Physics Book - User contributions [en]

Electrostatic Discharge

2017-04-12T00:45:31Z

Jledet:

Edited by Jonathan Ledet (Spring 2017)

Electrostatic Discharge (ESD) is the swift transfer of charges between objects at different potentials. ESD commonly occurs after the accumulation of static electricity on a material and can have devastating effects on solid-state electronics.

==Material Sources of this Phenomenon==

All materials (Both insulators and conductors) are defined on the Triboelectric series which essentially rates that material's affinity for electrons. When an object lower on the series is touched by an object higher on the series, the lower object will acquire a negative charge. When the objects are separated, their charges are equal and opposite-- just waiting for the opportunity to discharge. When the objects finally do discharge, a high voltage spark can form, turning the bridging air to plasma or frying circuits. This process is referred to as tribocharging.

You may have seen a demonstration in class involving a glass rod and a piece of cloth, or rubbed a balloon on your hair and observed its wacky behavior. Both of these are examples of the Triboelectric effect. Additionally, although friction greatly increases the magnitude of the effect, it is not required for the effect to occur. Only an initial contact and subsequent separation are required, friction only amplifies the effect due to the increased contact and separation of molecules on the microscopic level.

==Causes of Electrostatic Discharge==

Electrostatic Discharge can be caused by an electrical breakdown, a short circuit, and most commonly, Tribocharging. ESD is measured using an electrostatic voltmeter.

==Its Effect==

Sparks and lightning are visible Electrostatic Discharge events, but only represent part of the threat of ESD. For example, such a high voltage can be very damaging to the delicate pathways and components on circuit boards.

ESD events, like a spark from a human hand, allow current to travel to the ground through electronic devices, burning holes in integrated circuits and dealing heat damage to the circuit board. This can happen when working barehanded (without an electrostatic wrist strap) with circuit boards and other sensitive electronic equipment, when negatively charged synthetic materials are on or near sensitive electronic equipment, or due to the fast movement of air near electronic equipment.

==Prevention==

During the process in which electronic components are assembled most manufacturers implement Electrostatic Discharge Protected Areas (EPA). These areas are specially designed to prevent the build up of charge on the components, workers, and all other conductive materials. To protect against Electrostatic Discharge during transit, antistatic bags act as Faraday Cages to protect sensitive devices.

==ESD in Aerospace==

Electrostatic Discharge is connected to Aerospace Engineering by how potentially dangerous it is to not guard against ESD in environment's in which many different electronic devices are integrated into air and spacecraft. Aerospace research agencies, such as NASA, JAXA, or RKA, and corporation, such as Lockheed Martin, have implemented ESD protected areas and grounded workbenches, mandated the use of protective equipment, introduced protocol in which charge generating materials cannot be worn in protected areas, and have audits and inspections to make sure important aerospace electronics stay protected from ESD.

Additionally, ESD poses a threat in the operation of air and spacecraft due to its volatile nature and possible interaction with fuel. When fueling aircraft, it is mandated procedure to ground the air frame to the fuel truck in order to prevent a spark from jumping between the metal surfaces.

==The Physics Principals and Visual Aids==

[[File:U8l2a2.gif]]

The objects near the top (of the list above) will tend to gain negative charges, while those below them will gain positive charges. The law of Conservation of Charge is followed.

[[File:5255360854_b0db025afb.jpg]]

First, a tube made out of plastic is charged when rubbed with synthetic fur (top pictures). The tube, which is now charged, is brought close to neutral paper bits on the table (bottom left). You can see that the tube and paper now attract each other and that this attraction is strong enough to lift the pieces of paper off the table.

==Connectedness==
1. The concept of Electrostatic Discharge (ESD) can be applied to many practical scenarios; however, one of the most notable instances of ESD is in the electronics manufacturing industry. Due to the fact that charges can accumulate relatively easily in electronics manufacturing, companies often have to take ESD precautions by making employees wear special clothing and by designing their workbenches and flooring out of special material which prevents electrostatic build up.

2.Electrostatic Discharge is connected to my major because in chemical engineering plants there is a great deal of equipment that has the potential to acquire electrostatic charge. As a result it is important for safety reasons to be knowledgeable and cautious when dealing with such equipment in order to reduce work related injuries.

3.One interesting way that ESD can be used is to create sparks. When the dielectric between two oppositely charged sources is damaged or if the electric field due to the build up charge exceeds the dielectric then ESD can occur by means of a spark through the air or other dielectric medium.

==History==
The phenomena of electrostatic discharge (ESD) has been known for a very long time dating all the way back to the ancient Greeks. While ESD was mostly considered a non-factor throughout most of history, recently since solid state electronics started to become big in the 1950's companies and researchers have had to account for and study in greater detail the phenomena of ESD. As the prevalence of electronics increased people began to notice the ESD could have very negative effects on certain components causing them to short-circuit or malfunction. The 1960s and 70s were characterized by companies discovering methods and techniques to test for ESD some of which included the Human Body Discharge Model and the Horizontal Coupling Plate. In the 1980's the release of the IBM personal computer saw an increased need for materials with resistance to ESD and thus the focus shifted towards maximizing the ability of electronic components to avoid ESD and subsequent malfunctioning. Since the 1980's and well into modern times, companies have been working to hone and refine this process in order to maximize the efficacy of their circuit components by increasing their ability to resist ESD when in use.

== See also ==
http://www.physicsbook.gatech.edu/Charge_Transfer

http://www.physicsbook.gatech.edu/Charge_Motion_in_Metals

http://www.physicsbook.gatech.edu/Polarization

https://en.wikipedia.org/wiki/Michael_Faraday

===Further reading===
Electro Static Discharge: Understand, Simulate, and Fix ESD Problems, 3rd Edition

===External links===

http://www.physicsclassroom.com/class/estatics/Lesson-2/Charging-by-Friction

==References==

Aaq.auburn.edu,. 'Summary | Academy Of Aerospace Quality'. N.p., 2015. Web. 5 Dec. 2015. (http://aaq.auburn.edu/node/277)

Michaels, Ken, AYMAN ZAHER, and Stan Herron. 'Electrostatic Discharge: Causes, Effects, And Solutions'. Ecmweb.com. N.p., 2013. Web. 6 Dec. 2015. (http://ecmweb.com/content/electrostatic-discharge-causes-effects-and-solutions)

Physicsclassroom.com,. 'Charging By Friction'. N.p., 2015. Web. 6 Dec. 2015. (http://www.physicsclassroom.com/class/estatics/Lesson-2/Charging-by-Friction)

Hoolihan, Daniel D. "A Brief History of Electrostatic Discharge Testing of Electronic Products Read More: Http://incompliancemag.com/article/a-brief-history-of-electrostatic-discharge-testing-of-electronic-products/#ixzz4R5MRIIIQ Follow Us: @incompliancemag on Twitter | Incompliancemag on Facebook." INCompliance. ECM Consulting, 01 Mar. 2014. Web. 25 Nov. 2016.

[[Category: Fields]]

Quantized energy levels

2016-11-28T23:28:40Z

Jledet:

Created by Keller Porter 
Revision by Jonathan Ledet Fall 2016

==The Main Idea==

The electrons around an atomic nucleus are held in orbit by an electric field (created by the positively charged protons interacting with the negatively charges electrons). The atom behaves in such a way that there is only certain spaces, called 'stationary orbits', in which electron orbits can happily exist. This behavior occurs due to the wave-particle duality of electrons and results in a formulaic and regular behavior of energy levels in each stationary orbit. Because the energy levels of each orbit are not a continuous spectrum, and rather exist at discrete values, they are said to be 'quantized'. Quantization is a transition from a classical understanding of physical principles to a more modern understanding.

The various levels of energy associated with an atom are described using its principle quantum number (often denoted as <math>n</math>). A principle quantum number <math>n</math> of 1 indicates that the electron is in the orbit (or 'shell') closest to the nucleus; this state is of the lowest energy level and is referred to as the 'ground state'. A principle quantum number of greater than 1 indicates an electron in a larger orbit and higher energy level; this state is referred to as 'excited'. Less energy is required to free an electron from an excited state.

[[File:Absorption spectrum.jpg]]
[[File:emission spectrum.jpg]]

If light is shone through a gas, the gas will absorb the specific wavelengths characteristic of the atoms in the gas. If the light were to be put through a prism of light or a diffraction grating, then there would be absorption lines, or places where the wavelength of light had been absorbed into the gas. This process creates something called an absorption spectrum. Similarly, if this same gas was heated to the right temperature, it would emit the same wavelengths that it absorbed before. Putting this emitted light through a prism or diffraction grating would create an emission spectrum. This is the opposite of an absorption spectrum because it shows the emission lines from the gas instead of the absorption lines. 

===A Mathematical Model===

[[File:level change.jpg]]

The energy of each level can be found using the formula: 
<math>E_n = \frac{-2\pi^2me^4Z^2}{n^2h^2}</math>
 where <math>m</math> is the mass of an electron, <math>e</math> is the magnitude of the electric charge, <math>n</math> is the principle quantum number, <math>h</math> is Planck's constant, and <math>Z</math> is the atomic number of the atom. This gives the energy for a specific atom at each energy level. The value will always be negative because electrons in the electron cloud are in a bounded state, so the potential energy is negative. 

 The radius of a given orbital can be found using the equation <math>2pi = n</math>λ<math>_n</math>

 Energy is associated to wavelength by <math>E = \frac{hc}{\lambda}</math>

 While the value for each energy level is set in place, the energy of each individual electron can change. This can happen either by an interaction with another electron or a photon. For an electron, they can jump from the ground state to the fourth level if <math>E_{particle} \ge E_4-E_1</math>

==A Computational Model==

 The radii of orbits are restricted to certain values due to the wave nature of electrons. Electrons can only exist happily in standing waves and the waves created by an orbit will only be standing if the wavelength follows the formula <math>2pi*r = n</math>λ<math>_n</math>

 Consider a wave of λ = 1 and a series of orbits with varying radii. If that wave is laid along the circular path of the orbit, there are only a few specific circumferences that will allow the wave to fit perfectly, forming a standing wave. Any length where the wavelength does not form a standing wave will cause patterns of interference and a stable orbit would be impossible.

[[File:WaveLengthstoElectrons.jpg]]
==Example: Hydrogen Model==

Research done by Johannes Rydberg showed that hydrogen has a ground level energy of <math>E_R = 13.6eV</math>. With Rydberg's constant, the initial formula for energy levels can be altered to include this. This new formula is: 
<math>E_n = \frac{-E_R}{n^2}</math>

===Basic Level Calculation===

Find the energy level for the level <math>n=6</math>. 
 Solution: <math>E_6 = \frac{-13.6}{6^2} = -.378eV</math>

===Level Change Calculation===

Will an electron with energy <math>E_{electron} = 10.4eV</math> be able to bump a hydrogen electron in the ground state to the second level? 
 Solution: <math>E_1 = \frac{-13.6}{1} = -13.6eV</math> 
<math>E_2 = \frac{-13.6}{2^2} = \frac{-13.6}{4} = -3.4eV</math> 
<math>E_2 - E_1 = -3.4eV - -13.6eV = 10.2eV</math>, so it requires <math>10.2eV</math> to bump an electron from the ground state to the second level. 
<math>10.4eV \ge 10.2eV</math> 
Yes, the electron has enough energy to bump the electron from the ground state to the second energy level.

==Implications==

Until quantization of atomic energy levels occurred, there were a few different experiments that had already been performed that did not make sense. Once researchers discovered the actual way electrons make up the electron cloud as well as the mechanisms that help them jump from level to level, these experiments could be explained. Readings for these three experiments can be found below.

#[https://en.wikipedia.org/wiki/Black-body_radiation Blackbody Radiation]
#[https://en.wikipedia.org/wiki/Photoelectric_effect Photoelectric Effect]
#[https://en.wikipedia.org/wiki/Emission_spectrum Emission Spectra of Atoms]

==History==

In the 1814, Joseph von Fraunhofer and William Hyde Wollaston discovered that when viewed closely, the spectrum from sunlight contained dark lines. These lines represented wavelengths of sunlight that were not reaching us. These wavelengths were being absorbed by the sun's atmosphere. 

[[File:Bohr atom.gif|thumb|left|none|This is a model of the Bohr atom. It shows different levels for the electrons to orbit the nucleus.]]

In 1911, Rutherford came up with his model for the atom. It used all the same components of an atom that we know exist today, but it had one glaring issue. His model lacked stability. Classical electromagnetic theory said that the electrons surrounding the nucleus would quickly collapse because they were emitting electromagnetic waves, causing them to lose energy. If this were true, then the atom as we know it would not be able to exist. 

 Bohr's model of the atom solved this problem. He proposed that the laws of classical mechanics must be reconsidered. His model said that the electron cloud had stationary orbits, a specific set of orbits for electrons. This differed from the assumption that the electron cloud was just a continuum where the electrons were free to orbit the nucleus. His model was similar to the solar system in that electrons orbit the nucleus like planets orbit the sun. Electrons are held in place by electrostatic forces, and planets are held in place by gravitational forces.

==References==

*http://hyperphysics.phy-astr.gsu.edu/hbase/bohr.html
*http://www.chemistry.mcmaster.ca/esam/Chapter_3/section_1.html
*http://www.colorado.edu/UCB/AcademicAffairs/ArtsSciences/physics/TZD/PageProofs1/TAYL05-144-167.I.pdf
*"Emission spectrum-H" by Merikanto, Adrignola - File:Emission spectrum-H.png. Licensed under CC0 via Commons - https://commons.wikimedia.org/wiki/File:Emission_spectrum-H.svg#/media/File:Emission_spectrum-H.svg
*"Fraunhofer lines" by Fraunhofer_lines.jpg: nl:Gebruiker:MaureenVSpectrum-sRGB.svg: PhroodFraunhofer_lines_DE.svg: *Fraunhofer_lines.jpg: Saperaud 19:26, 5. Jul. 2005derivative work: Cepheiden (talk)derivative work: Cepheiden (talk) - Fraunhofer_lines.jpgSpectrum-sRGB.svgFraunhofer_lines_DE.svg. Licensed under Public Domain via Commons - https://commons.wikimedia.org/wiki/File:Fraunhofer_lines.svg#/media/File:Fraunhofer_lines.svg
*http://venables.asu.edu/quant/Dinesh/Bohratom2.html (bohr atom)
*"Energy levels" by SVG: Hazmat2 Original: Rozzychan - This file was derived from: Energylevels.png. Licensed under CC BY-SA 3.0 via Commons - https://commons.wikimedia.org/wiki/File:Energy_levels.svg#/media/File:Energy_levels.svg

[[Category:Which Category did you place this in?]]

Quantized energy levels

2016-11-28T04:49:34Z

Jledet:

Created by Keller Porter 
Revision by Jonathan Ledet Fall 2016

==The Main Idea==

The electrons around an atomic nucleus are held in orbit by an electric field (created by the positively charged protons interacting with the negatively charges electrons). The atom behaves in such a way that there is only certain spaces, called 'stationary orbits', in which electron orbits can happily exist. This behavior occurs due to the wave-particle duality of electrons and results in a formulaic and regular behavior of energy levels in each stationary orbit. Because the energy levels of each orbit are not a continuous spectrum, and rather exist at discrete values, they are said to be 'quantized'. Quantization is a transition from a classical understanding of physical principles to a more modern understanding.

The various levels of energy associated with an atom are described using its principle quantum number (often denoted as <math>n</math>). A principle quantum number <math>n</math> of 1 indicates that the electron is in the orbit (or 'shell') closest to the nucleus; this state is of the lowest energy level and is referred to as the 'ground state'. A principle quantum number of greater than 1 indicates an electron in a larger orbit and higher energy level; this state is referred to as 'excited'. Less energy is required to free an electron from an excited state.

[[File:Absorption spectrum.jpg|thumb|left|A typical absorption spectrum graph.]]
[[File:emission spectrum.jpg|thumb|left|An emission spectrum graph for hydrogen.]]

If light is shone through a gas, the gas will absorb the specific wavelengths characteristic of the atoms in the gas. If the light were to be put through a prism of light or a diffraction grating, then there would be absorption lines, or places where the wavelength of light had been absorbed into the gas. This process creates something called an absorption spectrum. Similarly, if this same gas was heated to the right temperature, it would emit the same wavelengths that it absorbed before. Putting this emitted light through a prism or diffraction grating would create an emission spectrum. This is the opposite of an absorption spectrum because it shows the emission lines from the gas instead of the absorption lines. 

===A Mathematical Model===

[[File:level change.jpg|thumb|left|This represents the different levels that electrons can jump between provided they acquire energy from either another electron or a photon.]]

The energy of each level can be found using the formula: 
<math>E_n = \frac{-2\pi^2me^4Z^2}{n^2h^2}</math>
 where <math>m</math> is the mass of an electron, <math>e</math> is the magnitude of the electric charge, <math>n</math> is the principle quantum number, <math>h</math> is Planck's constant, and <math>Z</math> is the atomic number of the atom. This gives the energy for a specific atom at each energy level. The value will always be negative because electrons in the electron cloud are in a bounded state, so the potential energy is negative. 

 The radius of a given orbital can be found using the equation <math>2pi = n</math>λ<math>_n</math>

 Energy is associated to wavelength by <math>E = \frac{hc}{\lambda}</math>

 While the value for each energy level is set in place, the energy of each individual electron can change. This can happen either by an interaction with another electron or a photon. For an electron, they can jump from the ground state to the fourth level if <math>E_{particle} \ge E_4-E_1</math>

==A Computational Model==

 The radii of orbits are restricted to certain values due to the wave nature of electrons. Electrons can only exist happily in standing waves and the waves created by an orbit will only be standing if the wavelength follows the formula <math>2pi = n</math>λ<math>_n</math>

 Consider a wave of λ = 1 and a series of orbits with varying radii. If that wave is laid along the circular path of the orbit, there are only a few specific circumferences that will allow the wave to fit perfectly, forming a standing wave. Any length where the wavelength does not form a standing wave will cause patterns of interference and a stable orbit would be impossible.

==Example: Hydrogen Model==

Research done by Johannes Rydberg showed that hydrogen has a ground level energy of <math>E_R = 13.6eV</math>. With Rydberg's constant, the initial formula for energy levels can be altered to include this. This new formula is: 
<math>E_n = \frac{-E_R}{n^2}</math>

===Basic Level Calculation===

Find the energy level for the level <math>n=6</math>. 
 Solution: <math>E_6 = \frac{-13.6}{6^2} = -.378eV</math>

===Level Change Calculation===

Will an electron with energy <math>E_{electron} = 10.4eV</math> be able to bump a hydrogen electron in the ground state to the second level? 
 Solution: <math>E_1 = \frac{-13.6}{1} = -13.6eV</math> 
<math>E_2 = \frac{-13.6}{2^2} = \frac{-13.6}{4} = -3.4eV</math> 
<math>E_2 - E_1 = -3.4eV - -13.6eV = 10.2eV</math>, so it requires <math>10.2eV</math> to bump an electron from the ground state to the second level. 
<math>10.4eV \ge 10.2eV</math> 
Yes, the electron has enough energy to bump the electron from the ground state to the second energy level.

==Implications==

Until quantization of atomic energy levels occurred, there were a few different experiments that had already been performed that did not make sense. Once researchers discovered the actual way electrons make up the electron cloud as well as the mechanisms that help them jump from level to level, these experiments could be explained. Readings for these three experiments can be found below.

#[https://en.wikipedia.org/wiki/Black-body_radiation Blackbody Radiation]
#[https://en.wikipedia.org/wiki/Photoelectric_effect Photoelectric Effect]
#[https://en.wikipedia.org/wiki/Emission_spectrum Emission Spectra of Atoms]

==History==

In the 1814, Joseph von Fraunhofer and William Hyde Wollaston discovered that when viewed closely, the spectrum from sunlight contained dark lines. These lines represented wavelengths of sunlight that were not reaching us. These wavelengths were being absorbed by the sun's atmosphere. 

[[File:Bohr atom.gif|thumb|left|none|This is a model of the Bohr atom. It shows different levels for the electrons to orbit the nucleus.]]

In 1911, Rutherford came up with his model for the atom. It used all the same components of an atom that we know exist today, but it had one glaring issue. His model lacked stability. Classical electromagnetic theory said that the electrons surrounding the nucleus would quickly collapse because they were emitting electromagnetic waves, causing them to lose energy. If this were true, then the atom as we know it would not be able to exist. 

 Bohr's model of the atom solved this problem. He proposed that the laws of classical mechanics must be reconsidered. His model said that the electron cloud had stationary orbits, a specific set of orbits for electrons. This differed from the assumption that the electron cloud was just a continuum where the electrons were free to orbit the nucleus. His model was similar to the solar system in that electrons orbit the nucleus like planets orbit the sun. Electrons are held in place by electrostatic forces, and planets are held in place by gravitational forces.

==References==

*http://hyperphysics.phy-astr.gsu.edu/hbase/bohr.html
*http://www.chemistry.mcmaster.ca/esam/Chapter_3/section_1.html
*http://www.colorado.edu/UCB/AcademicAffairs/ArtsSciences/physics/TZD/PageProofs1/TAYL05-144-167.I.pdf
*"Emission spectrum-H" by Merikanto, Adrignola - File:Emission spectrum-H.png. Licensed under CC0 via Commons - https://commons.wikimedia.org/wiki/File:Emission_spectrum-H.svg#/media/File:Emission_spectrum-H.svg
*"Fraunhofer lines" by Fraunhofer_lines.jpg: nl:Gebruiker:MaureenVSpectrum-sRGB.svg: PhroodFraunhofer_lines_DE.svg: *Fraunhofer_lines.jpg: Saperaud 19:26, 5. Jul. 2005derivative work: Cepheiden (talk)derivative work: Cepheiden (talk) - Fraunhofer_lines.jpgSpectrum-sRGB.svgFraunhofer_lines_DE.svg. Licensed under Public Domain via Commons - https://commons.wikimedia.org/wiki/File:Fraunhofer_lines.svg#/media/File:Fraunhofer_lines.svg
*http://venables.asu.edu/quant/Dinesh/Bohratom2.html (bohr atom)
*"Energy levels" by SVG: Hazmat2 Original: Rozzychan - This file was derived from: Energylevels.png. Licensed under CC BY-SA 3.0 via Commons - https://commons.wikimedia.org/wiki/File:Energy_levels.svg#/media/File:Energy_levels.svg

[[Category:Which Category did you place this in?]]

Quantized energy levels

2016-11-28T04:44:06Z

Jledet:

Created by Keller Porter 
Revision by Jonathan Ledet Fall 2016

==The Main Idea==

The electrons around an atomic nucleus are held in orbit by an electric field (created by the positively charged protons interacting with the negatively charges electrons). The atom behaves in such a way that there is only certain spaces, called 'stationary orbits', in which electron orbits can happily exist. This behavior occurs due to the wave-particle duality of electrons and results in a formulaic and regular behavior of energy levels in each stationary orbit. Because the energy levels of each orbit are not a continuous spectrum, and rather exist at discrete values, they are said to be 'quantized'. Quantization is a transition from a classical understanding of physical principles to a more modern understanding.

The various levels of energy associated with an atom are described using its principle quantum number (often denoted as <math>n</math>). A principle quantum number <math>n</math> of 1 indicates that the electron is in the orbit (or 'shell') closest to the nucleus; this state is of the lowest energy level and is referred to as the 'ground state'. A principle quantum number of greater than 1 indicates an electron in a larger orbit and higher energy level; this state is referred to as 'excited'. Less energy is required to free an electron from an excited state.

===A Mathematical Model===

[[File:level change.jpg|thumb|left|This represents the different levels that electrons can jump between provided they acquire energy from either another electron or a photon.]]

The energy of each level can be found using the formula: 
<math>E_n = \frac{-2\pi^2me^4Z^2}{n^2h^2}</math>
 where <math>m</math> is the mass of an electron, <math>e</math> is the magnitude of the electric charge, <math>n</math> is the principle quantum number, <math>h</math> is Planck's constant, and <math>Z</math> is the atomic number of the atom. This gives the energy for a specific atom at each energy level. The value will always be negative because electrons in the electron cloud are in a bounded state, so the potential energy is negative. 

 The radius of a given orbital can be found using the equation <math>2pi = n</math>λ<math>_n</math>

 Energy is associated to wavelength by <math>E = \frac{hc}{\lambda}</math>

 While the value for each energy level is set in place, the energy of each individual electron can change. This can happen either by an interaction with another electron or a photon. For an electron, they can jump from the ground state to the fourth level if <math>E_{particle} \ge E_4-E_1</math>

==A Computational Model==

 The radii of orbits are restricted to certain values due to the wave nature of electrons. Electrons can only exist happily in standing waves and the waves created by an orbit will only be standing if the wavelength follows the formula <math>2pi = n</math>λ<math>_n</math>

 Consider a wave of λ = 1 and a series of orbits with varying radii. If that wave is laid along the circular path of the orbit, there are only a few specific circumferences that will allow the wave to fit perfectly, forming a standing wave. Any length where the wavelength does not form a standing wave will cause patterns of interference and a stable orbit would be impossible.

==Example: Hydrogen Model==

Research done by Johannes Rydberg showed that hydrogen has a ground level energy of <math>E_R = 13.6eV</math>. With Rydberg's constant, the initial formula for energy levels can be altered to include this. This new formula is: 
<math>E_n = \frac{-E_R}{n^2}</math>

===Basic Level Calculation===

Find the energy level for the level <math>n=6</math>. 
 Solution: <math>E_6 = \frac{-13.6}{6^2} = -.378eV</math>

===Level Change Calculation===

Will an electron with energy <math>E_{electron} = 10.4eV</math> be able to bump a hydrogen electron in the ground state to the second level? 
 Solution: <math>E_1 = \frac{-13.6}{1} = -13.6eV</math> 
<math>E_2 = \frac{-13.6}{2^2} = \frac{-13.6}{4} = -3.4eV</math> 
<math>E_2 - E_1 = -3.4eV - -13.6eV = 10.2eV</math>, so it requires <math>10.2eV</math> to bump an electron from the ground state to the second level. 
<math>10.4eV \ge 10.2eV</math> 
Yes, the electron has enough energy to bump the electron from the ground state to the second energy level.

==Implications==

Until quantization of atomic energy levels occurred, there were a few different experiments that had already been performed that did not make sense. Once researchers discovered the actual way electrons make up the electron cloud as well as the mechanisms that help them jump from level to level, these experiments could be explained. Readings for these three experiments can be found below.

#[https://en.wikipedia.org/wiki/Black-body_radiation Blackbody Radiation]
#[https://en.wikipedia.org/wiki/Photoelectric_effect Photoelectric Effect]
#[https://en.wikipedia.org/wiki/Emission_spectrum Emission Spectra of Atoms]

==History==

In the 1814, Joseph von Fraunhofer and William Hyde Wollaston discovered that when viewed closely, the spectrum from sunlight contained dark lines. These lines represented wavelengths of sunlight that were not reaching us. These wavelengths were being absorbed by the sun's atmosphere. 

[[File:Bohr atom.gif|thumb|left|none|This is a model of the Bohr atom. It shows different levels for the electrons to orbit the nucleus.]]

In 1911, Rutherford came up with his model for the atom. It used all the same components of an atom that we know exist today, but it had one glaring issue. His model lacked stability. Classical electromagnetic theory said that the electrons surrounding the nucleus would quickly collapse because they were emitting electromagnetic waves, causing them to lose energy. If this were true, then the atom as we know it would not be able to exist. 

 Bohr's model of the atom solved this problem. He proposed that the laws of classical mechanics must be reconsidered. His model said that the electron cloud had stationary orbits, a specific set of orbits for electrons. This differed from the assumption that the electron cloud was just a continuum where the electrons were free to orbit the nucleus. His model was similar to the solar system in that electrons orbit the nucleus like planets orbit the sun. Electrons are held in place by electrostatic forces, and planets are held in place by gravitational forces.

==References==

*http://hyperphysics.phy-astr.gsu.edu/hbase/bohr.html
*http://www.chemistry.mcmaster.ca/esam/Chapter_3/section_1.html
*http://www.colorado.edu/UCB/AcademicAffairs/ArtsSciences/physics/TZD/PageProofs1/TAYL05-144-167.I.pdf
*"Emission spectrum-H" by Merikanto, Adrignola - File:Emission spectrum-H.png. Licensed under CC0 via Commons - https://commons.wikimedia.org/wiki/File:Emission_spectrum-H.svg#/media/File:Emission_spectrum-H.svg
*"Fraunhofer lines" by Fraunhofer_lines.jpg: nl:Gebruiker:MaureenVSpectrum-sRGB.svg: PhroodFraunhofer_lines_DE.svg: *Fraunhofer_lines.jpg: Saperaud 19:26, 5. Jul. 2005derivative work: Cepheiden (talk)derivative work: Cepheiden (talk) - Fraunhofer_lines.jpgSpectrum-sRGB.svgFraunhofer_lines_DE.svg. Licensed under Public Domain via Commons - https://commons.wikimedia.org/wiki/File:Fraunhofer_lines.svg#/media/File:Fraunhofer_lines.svg
*http://venables.asu.edu/quant/Dinesh/Bohratom2.html (bohr atom)
*"Energy levels" by SVG: Hazmat2 Original: Rozzychan - This file was derived from: Energylevels.png. Licensed under CC BY-SA 3.0 via Commons - https://commons.wikimedia.org/wiki/File:Energy_levels.svg#/media/File:Energy_levels.svg

[[Category:Which Category did you place this in?]]

Quantized energy levels

2016-11-28T04:43:27Z

Jledet:

Created by Keller Porter 
Claimed for Revision by Jonathan Ledet Fall 2016

==The Main Idea==

The electrons around an atomic nucleus are held in orbit by an electric field (created by the positively charged protons interacting with the negatively charges electrons). The atom behaves in such a way that there is only certain spaces, called 'stationary orbits', in which electron orbits can happily exist. This behavior occurs due to the wave-particle duality of electrons and results in a formulaic and regular behavior of energy levels in each stationary orbit. Because the energy levels of each orbit are not a continuous spectrum, and rather exist at discrete values, they are said to be 'quantized'. Quantization is a transition from a classical understanding of physical principles to a more modern understanding.

The various levels of energy associated with an atom are described using its principle quantum number (often denoted as <math>n</math>). A principle quantum number <math>n</math> of 1 indicates that the electron is in the orbit (or 'shell') closest to the nucleus; this state is of the lowest energy level and is referred to as the 'ground state'. A principle quantum number of greater than 1 indicates an electron in a larger orbit and higher energy level; this state is referred to as 'excited'. Less energy is required to free an electron from an excited state.

===A Mathematical Model===

[[File:level change.jpg|thumb|left|This represents the different levels that electrons can jump between provided they acquire energy from either another electron or a photon.]]

The energy of each level can be found using the formula: 
<math>E_n = \frac{-2\pi^2me^4Z^2}{n^2h^2}</math>
 where <math>m</math> is the mass of an electron, <math>e</math> is the magnitude of the electric charge, <math>n</math> is the principle quantum number, <math>h</math> is Planck's constant, and <math>Z</math> is the atomic number of the atom. This gives the energy for a specific atom at each energy level. The value will always be negative because electrons in the electron cloud are in a bounded state, so the potential energy is negative. 

 The radius of a given orbital can be found using the equation <math>2pi = n</math>λ<math>_n</math>

 Energy is associated to wavelength by <math>E = \frac{hc}{\lambda}</math>

 While the value for each energy level is set in place, the energy of each individual electron can change. This can happen either by an interaction with another electron or a photon. For an electron, they can jump from the ground state to the fourth level if <math>E_{particle} \ge E_4-E_1</math>

==A Computational Model==

 The radii of orbits are restricted to certain values due to the wave nature of electrons. Electrons can only exist happily in standing waves and the waves created by an orbit will only be standing if the wavelength follows the formula <math>2pi = n</math>λ<math>_n</math>

 Consider a wave of λ = 1 and a series of orbits with varying radii. If that wave is laid along the circular path of the orbit, there are only a few specific circumferences that will allow the wave to fit perfectly, forming a standing wave. Any length where the wavelength does not form a standing wave will cause patterns of interference and a stable orbit would be impossible.

==Example: Hydrogen Model==

Research done by Johannes Rydberg showed that hydrogen has a ground level energy of <math>E_R = 13.6eV</math>. With Rydberg's constant, the initial formula for energy levels can be altered to include this. This new formula is: 
<math>E_n = \frac{-E_R}{n^2}</math>

===Basic Level Calculation===

Find the energy level for the level <math>n=6</math>. 
 Solution: <math>E_6 = \frac{-13.6}{6^2} = -.378eV</math>

===Level Change Calculation===

Will an electron with energy <math>E_{electron} = 10.4eV</math> be able to bump a hydrogen electron in the ground state to the second level? 
 Solution: <math>E_1 = \frac{-13.6}{1} = -13.6eV</math> 
<math>E_2 = \frac{-13.6}{2^2} = \frac{-13.6}{4} = -3.4eV</math> 
<math>E_2 - E_1 = -3.4eV - -13.6eV = 10.2eV</math>, so it requires <math>10.2eV</math> to bump an electron from the ground state to the second level. 
<math>10.4eV \ge 10.2eV</math> 
Yes, the electron has enough energy to bump the electron from the ground state to the second energy level.

==Implications==

Until quantization of atomic energy levels occurred, there were a few different experiments that had already been performed that did not make sense. Once researchers discovered the actual way electrons make up the electron cloud as well as the mechanisms that help them jump from level to level, these experiments could be explained. Readings for these three experiments can be found below.

#[https://en.wikipedia.org/wiki/Black-body_radiation Blackbody Radiation]
#[https://en.wikipedia.org/wiki/Photoelectric_effect Photoelectric Effect]
#[https://en.wikipedia.org/wiki/Emission_spectrum Emission Spectra of Atoms]

==History==

In the 1814, Joseph von Fraunhofer and William Hyde Wollaston discovered that when viewed closely, the spectrum from sunlight contained dark lines. These lines represented wavelengths of sunlight that were not reaching us. These wavelengths were being absorbed by the sun's atmosphere. 

[[File:Bohr atom.gif|thumb|left|none|This is a model of the Bohr atom. It shows different levels for the electrons to orbit the nucleus.]]

In 1911, Rutherford came up with his model for the atom. It used all the same components of an atom that we know exist today, but it had one glaring issue. His model lacked stability. Classical electromagnetic theory said that the electrons surrounding the nucleus would quickly collapse because they were emitting electromagnetic waves, causing them to lose energy. If this were true, then the atom as we know it would not be able to exist. 

 Bohr's model of the atom solved this problem. He proposed that the laws of classical mechanics must be reconsidered. His model said that the electron cloud had stationary orbits, a specific set of orbits for electrons. This differed from the assumption that the electron cloud was just a continuum where the electrons were free to orbit the nucleus. His model was similar to the solar system in that electrons orbit the nucleus like planets orbit the sun. Electrons are held in place by electrostatic forces, and planets are held in place by gravitational forces.

==References==

*http://hyperphysics.phy-astr.gsu.edu/hbase/bohr.html
*http://www.chemistry.mcmaster.ca/esam/Chapter_3/section_1.html
*http://www.colorado.edu/UCB/AcademicAffairs/ArtsSciences/physics/TZD/PageProofs1/TAYL05-144-167.I.pdf
*"Emission spectrum-H" by Merikanto, Adrignola - File:Emission spectrum-H.png. Licensed under CC0 via Commons - https://commons.wikimedia.org/wiki/File:Emission_spectrum-H.svg#/media/File:Emission_spectrum-H.svg
*"Fraunhofer lines" by Fraunhofer_lines.jpg: nl:Gebruiker:MaureenVSpectrum-sRGB.svg: PhroodFraunhofer_lines_DE.svg: *Fraunhofer_lines.jpg: Saperaud 19:26, 5. Jul. 2005derivative work: Cepheiden (talk)derivative work: Cepheiden (talk) - Fraunhofer_lines.jpgSpectrum-sRGB.svgFraunhofer_lines_DE.svg. Licensed under Public Domain via Commons - https://commons.wikimedia.org/wiki/File:Fraunhofer_lines.svg#/media/File:Fraunhofer_lines.svg
*http://venables.asu.edu/quant/Dinesh/Bohratom2.html (bohr atom)
*"Energy levels" by SVG: Hazmat2 Original: Rozzychan - This file was derived from: Energylevels.png. Licensed under CC BY-SA 3.0 via Commons - https://commons.wikimedia.org/wiki/File:Energy_levels.svg#/media/File:Energy_levels.svg

[[Category:Which Category did you place this in?]]

File:WaveLengthstoElectrons.gif

2016-11-28T04:40:21Z

Jledet:

Quantized energy levels

2016-11-28T04:19:44Z

Jledet:

Created by Keller Porter 
Claimed for Revision by Jonathan Ledet Fall 2016

==The Main Idea==

The electrons around an atomic nucleus are held in orbit by an electric field (created by the positively charged protons interacting with the negatively charges electrons). The atom behaves in such a way that there is only certain spaces, called 'stationary orbits', in which electron orbits can happily exist. This behavior occurs due to the wave-particle duality of electrons and results in a formulaic and regular behavior of energy levels in each stationary orbit. Because the energy levels of each orbit are not a continuous spectrum, and rather exist at discrete values, they are said to be 'quantized'. Quantization is a transition from a classical understanding of physical principles to a more modern understanding.

The various levels of energy associated with an atom are described using its principle quantum number (often denoted as <math>n</math>). A principle quantum number <math>n</math> of 1 indicates that the electron is in the orbit (or 'shell') closest to the nucleus; this state is of the lowest energy level and is referred to as the 'ground state'. A principle quantum number of greater than 1 indicates an electron in a larger orbit and higher energy level; this state is referred to as 'excited'.

===A Mathematical Model===

[[File:level change.jpg|thumb|left|This represents the different levels that electrons can jump between provided they acquire energy from either another electron or a photon.]]

The energy of each level can be found using the formula: 
<math>E_n = \frac{-2\pi^2me^4Z^2}{n^2h^2}</math>
 where <math>m</math> is the mass of an electron, <math>e</math> is the magnitude of the electric charge, <math>n</math> is the principle quantum number, <math>h</math> is Planck's constant, and <math>Z</math> is the atomic number of the atom. This gives the energy for a specific atom at each energy level. The value will always be negative because electrons in the electron cloud are in a bounded state, so the potential energy is negative. 

 While the value for each energy level is set in place, the energy of each individual electron can change. This can happen either by an interaction with another electron or a photon. For an electron, they can jump from the ground state to the fourth level if <math>E_{particle} \ge E_4-E_1</math>
==A Computational Model==

==Example: Hydrogen Model==

Research done by Johannes Rydberg showed that hydrogen has a ground level energy of <math>E_R = 13.6eV</math>. With Rydberg's constant, the initial formula for energy levels can be altered to include this. This new formula is: 
<math>E_n = \frac{-E_R}{n^2}</math>

===Basic Level Calculation===

Find the energy level for the level <math>n=6</math>. 
 Solution: <math>E_6 = \frac{-13.6}{6^2} = -.378eV</math>

===Level Change Calculation===

Will an electron with energy <math>E_{electron} = 10.4eV</math> be able to bump a hydrogen electron in the ground state to the second level? 
 Solution: <math>E_1 = \frac{-13.6}{1} = -13.6eV</math> 
<math>E_2 = \frac{-13.6}{2^2} = \frac{-13.6}{4} = -3.4eV</math> 
<math>E_2 - E_1 = -3.4eV - -13.6eV = 10.2eV</math>, so it requires <math>10.2eV</math> to bump an electron from the ground state to the second level. 
<math>10.4eV \ge 10.2eV</math> 
Yes, the electron has enough energy to bump the electron from the ground state to the second energy level.

==Implications==

Until quantization of atomic energy levels occurred, there were a few different experiments that had already been performed that did not make sense. Once researchers discovered the actual way electrons make up the electron cloud as well as the mechanisms that help them jump from level to level, these experiments could be explained. Readings for these three experiments can be found below.

#[https://en.wikipedia.org/wiki/Black-body_radiation Blackbody Radiation]
#[https://en.wikipedia.org/wiki/Photoelectric_effect Photoelectric Effect]
#[https://en.wikipedia.org/wiki/Emission_spectrum Emission Spectra of Atoms]

==History==

In the 1814, Joseph von Fraunhofer and William Hyde Wollaston discovered that when viewed closely, the spectrum from sunlight contained dark lines. These lines represented wavelengths of sunlight that were not reaching us. These wavelengths were being absorbed by the sun's atmosphere. 

[[File:Bohr atom.gif|thumb|left|none|This is a model of the Bohr atom. It shows different levels for the electrons to orbit the nucleus.]]

In 1911, Rutherford came up with his model for the atom. It used all the same components of an atom that we know exist today, but it had one glaring issue. His model lacked stability. Classical electromagnetic theory said that the electrons surrounding the nucleus would quickly collapse because they were emitting electromagnetic waves, causing them to lose energy. If this were true, then the atom as we know it would not be able to exist. 

 Bohr's model of the atom solved this problem. He proposed that the laws of classical mechanics must be reconsidered. His model said that the electron cloud had stationary orbits, a specific set of orbits for electrons. This differed from the assumption that the electron cloud was just a continuum where the electrons were free to orbit the nucleus. His model was similar to the solar system in that electrons orbit the nucleus like planets orbit the sun. Electrons are held in place by electrostatic forces, and planets are held in place by gravitational forces. The base energy level, called the ground state, is the first stationary orbit. From there, there can be many more levels. The energy of each level can be denoted <math>E_n</math>, <math>n=1,2,3...</math>. At the ground state, the energy required to free the electron is greatest. It requires a specific level of energy to excite an electron to another energy level, and energy can be released to bring the electron back down to the ground state. 

==References==

*http://hyperphysics.phy-astr.gsu.edu/hbase/bohr.html
*http://www.chemistry.mcmaster.ca/esam/Chapter_3/section_1.html
*http://www.colorado.edu/UCB/AcademicAffairs/ArtsSciences/physics/TZD/PageProofs1/TAYL05-144-167.I.pdf
*"Emission spectrum-H" by Merikanto, Adrignola - File:Emission spectrum-H.png. Licensed under CC0 via Commons - https://commons.wikimedia.org/wiki/File:Emission_spectrum-H.svg#/media/File:Emission_spectrum-H.svg
*"Fraunhofer lines" by Fraunhofer_lines.jpg: nl:Gebruiker:MaureenVSpectrum-sRGB.svg: PhroodFraunhofer_lines_DE.svg: *Fraunhofer_lines.jpg: Saperaud 19:26, 5. Jul. 2005derivative work: Cepheiden (talk)derivative work: Cepheiden (talk) - Fraunhofer_lines.jpgSpectrum-sRGB.svgFraunhofer_lines_DE.svg. Licensed under Public Domain via Commons - https://commons.wikimedia.org/wiki/File:Fraunhofer_lines.svg#/media/File:Fraunhofer_lines.svg
*http://venables.asu.edu/quant/Dinesh/Bohratom2.html (bohr atom)
*"Energy levels" by SVG: Hazmat2 Original: Rozzychan - This file was derived from: Energylevels.png. Licensed under CC BY-SA 3.0 via Commons - https://commons.wikimedia.org/wiki/File:Energy_levels.svg#/media/File:Energy_levels.svg

[[Category:Which Category did you place this in?]]

File:WaveLengthstoElectrons.jpg

2016-11-28T04:14:29Z

Jledet: Jledet uploaded a new version of "File:WaveLengthstoElectrons.jpg"

Illustrates the wave property of electrons and its influence on acceptable energy levels.

File:WaveLengthstoElectrons.jpg

2016-11-28T04:10:15Z

Jledet: Illustrates the wave property of electrons and its influence on acceptable energy levels.

Illustrates the wave property of electrons and its influence on acceptable energy levels.

Quantized energy levels

2016-11-28T02:50:15Z

Jledet:

Created by Keller Porter 
Claimed for Revision by Jonathan Ledet Fall 2016

==The Main Idea==

The nucleus of each every atom creates an electric field, and it is composed of different levels, or stationary orbits, and each one requires a different energy level for an electron to reside there. The electrons in this electric field are in a bound state, requiring energy to be removed from their current energy level. These energy levels are considered quantized. Quantization is a transition from a classical understanding of physical principles to a more modern understanding.

[[File:Absorption spectrum.jpg|thumb|left|A typical absorption spectrum graph.]]
[[File:emission spectrum.jpg|thumb|left|An emission spectrum graph for hydrogen.]]

If light is shone through a gas, the gas will absorb the specific wavelengths characteristic of the atoms in the gas. If the light were to be put through a prism of light or a diffraction grating, then there would be absorption lines, or places where the wavelength of light had been absorbed into the gas. This process creates something called an absorption spectrum. Similarly, if this same gas was heated to the right temperature, it would emit the same wavelengths that it absorbed before. Putting this emitted light through a prism or diffraction grating would create an emission spectrum. This is the opposite of an absorption spectrum because it shows the emission lines from the gas instead of the absorption lines. 

===Energy Level Calculations===

[[File:level change.jpg|thumb|left|This represents the different levels that electrons can jump between provided they acquire energy from either another electron or a photon.]]

The energy of each level can be found using the formula: 
<math>E_n = \frac{-2\pi^2me^4Z^2}{n^2h^2}</math>
 where <math>m</math> is the mass of an electron, <math>e</math> is the magnitude of the electric charge, <math>n</math> is the quantum number, <math>h</math> is Planck's constant, and <math>Z</math> is the atomic number of the atom. This gives the energy for a specific atom at each energy level. The value will always be negative because electrons in the electron cloud are in a bounded state, so the potential energy is negative. 

 While the value for each energy level is set in place, the energy of each individual electron can change. This can happen either by an interaction with another electron or a photon. For an electron, they can jump from the ground state to the fourth level if <math>E_{particle} \ge E_4-E_1</math>

==Example: Hydrogen Model==

Research done by Johannes Rydberg showed that hydrogen has a ground level energy of <math>E_R = 13.6eV</math>. With Rydberg's constant, the initial formula for energy levels can be altered to include this. This new formula is: 
<math>E_n = \frac{-E_R}{n^2}</math>

===Basic Level Calculation===

Find the energy level for the level <math>n=6</math>. 
 Solution: <math>E_6 = \frac{-13.6}{6^2} = -.378eV</math>

===Level Change Calculation===

Will an electron with energy <math>E_{electron} = 10.4eV</math> be able to bump a hydrogen electron in the ground state to the second level? 
 Solution: <math>E_1 = \frac{-13.6}{1} = -13.6eV</math> 
<math>E_2 = \frac{-13.6}{2^2} = \frac{-13.6}{4} = -3.4eV</math> 
<math>E_2 - E_1 = -3.4eV - -13.6eV = 10.2eV</math>, so it requires <math>10.2eV</math> to bump an electron from the ground state to the second level. 
<math>10.4eV \ge 10.2eV</math> 
Yes, the electron has enough energy to bump the electron from the ground state to the second energy level.

==Implications==

Until quantization of atomic energy levels occurred, there were a few different experiments that had already been performed that did not make sense. Once researchers discovered the actual way electrons make up the electron cloud as well as the mechanisms that help them jump from level to level, these experiments could be explained. Readings for these three experiments can be found below.

#[https://en.wikipedia.org/wiki/Black-body_radiation Blackbody Radiation]
#[https://en.wikipedia.org/wiki/Photoelectric_effect Photoelectric Effect]
#[https://en.wikipedia.org/wiki/Emission_spectrum Emission Spectra of Atoms]

==History==

In the 1814, Joseph von Fraunhofer and William Hyde Wollaston discovered that when viewed closely, the spectrum from sunlight contained dark lines. These lines represented wavelengths of sunlight that were not reaching us. These wavelengths were being absorbed by the sun's atmosphere. 

[[File:Bohr atom.gif|thumb|left|none|This is a model of the Bohr atom. It shows different levels for the electrons to orbit the nucleus.]]

In 1911, Rutherford came up with his model for the atom. It used all the same components of an atom that we know exist today, but it had one glaring issue. His model lacked stability. Classical electromagnetic theory said that the electrons surrounding the nucleus would quickly collapse because they were emitting electromagnetic waves, causing them to lose energy. If this were true, then the atom as we know it would not be able to exist. 

 Bohr's model of the atom solved this problem. He proposed that the laws of classical mechanics must be reconsidered. His model said that the electron cloud had stationary orbits, a specific set of orbits for electrons. This differed from the assumption that the electron cloud was just a continuum where the electrons were free to orbit the nucleus. His model was similar to the solar system in that electrons orbit the nucleus like planets orbit the sun. Electrons are held in place by electrostatic forces, and planets are held in place by gravitational forces. The base energy level, called the ground state, is the first stationary orbit. From there, there can be many more levels. The energy of each level can be denoted <math>E_n</math>, <math>n=1,2,3...</math>. At the ground state, the energy required to free the electron is greatest. It requires a specific level of energy to excite an electron to another energy level, and energy can be released to bring the electron back down to the ground state. 

==References==

*http://hyperphysics.phy-astr.gsu.edu/hbase/bohr.html
*http://www.chemistry.mcmaster.ca/esam/Chapter_3/section_1.html
*http://www.colorado.edu/UCB/AcademicAffairs/ArtsSciences/physics/TZD/PageProofs1/TAYL05-144-167.I.pdf
*"Emission spectrum-H" by Merikanto, Adrignola - File:Emission spectrum-H.png. Licensed under CC0 via Commons - https://commons.wikimedia.org/wiki/File:Emission_spectrum-H.svg#/media/File:Emission_spectrum-H.svg
*"Fraunhofer lines" by Fraunhofer_lines.jpg: nl:Gebruiker:MaureenVSpectrum-sRGB.svg: PhroodFraunhofer_lines_DE.svg: *Fraunhofer_lines.jpg: Saperaud 19:26, 5. Jul. 2005derivative work: Cepheiden (talk)derivative work: Cepheiden (talk) - Fraunhofer_lines.jpgSpectrum-sRGB.svgFraunhofer_lines_DE.svg. Licensed under Public Domain via Commons - https://commons.wikimedia.org/wiki/File:Fraunhofer_lines.svg#/media/File:Fraunhofer_lines.svg
*http://venables.asu.edu/quant/Dinesh/Bohratom2.html (bohr atom)
*"Energy levels" by SVG: Hazmat2 Original: Rozzychan - This file was derived from: Energylevels.png. Licensed under CC BY-SA 3.0 via Commons - https://commons.wikimedia.org/wiki/File:Energy_levels.svg#/media/File:Energy_levels.svg

[[Category:Which Category did you place this in?]]

Quantized energy levels

2016-11-28T02:33:57Z

Jledet:

Created by Keller Porter 
Claimed for Revision by Jonathan Ledet Fall 2016

The nucleus of each every atom creates an electric field, and it is composed of different levels, or stationary orbits, and each one requires a different energy level for an electron to reside there. The electrons in this electric field are in a bound state, requiring energy to be removed from their current energy level. These energy levels are considered quantized. Quantization is a transition from a classical understanding of physical principles to a more modern understanding.

===Background===

In the 1814, Joseph von Fraunhofer and William Hyde Wollaston discovered that when viewed closely, the spectrum from sunlight contained dark lines. These lines represented wavelengths of sunlight that were not reaching us. These wavelengths were being absorbed by the sun's atmosphere. 

[[File:Absorption spectrum.jpg|thumb|right|A typical absorption spectrum graph.]]
[[File:emission spectrum.jpg|thumb|right|An emission spectrum graph for hydrogen.]]

If light is shone through a gas, the gas will absorb the specific wavelengths characteristic of the atoms in the gas. If the light were to be put through a prism of light or a diffraction grating, then there would be absorption lines, or places where the wavelength of light had been absorbed into the gas. This process creates something called an absorption spectrum. Similarly, if this same gas was heated to the right temperature, it would emit the same wavelengths that it absorbed before. Putting this emitted light through a prism or diffraction grating would create an emission spectrum. This is the opposite of an absorption spectrum because it shows the emission lines from the gas instead of the absorption lines. 

===Atom Energy Stability===

In 1911, Rutherford came up with his model for the atom. It used all the same components of an atom that we know exist today, but it had one glaring issue. His model lacked stability. Classical electromagnetic theory said that the electrons surrounding the nucleus would quickly collapse because they were emitting electromagnetic waves, causing them to lose energy. If this were true, then the atom as we know it would not be able to exist. 

[[File:Bohr atom.gif|thumb|right|This is a model of the Bohr atom. It shows different levels for the electrons to orbit the nucleus.]]

 Bohr's model of the atom solved this problem. He proposed that the laws of classical mechanics must be reconsidered. His model said that the electron cloud had stationary orbits, a specific set of orbits for electrons. This differed from the assumption that the electron cloud was just a continuum where the electrons were free to orbit the nucleus. His model was similar to the solar system in that electrons orbit the nucleus like planets orbit the sun. Electrons are held in place by electrostatic forces, and planets are held in place by gravitational forces. The base energy level, called the ground state, is the first stationary orbit. From there, there can be many more levels. The energy of each level can be denoted <math>E_n</math>, <math>n=1,2,3...</math>. At the ground state, the energy required to free the electron is greatest. It requires a specific level of energy to excite an electron to another energy level, and energy can be released to bring the electron back down to the ground state. 

===Energy Level Calculations===

The energy of each level can be found using the formula: 
<math>E_n = \frac{-2\pi^2me^4Z^2}{n^2h^2}</math>
 where <math>m</math> is the mass of an electron, <math>e</math> is the magnitude of the electric charge, <math>n</math> is the quantum number, <math>h</math> is Planck's constant, and <math>Z</math> is the atomic number of the atom. This gives the energy for a specific atom at each energy level. The value will always be negative because electrons in the electron cloud are in a bounded state, so the potential energy is negative. 

[[File:level change.jpg|thumb|left|This represents the different levels that electrons can jump between provided they acquire energy from either another electron or a photon.]]

 While the value for each energy level is set in place, the energy of each individual electron can change. This can happen either by an interaction with another electron or a photon. For an electron, they can jump from the ground state to the fourth level if <math>E_{particle} \ge E_4-E_1</math>

==Example: Hydrogen Model==

Research done by Johannes Rydberg showed that hydrogen has a ground level energy of <math>E_R = 13.6eV</math>. With Rydberg's constant, the initial formula for energy levels can be altered to include this. This new formula is: 
<math>E_n = \frac{-E_R}{n^2}</math>

===Basic Level Calculation===

Find the energy level for the level <math>n=6</math>. 
 Solution: <math>E_6 = \frac{-13.6}{6^2} = -.378eV</math>

===Level Change Calculation===

Will an electron with energy <math>E_{electron} = 10.4eV</math> be able to bump a hydrogen electron in the ground state to the second level? 
 Solution: <math>E_1 = \frac{-13.6}{1} = -13.6eV</math> 
<math>E_2 = \frac{-13.6}{2^2} = \frac{-13.6}{4} = -3.4eV</math> 
<math>E_2 - E_1 = -3.4eV - -13.6eV = 10.2eV</math>, so it requires <math>10.2eV</math> to bump an electron from the ground state to the second level. 
<math>10.4eV \ge 10.2eV</math> 
Yes, the electron has enough energy to bump the electron from the ground state to the second energy level.

==Implications==

Until quantization of atomic energy levels occurred, there were a few different experiments that had already been performed that did not make sense. Once researchers discovered the actual way electrons make up the electron cloud as well as the mechanisms that help them jump from level to level, these experiments could be explained. Readings for these three experiments can be found below.

#[https://en.wikipedia.org/wiki/Black-body_radiation Blackbody Radiation]
#[https://en.wikipedia.org/wiki/Photoelectric_effect Photoelectric Effect]
#[https://en.wikipedia.org/wiki/Emission_spectrum Emission Spectra of Atoms]

==References==

*http://hyperphysics.phy-astr.gsu.edu/hbase/bohr.html
*http://www.chemistry.mcmaster.ca/esam/Chapter_3/section_1.html
*http://www.colorado.edu/UCB/AcademicAffairs/ArtsSciences/physics/TZD/PageProofs1/TAYL05-144-167.I.pdf
*"Emission spectrum-H" by Merikanto, Adrignola - File:Emission spectrum-H.png. Licensed under CC0 via Commons - https://commons.wikimedia.org/wiki/File:Emission_spectrum-H.svg#/media/File:Emission_spectrum-H.svg
*"Fraunhofer lines" by Fraunhofer_lines.jpg: nl:Gebruiker:MaureenVSpectrum-sRGB.svg: PhroodFraunhofer_lines_DE.svg: *Fraunhofer_lines.jpg: Saperaud 19:26, 5. Jul. 2005derivative work: Cepheiden (talk)derivative work: Cepheiden (talk) - Fraunhofer_lines.jpgSpectrum-sRGB.svgFraunhofer_lines_DE.svg. Licensed under Public Domain via Commons - https://commons.wikimedia.org/wiki/File:Fraunhofer_lines.svg#/media/File:Fraunhofer_lines.svg
*http://venables.asu.edu/quant/Dinesh/Bohratom2.html (bohr atom)
*"Energy levels" by SVG: Hazmat2 Original: Rozzychan - This file was derived from: Energylevels.png. Licensed under CC BY-SA 3.0 via Commons - https://commons.wikimedia.org/wiki/File:Energy_levels.svg#/media/File:Energy_levels.svg

[[Category:Which Category did you place this in?]]

Quantized energy levels

2016-11-28T02:32:43Z

Jledet:

Created by Keller Porter
Claimed for Revision by Jonathan Ledet Fall 2016

The nucleus of each every atom creates an electric field, and it is composed of different levels, or stationary orbits, and each one requires a different energy level for an electron to reside there. The electrons in this electric field are in a bound state, requiring energy to be removed from their current energy level. These energy levels are considered quantized. Quantization is a transition from a classical understanding of physical principles to a more modern understanding.

===Background===

In the 1814, Joseph von Fraunhofer and William Hyde Wollaston discovered that when viewed closely, the spectrum from sunlight contained dark lines. These lines represented wavelengths of sunlight that were not reaching us. These wavelengths were being absorbed by the sun's atmosphere. 

[[File:Absorption spectrum.jpg|thumb|right|A typical absorption spectrum graph.]]
[[File:emission spectrum.jpg|thumb|right|An emission spectrum graph for hydrogen.]]

If light is shone through a gas, the gas will absorb the specific wavelengths characteristic of the atoms in the gas. If the light were to be put through a prism of light or a diffraction grating, then there would be absorption lines, or places where the wavelength of light had been absorbed into the gas. This process creates something called an absorption spectrum. Similarly, if this same gas was heated to the right temperature, it would emit the same wavelengths that it absorbed before. Putting this emitted light through a prism or diffraction grating would create an emission spectrum. This is the opposite of an absorption spectrum because it shows the emission lines from the gas instead of the absorption lines. 

===Atom Energy Stability===

In 1911, Rutherford came up with his model for the atom. It used all the same components of an atom that we know exist today, but it had one glaring issue. His model lacked stability. Classical electromagnetic theory said that the electrons surrounding the nucleus would quickly collapse because they were emitting electromagnetic waves, causing them to lose energy. If this were true, then the atom as we know it would not be able to exist. 

[[File:Bohr atom.gif|thumb|right|This is a model of the Bohr atom. It shows different levels for the electrons to orbit the nucleus.]]

 Bohr's model of the atom solved this problem. He proposed that the laws of classical mechanics must be reconsidered. His model said that the electron cloud had stationary orbits, a specific set of orbits for electrons. This differed from the assumption that the electron cloud was just a continuum where the electrons were free to orbit the nucleus. His model was similar to the solar system in that electrons orbit the nucleus like planets orbit the sun. Electrons are held in place by electrostatic forces, and planets are held in place by gravitational forces. The base energy level, called the ground state, is the first stationary orbit. From there, there can be many more levels. The energy of each level can be denoted <math>E_n</math>, <math>n=1,2,3...</math>. At the ground state, the energy required to free the electron is greatest. It requires a specific level of energy to excite an electron to another energy level, and energy can be released to bring the electron back down to the ground state. 

===Energy Level Calculations===

The energy of each level can be found using the formula: 
<math>E_n = \frac{-2\pi^2me^4Z^2}{n^2h^2}</math>
 where <math>m</math> is the mass of an electron, <math>e</math> is the magnitude of the electric charge, <math>n</math> is the quantum number, <math>h</math> is Planck's constant, and <math>Z</math> is the atomic number of the atom. This gives the energy for a specific atom at each energy level. The value will always be negative because electrons in the electron cloud are in a bounded state, so the potential energy is negative. 

[[File:level change.jpg|thumb|left|This represents the different levels that electrons can jump between provided they acquire energy from either another electron or a photon.]]

 While the value for each energy level is set in place, the energy of each individual electron can change. This can happen either by an interaction with another electron or a photon. For an electron, they can jump from the ground state to the fourth level if <math>E_{particle} \ge E_4-E_1</math>

==Example: Hydrogen Model==

Research done by Johannes Rydberg showed that hydrogen has a ground level energy of <math>E_R = 13.6eV</math>. With Rydberg's constant, the initial formula for energy levels can be altered to include this. This new formula is: 
<math>E_n = \frac{-E_R}{n^2}</math>

===Basic Level Calculation===

Find the energy level for the level <math>n=6</math>. 
 Solution: <math>E_6 = \frac{-13.6}{6^2} = -.378eV</math>

===Level Change Calculation===

Will an electron with energy <math>E_{electron} = 10.4eV</math> be able to bump a hydrogen electron in the ground state to the second level? 
 Solution: <math>E_1 = \frac{-13.6}{1} = -13.6eV</math> 
<math>E_2 = \frac{-13.6}{2^2} = \frac{-13.6}{4} = -3.4eV</math> 
<math>E_2 - E_1 = -3.4eV - -13.6eV = 10.2eV</math>, so it requires <math>10.2eV</math> to bump an electron from the ground state to the second level. 
<math>10.4eV \ge 10.2eV</math> 
Yes, the electron has enough energy to bump the electron from the ground state to the second energy level.

==Implications==

Until quantization of atomic energy levels occurred, there were a few different experiments that had already been performed that did not make sense. Once researchers discovered the actual way electrons make up the electron cloud as well as the mechanisms that help them jump from level to level, these experiments could be explained. Readings for these three experiments can be found below.

#[https://en.wikipedia.org/wiki/Black-body_radiation Blackbody Radiation]
#[https://en.wikipedia.org/wiki/Photoelectric_effect Photoelectric Effect]
#[https://en.wikipedia.org/wiki/Emission_spectrum Emission Spectra of Atoms]

==References==

*http://hyperphysics.phy-astr.gsu.edu/hbase/bohr.html
*http://www.chemistry.mcmaster.ca/esam/Chapter_3/section_1.html
*http://www.colorado.edu/UCB/AcademicAffairs/ArtsSciences/physics/TZD/PageProofs1/TAYL05-144-167.I.pdf
*"Emission spectrum-H" by Merikanto, Adrignola - File:Emission spectrum-H.png. Licensed under CC0 via Commons - https://commons.wikimedia.org/wiki/File:Emission_spectrum-H.svg#/media/File:Emission_spectrum-H.svg
*"Fraunhofer lines" by Fraunhofer_lines.jpg: nl:Gebruiker:MaureenVSpectrum-sRGB.svg: PhroodFraunhofer_lines_DE.svg: *Fraunhofer_lines.jpg: Saperaud 19:26, 5. Jul. 2005derivative work: Cepheiden (talk)derivative work: Cepheiden (talk) - Fraunhofer_lines.jpgSpectrum-sRGB.svgFraunhofer_lines_DE.svg. Licensed under Public Domain via Commons - https://commons.wikimedia.org/wiki/File:Fraunhofer_lines.svg#/media/File:Fraunhofer_lines.svg
*http://venables.asu.edu/quant/Dinesh/Bohratom2.html (bohr atom)
*"Energy levels" by SVG: Hazmat2 Original: Rozzychan - This file was derived from: Energylevels.png. Licensed under CC BY-SA 3.0 via Commons - https://commons.wikimedia.org/wiki/File:Energy_levels.svg#/media/File:Energy_levels.svg

[[Category:Which Category did you place this in?]]

Eulerian Angles

2016-11-28T02:30:32Z

Jledet:

==Introduction==
When you have a body that rotates in plane motion (2-D), it is easy to find the orientation of the body if you have the angular velocity as a function of time. You can integrate this value to find the orientation of the body at any position. In the image shown, we can find out the position of an object at any place in the ''xy'' plane.

[[File:AngularVelocityPosition2D.PNG|thumb|Simple angular velocity equation in 2D.]]

Unfortunately, you cannot integrate an angular velocity vector with 3-D components to get the orientation of the body in three dimensional space. This requires the concept of '''Eulerian Angles''', which are used in determining a body's orientation in space using angular velocity in the x, y, and z axes.

===Eulerian Angles===

Essentially, to describe the orientation of a body in 3 dimensions we must describe its rotation about three specific axes. In our example shown in the image, we will first rotate our body's reference frame about the '''k''' axis (black to blue), then the '''j''' axes (blue to green), and finally the '''k''' axis again (green to red).

[[File:RotationsEulerianAngles3D.PNG|thumb|Rotationsabouteulerianangles]]

Note, we moved from the black '''i, j, k''' axes to the blue '''i, j, k''' axes, where the k axis remained the same for both black and blue frames. Then we moved from the blue '''i, j, k''' axes to the green '''i, j, k''' axes, where the j axis remained the same for both the blue and green frames. Finally, we moved from the green '''i, j, k''' axes to the red '''i, j, k''' axes, where the k axis remained the same for both the green and the red frames.

'''Angular Velocity'''
Using the addition theorem (can be further studied at [https://www.coursera.org/learn/motion-and-kinetics/lecture/ohKPT/module-3-define-the-properties-of-angular-velocity-for-3d-motion Coursera]) we find that the body ''A'' with respect to the inertial frame ''I'' is defined to be '''w''' = θ' '''k (black/blue axis)''' + φ' '''j (blue/green axis)''' + ψ' '''k (green/red axis)'''. However, everything here is defined in different frames and we must consolidate our equations into one coordinate system.

'''Converting Into One Frame'''
Please view the image on the bottom right to see how we described a bodies orientation into one frame even though it started off with three separate orientations.

[[File:Changing orientation to one frame.PNG|thumb|Changing orientation to one frame]]

==Example of a Gyroscope==

We can use the procedure outlined above to describe the orientation of a gyroscope at any time given the components of its angular velocity. An example of a rotation gyroscope is shown in the image.

[[File:Gyroscope operation.gif|thumb|Gyroscope operation]]

[http://ocw.mit.edu/courses/aeronautics-and-astronautics/16-07-dynamics-fall-2009/lecture-notes/MIT16_07F09_Lec30.pdf Proof from MIT course]

==Connectedness==
#How is this topic connected to something that you are interested in?
All objects in the real world move in complex ways. Luckily for us, we only experience 3 dimensions. Hence, we can use the Eulerian Angles to classify all sorts of rotational behaviors. Knowing how much angular velocity an object has in any direction can give us its position at any time.

#How is it connected to your major?
This topic is vastly connected to any major related to engineering mechanics. Mechanical engineering students and aerospace students will find this to be one of the fundamental building blocks of their field of study, as it is an important tool for engineers working in 3 dimensions. Imagine trying to position a satellite in space but not being able to determine where it's facing at a given time! Even video game creators and animators require Eulerian angles for mouse control and orienting animated objects (links below).

===Further reading===
Euler Angles in Video Games
[https://www.youtube.com/watch?v=zZM2uUkEoFw Mouse Control]

Euler Angles Related Examples
[http://www.chrobotics.com/library/understanding-euler-angles CHRO Robotics]

Euler Angles for Animations
[https://www.youtube.com/watch?v=zc8b2Jo7mno Euler (Gimbal lock) Explained]

==References==
Dr. Wayne Whiteman
DEFINE THE PROPERTIES OF ANGULAR VELOCITY FOR 3D MOTION
[https://www.coursera.org/learn/motion-and-kinetics/lecture/nkGSe/module-13-eulerian-angles-for-3d-rotational-motion Coursera Lesson on Eulerian Angles]

McGill, David J., and Wilton W. King. An Introduction to Dynamics. Monterey, CA: Brooks/Cole Engineering Division, 1984. Print.

Eulerian Angles

2016-11-28T02:14:34Z

Jledet:

Claimed by Jonathan Ledet Fall 2016

==Introduction==
When you have a body that rotates in plane motion (2-D), it is easy to find the orientation of the body if you have the angular velocity as a function of time. You can integrate this value to find the orientation of the body at any position. In the image shown, we can find out the position of an object at any place in the ''xy'' plane.

[[File:AngularVelocityPosition2D.PNG|thumb|Simple angular velocity equation in 2D.]]

Unfortunately, you cannot integrate an angular velocity vector with 3-D components to get the orientation of the body in three dimensional space. This requires the concept of '''Eulerian Angles''', which are used in determining a body's orientation in space using angular velocity in the x, y, and z axes.

===Eulerian Angles===

Essentially, to describe the orientation of a body in 3 dimensions we must describe its rotation about three specific axes. In our example shown in the image, we will first rotate our body's reference frame about the '''k''' axis (black to blue), then the '''j''' axes (blue to green), and finally the '''k''' axis again (green to red).

[[File:RotationsEulerianAngles3D.PNG|thumb|Rotationsabouteulerianangles]]

Note, we moved from the black '''i, j, k''' axes to the blue '''i, j, k''' axes, where the k axis remained the same for both black and blue frames. Then we moved from the blue '''i, j, k''' axes to the green '''i, j, k''' axes, where the j axis remained the same for both the blue and green frames. Finally, we moved from the green '''i, j, k''' axes to the red '''i, j, k''' axes, where the k axis remained the same for both the green and the red frames.

'''Angular Velocity'''
Using the addition theorem (can be further studied at [https://www.coursera.org/learn/motion-and-kinetics/lecture/ohKPT/module-3-define-the-properties-of-angular-velocity-for-3d-motion Coursera]) we find that the body ''A'' with respect to the inertial frame ''I'' is defined to be '''w''' = θ' '''k (black/blue axis)''' + φ' '''j (blue/green axis)''' + ψ' '''k (green/red axis)'''. However, everything here is defined in different frames and we must consolidate our equations into one coordinate system.

'''Converting Into One Frame'''
Please view the image on the bottom right to see how we described a bodies orientation into one frame even though it started off with three separate orientations.

[[File:Changing orientation to one frame.PNG|thumb|Changing orientation to one frame]]

==Example of a Gyroscope==

We can use the procedure outlined above to describe the orientation of a gyroscope at any time given the components of its angular velocity. An example of a rotation gyroscope is shown in the image.

[[File:Gyroscope operation.gif|thumb|Gyroscope operation]]

[http://ocw.mit.edu/courses/aeronautics-and-astronautics/16-07-dynamics-fall-2009/lecture-notes/MIT16_07F09_Lec30.pdf Proof from MIT course]

==Connectedness==
#How is this topic connected to something that you are interested in?
All objects in the real world move in complex ways. Luckily for us, we only experience 3 dimensions. Hence, we can use the Eulerian Angles to classify all sorts of rotational behaviors. Knowing how much angular velocity an object has in any direction can give us its position at any time.

#How is it connected to your major?
This topic is vastly connected to any major related to engineering mechanics. Mechanical engineering students and aerospace students will find this to be one of the fundamental building blocks of their field of study, as it is an important tool for engineers working in 3 dimensions. Imagine trying to position a satellite in space but not being able to determine where it's facing at a given time! Even video game creators and animators require Eulerian angles for mouse control and orienting animated objects (links below).

===Further reading===
Euler Angles in Video Games
[https://www.youtube.com/watch?v=zZM2uUkEoFw Mouse Control]

Euler Angles Related Examples
[http://www.chrobotics.com/library/understanding-euler-angles CHRO Robotics]

Euler Angles for Animations
[https://www.youtube.com/watch?v=zc8b2Jo7mno Euler (Gimbal lock) Explained]

==References==
Dr. Wayne Whiteman
DEFINE THE PROPERTIES OF ANGULAR VELOCITY FOR 3D MOTION
[https://www.coursera.org/learn/motion-and-kinetics/lecture/nkGSe/module-13-eulerian-angles-for-3d-rotational-motion Coursera Lesson on Eulerian Angles]

McGill, David J., and Wilton W. King. An Introduction to Dynamics. Monterey, CA: Brooks/Cole Engineering Division, 1984. Print.