The Bohr model for a Hydrogen atom with its electron moving between energy levels]]
As quantum mechanics progressed through the work of [[Albert Einstein]] and [[Max Planck]], [[Niels Bohr]] updated the atomic model in 1913 to account for quantum phenomena. Bohr, who was also one of Rutherford's students, suggested that electrostatic forces kept electrons in circular orbit around the positively charged central nucleus. In support of his theory, Bohr examined the behavior of electrons in hydrogen molecules and noted that they followed distinct energy levels. When an electron changed energy levels, it gained or lost energy, which could be emitted in the form of light. While the Bohr model holds true for hydrogen, it isn't accurate for multi-electron elements.

===James Chadwick: Neutrons===
James Chadwick won a Nobel Prize in 1935 for his discovery of the neutron. Starting with Rutherford's work, Chadwick continued experimenting to determine the excess mass in the nucleus that wasn't accounted for by protons. He found that neutrally charged particles, dubbed neutrons, were also inside the nucleus.

===The Current Model: Quantum Physics and Electron Orbitals===
Erwin Schrödinger examined the possibility that moving electrons behaved more like waves than particles, and published "Schrödinger's Equation" in 1926. Although this resolved many issues encountered with the Bohr model, it faced opposition from physicist [[Max Born]]. Instead, Born suggested a wave-particle duality of electrons, which stated that electrons could behave both like a wave and a particle.
As electrons were now given properties of waves, it was impossible to simultaneously determine an electron's exact location and momentum around the nucleus. Werner Heisenberg, first described this phenomena in 1927, and it was later named the Heisenberg Uncertainty Principle. This refuted the Bohr model of the atom, and replaced it with a pattern of probabilities as to where electrons are located around the nucleus. These patterns are referred to as atomic orbitals and come in a variety of shapes (basic spheres, rings, dumbbells, etc.) and the nucleus is always at the center.
[[File:Neon_orbitals.JPG|thumb|center|The first five atomic orbitals: 1s, 2s, 2px, 2py, and 2pz.]]

==Connectedness==
While classical physics applies to large objects moving much slower than the speed of light, modern physics deals with special cases of tiny objects, like atoms, subject to relativistic effects. Atomic theory is vital to understanding many quantum physics concepts that are covered in both Physics 2211 and 2212, like the ball-and-spring model of solids, point charges, and conductivity.

Although one can argue physics applies to just about every aspect of life, and atomic theory is critical to understanding physics, atomic theory has directly influenced material science, power generation, electronics, and even food processing, to name a few.

<gallery>
File:Apollo_synthetic_diamond.jpg|'''Material Science:''' Synthetic diamonds are used for both cosmetic retail and in manufacturing cutting tools.
File:Electrical_and_Mechanical_Services_Department_Headquarters_Photovoltaics.jpg|'''Power:''' Solar cells and power rely on the photovoltaic effect and the wave-particle duality of subatomic particles (like photons).
File:Monokristalines_Silizium_f%C3%BCr_die_Waferherstellung.jpg|'''Electronics:''' Silicon, a popular semiconductor used in electronics, is produced industrially in a single-crystal form.
File:Sodium-chloride-3D-ionic.png|'''Food processing:''' An atomic view of table salt. Purple particles are sodium (Na), and green particles are chlorine (Cl).
File:Nagasakibomb.jpg|'''Defense:''' Nuclear weapons were used during World War II.
File:White_Matter_Connections_Obtained_with_MRI_Tractography.png|'''Medicine:''' MRI's provide doctors critical information without the risks of surgery.
File:Plastic_household_items.jpg|'''Manufacturing:''' Many common household items are made with plastic.
</gallery>

== See also ==

*[[Bohr Model]]
*[[Electronic Energy Levels and Photons]]
*[[Rutherford Experiment and Atomic Collisions]]

===Notable Scientists===
*[[Amedeo Avogadro]]
*[[J.J. Thomson]]
*[[Ernest Rutherford]]
*[[Albert Einstein]]
*[[Max Planck]]
*[[Niels Bohr]]
*[[Max Born]]

===Related Theories===
*[[Quantum Theory]]
*[[Einstein's Theory of Special Relativity]]

===Concept Application===
*[[Ball and Spring Model of Matter]], [[Ball and Spring Model]]
*[[Length and Stiffness of an Interatomic Bond]], [[Young's Modulus]]
*[[Density]], [[Charge]], [[Spin]], and [[Conductivity]]
*[[The Photoelectric Effect]], [[Photons]]
*[[Rest Mass Energy]]
*[[Potential Energy of a Pair of Neutral Atoms]]

===External links===
*Physics Portal description of [https://en.wikipedia.org/wiki/History_of_molecular_theory Molecular Theory] and [https://en.wikipedia.org/wiki/Elementary_particle Subatomic Particles]
*HyperPhysics summary of [http://hyperphysics.phy-astr.gsu.edu/hbase/quacon.html#quacon Quantum Physics]
*Demonstration of the [https://phet.colorado.edu/en/simulation/legacy/hydrogen-atom various models] of a hydrogen atom

==References==

Chapter 30 of [https://openstaxcollege.org/files/textbook_version/hi_res_pdf/9/CollegePhysics-OP.pdf OpenStax Textbook]

Physics Portal page on [https://en.wikipedia.org/wiki/Atomic_theory Atomic Theory]

[[Category: Theory]]

Atomic Theory

2022-04-17T21:01:59Z

Erinhorbacz:

Claimed by: Erin Horbacz (4/17/2022)

Atomic theory states that matter is composed of discrete units, called atoms. The word "atom" comes from the Greek word for uncuttable, ''atomos''. Scientists later discovered that atoms were indeed able to be broken into subatomic, or elementary, particles including protons, neutrons, and electrons. Atomic theory has evolved greatly over time, but the most recent model stems from quantum mechanics.

==The Main Idea==
===A Mathematical Model===
===A Computational Model===

==History==

===John Dalton: The Law of Multiple Proportions and Atomic Mass===
[[File:Daltons_symbols.gif|thumb|Dalton's concept of atoms and molecules]]
Working from the conservation of mass principle, chemist John Dalton determined the law of multiple proportions to understand how different elements combined in compounds. In 1803, he proposed that each element of the periodic table was composed of identical components, atoms, that were unique to each element. He also suggested that these atoms were not created nor destroyed when one element was combined with another. Dalton's empirical, experimentally-based work marked the first scientific theory of the atom.

Dalton proposed a list of atomic weights in 1805. However, Dalton failed to recognize natural tendencies of elements in nature (for example, oxygen typically exists as a diatomic molecule as <math>\text{O}_2</math>). Dalton was unable to distinguish between atoms and molecules (groups of atoms).

===Amedeo Avogadro: Avogadro's Law===
In 1811, [[Amedeo Avogadro]] studied gases and determined that the amount of volume a gas occupies is not determined by the mass of the gas. This allowed Avogadro to take more accurate atomic measurements of gases than Dalton, and differentiate atoms from molecules.

===Robert Brown: Brownian Motion===
A Scottish botanist, Robert Brown, studied the motion of tiny pollen particles in water in 1827. The particles followed complex paths, dubbed Brownian Motion. As early as 1905, [[Albert Einstein]] used Brownian Motion to predict the size of atoms and molecules.

===J.J. Thomson: The Plum-Pudding Model and Electrons===
[[File:Plum_pudding_model.svg|thumb|Tomson's Plum-Pudding Model]]
Through his work with cathode rays, [[J.J. Thomson]] discovered the electron in 1897, and was the first to learn that atoms weren't actually "uncuttable" as initially thought. Thomson knew that atoms had a net neutral charge, but he only knew that negative particles existed. Thus, Thomson developed the "plum-pudding" model of negatively charged electrons floating in a sea of positive charge. (He likened the relationship of electrons to the sea of positive charge to that of plums in plum pudding.)

===Ernest Rutherford: Gold Foil Experiment and the Nucleus===
In 1909, one of Thomson's students, [[Ernest Rutherford]], determined that the positive charge of atoms was located in a central nucleus. He shot small, positively charged alpha particles at thin sheets of gold foil and noted that some particles were sharply deflected. This deflection could only occur if the positive components of atoms were located in a small area, which Rutherford assumed to be the center. He proposed a planetary model of atoms where a cloud of electrons surrounded a central, positively charged nucleus.

===Niels Bohr: Introducing Quantum Physics===
[[File:Bohr_atom_animation_2.gif|thumb|The Bohr model for a Hydrogen atom with its electron moving between energy levels]]
As quantum mechanics progressed through the work of [[Albert Einstein]] and [[Max Planck]], [[Niels Bohr]] updated the atomic model in 1913 to account for quantum phenomena. Bohr, who was also one of Rutherford's students, suggested that electrostatic forces kept electrons in circular orbit around the positively charged central nucleus. In support of his theory, Bohr examined the behavior of electrons in hydrogen molecules and noted that they followed distinct energy levels. When an electron changed energy levels, it gained or lost energy, which could be emitted in the form of light. While the Bohr model holds true for hydrogen, it isn't accurate for multi-electron elements.

===James Chadwick: Neutrons===
James Chadwick won a Nobel Prize in 1935 for his discovery of the neutron. Starting with Rutherford's work, Chadwick continued experimenting to determine the excess mass in the nucleus that wasn't accounted for by protons. He found that neutrally charged particles, dubbed neutrons, were also inside the nucleus.

===The Current Model: Quantum Physics and Electron Orbitals===
Erwin Schrödinger examined the possibility that moving electrons behaved more like waves than particles, and published "Schrödinger's Equation" in 1926. Although this resolved many issues encountered with the Bohr model, it faced opposition from physicist [[Max Born]]. Instead, Born suggested a wave-particle duality of electrons, which stated that electrons could behave both like a wave and a particle.
As electrons were now given properties of waves, it was impossible to simultaneously determine an electron's exact location and momentum around the nucleus. Werner Heisenberg, first described this phenomena in 1927, and it was later named the Heisenberg Uncertainty Principle. This refuted the Bohr model of the atom, and replaced it with a pattern of probabilities as to where electrons are located around the nucleus. These patterns are referred to as atomic orbitals and come in a variety of shapes (basic spheres, rings, dumbbells, etc.) and the nucleus is always at the center.
[[File:Neon_orbitals.JPG|thumb|center|The first five atomic orbitals: 1s, 2s, 2px, 2py, and 2pz.]]

==Connectedness==
While classical physics applies to large objects moving much slower than the speed of light, modern physics deals with special cases of tiny objects, like atoms, subject to relativistic effects. Atomic theory is vital to understanding many quantum physics concepts that are covered in both Physics 2211 and 2212, like the ball-and-spring model of solids, point charges, and conductivity.

Although one can argue physics applies to just about every aspect of life, and atomic theory is critical to understanding physics, atomic theory has directly influenced material science, power generation, electronics, and even food processing, to name a few.

<gallery>
File:Apollo_synthetic_diamond.jpg|'''Material Science:''' Synthetic diamonds are used for both cosmetic retail and in manufacturing cutting tools.
File:Electrical_and_Mechanical_Services_Department_Headquarters_Photovoltaics.jpg|'''Power:''' Solar cells and power rely on the photovoltaic effect and the wave-particle duality of subatomic particles (like photons).
File:Monokristalines_Silizium_f%C3%BCr_die_Waferherstellung.jpg|'''Electronics:''' Silicon, a popular semiconductor used in electronics, is produced industrially in a single-crystal form.
File:Sodium-chloride-3D-ionic.png|'''Food processing:''' An atomic view of table salt. Purple particles are sodium (Na), and green particles are chlorine (Cl).
File:Nagasakibomb.jpg|'''Defense:''' Nuclear weapons were used during World War II.
File:White_Matter_Connections_Obtained_with_MRI_Tractography.png|'''Medicine:''' MRI's provide doctors critical information without the risks of surgery.
File:Plastic_household_items.jpg|'''Manufacturing:''' Many common household items are made with plastic.
</gallery>

== See also ==

*[[Bohr Model]]
*[[Electronic Energy Levels and Photons]]
*[[Rutherford Experiment and Atomic Collisions]]

===Notable Scientists===
*[[Amedeo Avogadro]]
*[[J.J. Thomson]]
*[[Ernest Rutherford]]
*[[Albert Einstein]]
*[[Max Planck]]
*[[Niels Bohr]]
*[[Max Born]]

===Related Theories===
*[[Quantum Theory]]
*[[Einstein's Theory of Special Relativity]]

===Concept Application===
*[[Ball and Spring Model of Matter]], [[Ball and Spring Model]]
*[[Length and Stiffness of an Interatomic Bond]], [[Young's Modulus]]
*[[Density]], [[Charge]], [[Spin]], and [[Conductivity]]
*[[The Photoelectric Effect]], [[Photons]]
*[[Rest Mass Energy]]
*[[Potential Energy of a Pair of Neutral Atoms]]

===External links===
*Physics Portal description of [https://en.wikipedia.org/wiki/History_of_molecular_theory Molecular Theory] and [https://en.wikipedia.org/wiki/Elementary_particle Subatomic Particles]
*HyperPhysics summary of [http://hyperphysics.phy-astr.gsu.edu/hbase/quacon.html#quacon Quantum Physics]
*Demonstration of the [https://phet.colorado.edu/en/simulation/legacy/hydrogen-atom various models] of a hydrogen atom

==References==

Chapter 30 of [https://openstaxcollege.org/files/textbook_version/hi_res_pdf/9/CollegePhysics-OP.pdf OpenStax Textbook]

Physics Portal page on [https://en.wikipedia.org/wiki/Atomic_theory Atomic Theory]

[[Category: Theory]]

Atomic Theory

2022-04-17T06:03:26Z

Erinhorbacz:

Claimed by: Erin Horbacz (4/17/2022)

Atomic theory states that matter is composed of discrete units, called atoms. The word "atom" comes from the Greek word for uncuttable, ''atomos''. Scientists later discovered that atoms were indeed able to be broken into subatomic, or elementary, particles including protons, neutrons, and electrons. Atomic theory has evolved greatly over time, but the most recent model stems from quantum mechanics.

==History==

===John Dalton: The Law of Multiple Proportions and Atomic Mass===
[[File:Daltons_symbols.gif|thumb|Dalton's concept of atoms and molecules]]
Working from the conservation of mass principle, chemist John Dalton determined the law of multiple proportions to understand how different elements combined in compounds. In 1803, he proposed that each element of the periodic table was composed of identical components, atoms, that were unique to each element. He also suggested that these atoms were not created nor destroyed when one element was combined with another. Dalton's empirical, experimentally-based work marked the first scientific theory of the atom.

Dalton proposed a list of atomic weights in 1805. However, Dalton failed to recognize natural tendencies of elements in nature (for example, oxygen typically exists as a diatomic molecule as <math>\text{O}_2</math>). Dalton was unable to distinguish between atoms and molecules (groups of atoms).

===Amedeo Avogadro: Avogadro's Law===
In 1811, [[Amedeo Avogadro]] studied gases and determined that the amount of volume a gas occupies is not determined by the mass of the gas. This allowed Avogadro to take more accurate atomic measurements of gases than Dalton, and differentiate atoms from molecules.

===Robert Brown: Brownian Motion===
A Scottish botanist, Robert Brown, studied the motion of tiny pollen particles in water in 1827. The particles followed complex paths, dubbed Brownian Motion. As early as 1905, [[Albert Einstein]] used Brownian Motion to predict the size of atoms and molecules.

===J.J. Thomson: The Plum-Pudding Model and Electrons===
[[File:Plum_pudding_model.svg|thumb|Tomson's Plum-Pudding Model]]
Through his work with cathode rays, [[J.J. Thomson]] discovered the electron in 1897, and was the first to learn that atoms weren't actually "uncuttable" as initially thought. Thomson knew that atoms had a net neutral charge, but he only knew that negative particles existed. Thus, Thomson developed the "plum-pudding" model of negatively charged electrons floating in a sea of positive charge. (He likened the relationship of electrons to the sea of positive charge to that of plums in plum pudding.)

===Ernest Rutherford: Gold Foil Experiment and the Nucleus===
In 1909, one of Thomson's students, [[Ernest Rutherford]], determined that the positive charge of atoms was located in a central nucleus. He shot small, positively charged alpha particles at thin sheets of gold foil and noted that some particles were sharply deflected. This deflection could only occur if the positive components of atoms were located in a small area, which Rutherford assumed to be the center. He proposed a planetary model of atoms where a cloud of electrons surrounded a central, positively charged nucleus.

===Niels Bohr: Introducing Quantum Physics===
[[File:Bohr_atom_animation_2.gif|thumb|The Bohr model for a Hydrogen atom with its electron moving between energy levels]]
As quantum mechanics progressed through the work of [[Albert Einstein]] and [[Max Planck]], [[Niels Bohr]] updated the atomic model in 1913 to account for quantum phenomena. Bohr, who was also one of Rutherford's students, suggested that electrostatic forces kept electrons in circular orbit around the positively charged central nucleus. In support of his theory, Bohr examined the behavior of electrons in hydrogen molecules and noted that they followed distinct energy levels. When an electron changed energy levels, it gained or lost energy, which could be emitted in the form of light. While the Bohr model holds true for hydrogen, it isn't accurate for multi-electron elements.

===James Chadwick: Neutrons===
James Chadwick won a Nobel Prize in 1935 for his discovery of the neutron. Starting with Rutherford's work, Chadwick continued experimenting to determine the excess mass in the nucleus that wasn't accounted for by protons. He found that neutrally charged particles, dubbed neutrons, were also inside the nucleus.

===The Current Model: Quantum Physics and Electron Orbitals===
Erwin Schrödinger examined the possibility that moving electrons behaved more like waves than particles, and published "Schrödinger's Equation" in 1926. Although this resolved many issues encountered with the Bohr model, it faced opposition from physicist [[Max Born]]. Instead, Born suggested a wave-particle duality of electrons, which stated that electrons could behave both like a wave and a particle.
As electrons were now given properties of waves, it was impossible to simultaneously determine an electron's exact location and momentum around the nucleus. Werner Heisenberg, first described this phenomena in 1927, and it was later named the Heisenberg Uncertainty Principle. This refuted the Bohr model of the atom, and replaced it with a pattern of probabilities as to where electrons are located around the nucleus. These patterns are referred to as atomic orbitals and come in a variety of shapes (basic spheres, rings, dumbbells, etc.) and the nucleus is always at the center.
[[File:Neon_orbitals.JPG|thumb|center|The first five atomic orbitals: 1s, 2s, 2px, 2py, and 2pz.]]

==Connectedness==
While classical physics applies to large objects moving much slower than the speed of light, modern physics deals with special cases of tiny objects, like atoms, subject to relativistic effects. Atomic theory is vital to understanding many quantum physics concepts that are covered in both Physics 2211 and 2212, like the ball-and-spring model of solids, point charges, and conductivity.

Although one can argue physics applies to just about every aspect of life, and atomic theory is critical to understanding physics, atomic theory has directly influenced material science, power generation, electronics, and even food processing, to name a few.

<gallery>
File:Apollo_synthetic_diamond.jpg|'''Material Science:''' Synthetic diamonds are used for both cosmetic retail and in manufacturing cutting tools.
File:Electrical_and_Mechanical_Services_Department_Headquarters_Photovoltaics.jpg|'''Power:''' Solar cells and power rely on the photovoltaic effect and the wave-particle duality of subatomic particles (like photons).
File:Monokristalines_Silizium_f%C3%BCr_die_Waferherstellung.jpg|'''Electronics:''' Silicon, a popular semiconductor used in electronics, is produced industrially in a single-crystal form.
File:Sodium-chloride-3D-ionic.png|'''Food processing:''' An atomic view of table salt. Purple particles are sodium (Na), and green particles are chlorine (Cl).
File:Nagasakibomb.jpg|'''Defense:''' Nuclear weapons were used during World War II.
File:White_Matter_Connections_Obtained_with_MRI_Tractography.png|'''Medicine:''' MRI's provide doctors critical information without the risks of surgery.
File:Plastic_household_items.jpg|'''Manufacturing:''' Many common household items are made with plastic.
</gallery>

== See also ==

*[[Bohr Model]]
*[[Electronic Energy Levels and Photons]]
*[[Rutherford Experiment and Atomic Collisions]]

===Notable Scientists===
*[[Amedeo Avogadro]]
*[[J.J. Thomson]]
*[[Ernest Rutherford]]
*[[Albert Einstein]]
*[[Max Planck]]
*[[Niels Bohr]]
*[[Max Born]]

===Related Theories===
*[[Quantum Theory]]
*[[Einstein's Theory of Special Relativity]]

===Concept Application===
*[[Ball and Spring Model of Matter]], [[Ball and Spring Model]]
*[[Length and Stiffness of an Interatomic Bond]], [[Young's Modulus]]
*[[Density]], [[Charge]], [[Spin]], and [[Conductivity]]
*[[The Photoelectric Effect]], [[Photons]]
*[[Rest Mass Energy]]
*[[Potential Energy of a Pair of Neutral Atoms]]

===External links===
*Physics Portal description of [https://en.wikipedia.org/wiki/History_of_molecular_theory Molecular Theory] and [https://en.wikipedia.org/wiki/Elementary_particle Subatomic Particles]
*HyperPhysics summary of [http://hyperphysics.phy-astr.gsu.edu/hbase/quacon.html#quacon Quantum Physics]
*Demonstration of the [https://phet.colorado.edu/en/simulation/legacy/hydrogen-atom various models] of a hydrogen atom

==References==

Chapter 30 of [https://openstaxcollege.org/files/textbook_version/hi_res_pdf/9/CollegePhysics-OP.pdf OpenStax Textbook]

Physics Portal page on [https://en.wikipedia.org/wiki/Atomic_theory Atomic Theory]

[[Category: Theory]]

Wave-Particle Duality

2022-04-14T20:53:10Z

Erinhorbacz: /* History */

===Claimed by Arghya Roy===
'''Wave-particle duality''' is the concept that states every elementary particle behaves like both a wave and a particle.

==The Main Idea==

In the 1920s, a French physicist named [[Louis de Broglie]] suggested that all matter has wave-like properties. This conclusion was largely the result of two landmark experiments that contradicted each other in almost every way. The first experiment was Thomas Young's double slit experiment, which showed light behaved like a wave. The second experiment was by Albert Einstein, who showed, through his research on the photoelectric effect, that light was made up of discrete packets of energy called photons -- which meant that light also behaved as a particle. This contradiction sent the world of physics as humans knew it into panic.

===Double slit experiment===

The [http://micro.magnet.fsu.edu/primer/java/interference/doubleslit/ double slit experiment] is a deceptively simple experiment that was originally conducted by Thomas Young in the 17th century. In the experiment, Young simply sent a beam of light through two slits and observed the pattern on the surface behind the slits. What he saw was an interference pattern that only could have been present if waves were what went inside two slits. The bright spots occur where the amplitudes of the two waves match (both waves are at their peaks) and the dark spots occur when one wave is at its maximum amplitude and the other is at its minimum.

[[File:Double-slit.PNG|Double-slit]]

[[File:Single slit and double slit2.jpg|Single slit and double slit2]]

===Photoelectric effect===

It was known that when light struck a metal, electrons were liberated from the surface. The intuition was that increasing the intensity of light (shining more light) would liberate more electrons. Albert Einstein found something interesting, though. Varying intensity of light had no effect on how many electrons were liberated. Rather, the ''frequency'' of the light determined how many electrons, if any, would be freed. Furthermore, the original theory was that the electrons that would be freed was continuous -- even the smallest amount of light would free some electrons. In fact, this was not the case. Einstein found that there was a minimum threshold frequency that must have been present in order to release electrons at all. This implied there was a ''minimum amount of energy'', or '''quantum''' involved in the interaction. This pointed to the fact that light in fact behaved as particles (called photons) which were packets of these quantum energies. This directly conflicted with the double slit experiment.

[[File:Photoelectric effect.svg|Photoelectric effect]]

[https://phet.colorado.edu/en/simulation/legacy/photoelectric PhET Simulation for Photoelectric effect]

(will be expanded by Erin Horbacz 4/14/2022)

===A Mathematical Model===

Now that we can treat these particles at the quantum level as waves, we can use many different equations from wave mechanics to describe their behavior. One of the most important equations in dealing with wave like properties of these quantum systems and particles is the [https://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation Schrödinger equation]. The Schrödinger equation is the analog of [https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion Newton's second law] ('''F''' = ''m'''''a''') in quantum mechanics, and describes the wave function over time of a system such as a particle moving in a magnetic field. But rather than a simple linear equation, the Schrödinger equation is a linear partial differential equation:

<math>i \hbar \frac{\partial}{\partial t}\Psi(\mathbf{r},t) = \hat H \Psi(\mathbf{r},t)</math>

is the general, relativistic (works for particles moving up to close to the speed of light) equation, where <math>i</math> is the square root of negative 1, <math>ħ</math> is the [https://en.wikipedia.org/wiki/Planck_constant Planck constant] divided by <math>2pi</math>, the symbol ∂/∂t indicates a partial derivative with respect to time, Ψ is the [[wave function]] of the quantum system, and <math>Ĥ</math> is the Hamiltonian operator, which represents the total energy of the wave function at different times.

Using the Schrödinger equation involves using the proper form of the Hamiltonian operator that accounts for the kinetic and potential energy of the particles, and using that operator to then solve the partial differential equation. The output wave function contains information about the system at different times.

==Examples==

The mathematics in solving the Schrodinger equation is quite complicated, but using other simple wave formulas is not very difficult. Two very straightforward formulas involving Planck's constant ''h'', which has a value of <math>6.62607004*10^-34 m^2</math> m^2 kg / s, can be used to relate fundamental properties such as energy ''E'', frequency <math>\nu</math>, and wavelength <math>\lambda</math>.

:<math>E = h \nu</math> (1)

:<math>\lambda = \frac{h}{p} .</math> (2)

Another very useful equation is that the frequency and the wavelength of a particle are inversely proportional, and multiply to the speed of light, ''c''.

:<math>c = \lambda\nu</math> (3)

===Ex. 1===

Microwave ovens emit microwave energy with a wavelength of 12.9 cm. What is the energy of exactly one photon of this microwave radiation?

Here we need to use equations 1 and 3.

Next we define our constants.

<math>c= 2.998*10^8 m/s</math> (this problem wants us to use this number for speed of light), <math>h=6.626*10^34J-s</math>

Now we simply plug in, making sure that our units match (convert 12.9cm to meters = 0.129m)

<math>2.998*10^8 m/s = .129 * v</math>

<math>v = 2,324,031,008 Hz</math>

Now that we found v, we can solve for E.

<math>E = 2,324,031,008 Hz * 6.626*10^-34</math>

<math>E= 1.53990294*10^-24</math>

<math>E= 1.54*10^-24</math>

===Ex. 2===

A radio station broadcasts at a frequency of 590 KHz. What is the wavelength of the radio waves?

We need to use equation 3.

First we convert KHz to Hz.

<math>590</math> KHz = <math>590*10^3</math> Hz

<math>(3*10^8)/(590*10^3)</math> = <math>500</math>m = <math>\lambda</math>

<math>\lambda</math> = 500m.

==Connectedness==

1. How is this topic connected to something that you are interested in?

For a while I had been interested in the strange nature of quantum mechanics. The pure fact that particles could act as waves was simply alluring. In the future it would be great if, even as a biology major, work in a field that had some aspect of quantum research associated.

2. How is it connected to your major?

Extensive, high level research in biology, my major, has shown that during photosynthesis, plants benefit from the quantum properties of the light coming from the sun, and are able to use it to transport energy more efficiently. This groundbreaking discovery could be the key to discovering extremely effective cures for diseases that currently are uncurable or are very costly to treat.

3. Is there an interesting industrial application?

Right now, since quantum computing is not effective or cheap enough for companies to use, industry use is limited. But common lab use is in electron microscopy - it is possible by exploiting the high frequencies of electrons, meaning that one can see objects much smaller than those that can only be seen with visible light.

==History==

Throughout the 1800s, scientists one by one, such as [https://en.wikipedia.org/wiki/John_Dalton John Dalton] and [https://en.wikipedia.org/wiki/Ernest_Rutherford Ernest Rutherford] theorized and discovered elementary particles. Those discoveries in and of themselves were groundbreaking, but of course, scientists pursued these further. It was then that a contradiction arose in two experiments, as mentioned in the above sections, and things went haywire. Newton's classical mechanics had no way of explaining phenomenon like this, so a new field of quantum mechanics was born to study physics of particles on minute scales. The 1900s included scientists like [https://en.wikipedia.org/wiki/Richard_Feynman Richard Feynman] and [https://en.wikipedia.org/wiki/Erwin_Schr%C3%B6dinger Erwin_Schr%C3%B6dinger] (the scientist the above differential equation was named after) that made leaps in QM. Currently, scientists are working on applying [https://en.wikipedia.org/wiki/Quantum_computing quantum effects to computing].

(will be expanded by Erin Horbacz 4/14/2022)

== See also ==

This topic is a big idea in the field of quantum mechanics, but there are many other interesting concepts to further explore:

-[https://en.wikipedia.org/wiki/Quantum_entanglement Quantum entanglement]

-[https://en.wikipedia.org/wiki/Theory_of_everything Theory of everything]

-[https://en.wikipedia.org/wiki/Standard_Model Standard Model]

==References==

All pictures were from Wikimedia Commons, and references are already hyperlinked to key words in the text.

[[Category:Waves]]

Wave-Particle Duality

2022-04-14T20:52:29Z

Erinhorbacz: /* Photoelectric effect */

===Claimed by Arghya Roy===
'''Wave-particle duality''' is the concept that states every elementary particle behaves like both a wave and a particle.

==The Main Idea==

In the 1920s, a French physicist named [[Louis de Broglie]] suggested that all matter has wave-like properties. This conclusion was largely the result of two landmark experiments that contradicted each other in almost every way. The first experiment was Thomas Young's double slit experiment, which showed light behaved like a wave. The second experiment was by Albert Einstein, who showed, through his research on the photoelectric effect, that light was made up of discrete packets of energy called photons -- which meant that light also behaved as a particle. This contradiction sent the world of physics as humans knew it into panic.

===Double slit experiment===

The [http://micro.magnet.fsu.edu/primer/java/interference/doubleslit/ double slit experiment] is a deceptively simple experiment that was originally conducted by Thomas Young in the 17th century. In the experiment, Young simply sent a beam of light through two slits and observed the pattern on the surface behind the slits. What he saw was an interference pattern that only could have been present if waves were what went inside two slits. The bright spots occur where the amplitudes of the two waves match (both waves are at their peaks) and the dark spots occur when one wave is at its maximum amplitude and the other is at its minimum.

[[File:Double-slit.PNG|Double-slit]]

[[File:Single slit and double slit2.jpg|Single slit and double slit2]]

===Photoelectric effect===

It was known that when light struck a metal, electrons were liberated from the surface. The intuition was that increasing the intensity of light (shining more light) would liberate more electrons. Albert Einstein found something interesting, though. Varying intensity of light had no effect on how many electrons were liberated. Rather, the ''frequency'' of the light determined how many electrons, if any, would be freed. Furthermore, the original theory was that the electrons that would be freed was continuous -- even the smallest amount of light would free some electrons. In fact, this was not the case. Einstein found that there was a minimum threshold frequency that must have been present in order to release electrons at all. This implied there was a ''minimum amount of energy'', or '''quantum''' involved in the interaction. This pointed to the fact that light in fact behaved as particles (called photons) which were packets of these quantum energies. This directly conflicted with the double slit experiment.

[[File:Photoelectric effect.svg|Photoelectric effect]]

[https://phet.colorado.edu/en/simulation/legacy/photoelectric PhET Simulation for Photoelectric effect]

(will be expanded by Erin Horbacz 4/14/2022)

===A Mathematical Model===

Now that we can treat these particles at the quantum level as waves, we can use many different equations from wave mechanics to describe their behavior. One of the most important equations in dealing with wave like properties of these quantum systems and particles is the [https://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation Schrödinger equation]. The Schrödinger equation is the analog of [https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion Newton's second law] ('''F''' = ''m'''''a''') in quantum mechanics, and describes the wave function over time of a system such as a particle moving in a magnetic field. But rather than a simple linear equation, the Schrödinger equation is a linear partial differential equation:

<math>i \hbar \frac{\partial}{\partial t}\Psi(\mathbf{r},t) = \hat H \Psi(\mathbf{r},t)</math>

is the general, relativistic (works for particles moving up to close to the speed of light) equation, where <math>i</math> is the square root of negative 1, <math>ħ</math> is the [https://en.wikipedia.org/wiki/Planck_constant Planck constant] divided by <math>2pi</math>, the symbol ∂/∂t indicates a partial derivative with respect to time, Ψ is the [[wave function]] of the quantum system, and <math>Ĥ</math> is the Hamiltonian operator, which represents the total energy of the wave function at different times.

Using the Schrödinger equation involves using the proper form of the Hamiltonian operator that accounts for the kinetic and potential energy of the particles, and using that operator to then solve the partial differential equation. The output wave function contains information about the system at different times.

==Examples==

The mathematics in solving the Schrodinger equation is quite complicated, but using other simple wave formulas is not very difficult. Two very straightforward formulas involving Planck's constant ''h'', which has a value of <math>6.62607004*10^-34 m^2</math> m^2 kg / s, can be used to relate fundamental properties such as energy ''E'', frequency <math>\nu</math>, and wavelength <math>\lambda</math>.

:<math>E = h \nu</math> (1)

:<math>\lambda = \frac{h}{p} .</math> (2)

Another very useful equation is that the frequency and the wavelength of a particle are inversely proportional, and multiply to the speed of light, ''c''.

:<math>c = \lambda\nu</math> (3)

===Ex. 1===

Microwave ovens emit microwave energy with a wavelength of 12.9 cm. What is the energy of exactly one photon of this microwave radiation?

Here we need to use equations 1 and 3.

Next we define our constants.

<math>c= 2.998*10^8 m/s</math> (this problem wants us to use this number for speed of light), <math>h=6.626*10^34J-s</math>

Now we simply plug in, making sure that our units match (convert 12.9cm to meters = 0.129m)

<math>2.998*10^8 m/s = .129 * v</math>

<math>v = 2,324,031,008 Hz</math>

Now that we found v, we can solve for E.

<math>E = 2,324,031,008 Hz * 6.626*10^-34</math>

<math>E= 1.53990294*10^-24</math>

<math>E= 1.54*10^-24</math>

===Ex. 2===

A radio station broadcasts at a frequency of 590 KHz. What is the wavelength of the radio waves?

We need to use equation 3.

First we convert KHz to Hz.

<math>590</math> KHz = <math>590*10^3</math> Hz

<math>(3*10^8)/(590*10^3)</math> = <math>500</math>m = <math>\lambda</math>

<math>\lambda</math> = 500m.

==Connectedness==

1. How is this topic connected to something that you are interested in?

For a while I had been interested in the strange nature of quantum mechanics. The pure fact that particles could act as waves was simply alluring. In the future it would be great if, even as a biology major, work in a field that had some aspect of quantum research associated.

2. How is it connected to your major?

Extensive, high level research in biology, my major, has shown that during photosynthesis, plants benefit from the quantum properties of the light coming from the sun, and are able to use it to transport energy more efficiently. This groundbreaking discovery could be the key to discovering extremely effective cures for diseases that currently are uncurable or are very costly to treat.

3. Is there an interesting industrial application?

Right now, since quantum computing is not effective or cheap enough for companies to use, industry use is limited. But common lab use is in electron microscopy - it is possible by exploiting the high frequencies of electrons, meaning that one can see objects much smaller than those that can only be seen with visible light.

==History==

Throughout the 1800s, scientists one by one, such as [https://en.wikipedia.org/wiki/John_Dalton John Dalton] and [https://en.wikipedia.org/wiki/Ernest_Rutherford Ernest Rutherford] theorized and discovered elementary particles. Those discoveries in and of themselves were groundbreaking, but of course, scientists pursued these further. It was then that a contradiction arose in two experiments, as mentioned in the above sections, and things went haywire. Newton's classical mechanics had no way of explaining phenomenon like this, so a new field of quantum mechanics was born to study physics of particles on minute scales. The 1900s included scientists like [https://en.wikipedia.org/wiki/Richard_Feynman Richard Feynman] and [https://en.wikipedia.org/wiki/Erwin_Schr%C3%B6dinger Erwin_Schr%C3%B6dinger] (the scientist the above differential equation was named after) that made leaps in QM. Currently, scientists are working on applying [https://en.wikipedia.org/wiki/Quantum_computing quantum effects to computing].

== See also ==

This topic is a big idea in the field of quantum mechanics, but there are many other interesting concepts to further explore:

-[https://en.wikipedia.org/wiki/Quantum_entanglement Quantum entanglement]

-[https://en.wikipedia.org/wiki/Theory_of_everything Theory of everything]

-[https://en.wikipedia.org/wiki/Standard_Model Standard Model]

==References==

All pictures were from Wikimedia Commons, and references are already hyperlinked to key words in the text.

[[Category:Waves]]