Polarization of an Atom

Claimed and Edited by Julia Woodall Spring 2019

Claimed by Owen Fisher (ofisher3)

Edited by Aniruddha Nadkarni Fall 2016

This page serves to outline and explain the inner workings and hidden mechanisms of the polarization of an atom.

The Main Idea

Atoms are basic units of matter, consisting of different charged particles. An atom contains a nucleus made of protons (with +e charge) and neutrons (neutral) which is surrounded by an "electron cloud" defined by a space where electrons (with -e charge) exist. While electrons are attracted to the nucleus and therefore generally remain near the the nucleus, electrons can also be shifted by external charges. These external charges therefore allow electrons to shift so that the electron cloud is no longer centered on the nucleus, and this results in an symmetric distribution of charge allowing the atom to be "polarized".

More specifically, these external charges create apply an electric force on atom constituents. For example, if a positive charge is placed to the left of an atom, an electric field will be created that shifts the electron cloud of the atom towards the positive charge (to the left) and will shift the net positive nucleus away from the charge (to the right) as two objects of the same charge repel each other. In this case, it is now more probable to find an electron to the left of the nucleus, rather than the right.

A Mathematical Model

The following are equations mediating these interactions. First and most importantly, electric fields are the product of field source charge and the distance to the observation location at which you would like to find the electric field value. Coulomb's Law allows us to calculate this for a point charge:

[math]\displaystyle{ {\vec{E} = \frac{1}{4\pi\varepsilon_0} \frac{q}{r^2}} }[/math] [math]\displaystyle{ {\hat r} }[/math]

where E is the electric field at the observation point, q is the charge of the particle creating the electric field, and q is a vector from the source of the field to the observation location.

This electric field then can apply a force onto charge particles at the observation locations, a force that is quantified by the following equation.

[math]\displaystyle{ {\vec{F} = q\vec{E}} }[/math]

where F is the force created by the electric field E and the charge of a particle q. Note that q in this equation is the charge of the particle being affected by the electric field, NOT the charge of the particle causing the electric field. For example, this would be the charge of an electron if we were calculating the force on the electron by an external electric field.

This force is what causes the atom to become polarized. This force is responsible for "polarizing" an atom by accelerating the electrons and shifting the electron cloud of an atom.

Once an atom is polarized, it forms an induced dipole. A "dipole" is a pair of equal and oppositely charged particles. In this case, these particles are comprised of the nucleus (which is positively charged) and the electron cloud (which is negatively charged). This dipole is "induced" as it was formed as a result of an external, temporary force and would return in a non-dipole state if this external force was removed. In physics, this dipole is quantifiably characterized by it's dipole moment, which can be calculated through the following equation:

[math]\displaystyle{ {\vec{p} = qs} }[/math]

where p is the dipole moment of the polarized atom, q is the magnitude of their charge, s is the distance between the constituents of the dipole. Note that q is NOT the cumulative charge of each dipole constituent, but rather their individual, shared charge. For example, if I had a dipole made of one electron and one proton (which would be accompanied by a neutron, but this does not affect the charge) q would equal e (the charge of a proton), not 2e.

The previous equation characterizes the dipole moment solely from values describing the dipole. A dipole moment can also be predicted if the electric field inducing the dipole moment, and the "polarizability" of the material being polarized is known via the following equation:

[math]\displaystyle{ {\vec{p} = α\vec{E}} }[/math]

This shows that the dipole moment is directly proportional to the magnitude of the applied electric field E. The constant α is called the "polarizability" of a particular material. Many of these polarizability values have been measured experimentally and can be found in reference volumes.

Examples

Be sure to show all steps in your solution and include diagrams whenever possible

Easy

Suppose that you have a negatively charged tape hanging from the desk, and you rub a wooden pencil on a wool sweater and bring it near the tape.

• If the tape swings toward the pencil, does this show that the pencil had been positively by rubbing it on the wool?

Not necessarily. Even if the pencil is uncharged, the charged tape will polarize the and be attracted by the induced dipoles.

• Can a charged object repel a neutral object? Why or why not?

Polarization always brings the unlike-sign charge closer, yielding a net attraction. Repulsion of an induced dipole can't happen. Therefore repulsion is the better test of whether an object is charged.

Medium

• Question Why are charged objects attracted to neutral objects?

The attraction of both positively and negatively charged invisible tape to your hand, and to many other neutral objects, is deeply mysterious. The net charge of a neutral object is zero, so your neutral hand should not make an electric field that could act on a charged tape, nor should your neutral hand experience a force due to the electric field made by a charged tape. Nothing in our statement of the properties of electric interactions allows us to explain this attraction!

A positive point charge with charge q acts on a an atom as shown below.

What is the electric dipole moment p of the atom?

[math]\displaystyle{ {\vec{p} = α\vec{E}} }[/math]

[math]\displaystyle{ E=\frac{1}{4 \pi \epsilon_0 } \frac{q}{r^2} \hat{r} }[/math]

[math]\displaystyle{ p=\frac{\alpha}{4 \pi \epsilon_0 } \frac{q}{r^2} \hat{r} }[/math]

What is the magnitude and direction of the electric force due to the induced electric field on the point charge? Assume the magnitude of the charge for either end of the dipole is q, and that r is much larger than s.

[math]\displaystyle{ {|{E_{dipole,axis}}|=\frac{1}{4 \pi \epsilon_0 } \frac{2q^2s}{r^3} \hat{r} }[/math]

The [math]\displaystyle{ q^2 }[/math] in this equation comes from the fact that we multiply the Electric field by the charge it is acting on to get the electric force. The direction of this force will be in the negative x direction, since the negative end of the atom would be polarized closer to the positive point charge, and thus the force acting due to the electric field would also be in that direction.

Difficult

Connectedness

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

• Atoms are the composition of all life. Anything can be broken down into atoms and subatomic particles. If we are able to understand atoms we understand the fundamental concepts of all life, and that is pretty interesting in my opinion.

How is it connected to your major?

• Polarization of atoms is not directly related to my major of Mechanical Engineering; however, there are classes I am required to take such as Intro to Physics 2 and Chemistry where the polarization of atoms directly applies.

Is there an interesting industrial application?

• There are many interesting industrial applications of the polarization of atoms over a broad scope of fields.
• The polarization of atoms is what causes something known as van Der Waals forces, which are attractive forces between molecules or atoms that are weaker than traditional covalent or ionic bonds, but still play a fundamental role in the behavior of such particles. These forces are what allow creatures like spiders and geckos to scale walls, as the van Der Waals forces between small hairs for spiders and another adhesive material for geckos interact with the particles of the surface being scaled, and are strong enough to support the animal. Using technology that mimics this behavior, mechanical and materials engineering labs have created basic prototypes for tools that can allow humans to scale walls in the same fashion, which could be applied for construction work, rescue utility, and countless other applications.

Some of these include:

Chemistry

• Checking chirality of organic compounds
• Infrared spectroscopy

Astronomy

• Providing information on sources of radiation and scattering, polarization probes the interstellar magnetic field
• Polarization of cosmic microwave background is being used to study the physics of the early universe

3D Movies

• Images are projected from the projector with multiplexed polarization
• 3D glasses with suitable polarized filters ensure that each eye receives only the intended image

Communication and Radar

• All radio transmitting and receiving antennas are intrinsically polarized-think FM and AM radio
• Vertical polarization is used to radiate a radio signal in all directions, such as those used in mobile phones
• Alternating vertical and horizontal polarization allows satellite communication systems to broadcast two separate transmissions on a single frequency

Material Science Engineering

• the relationship between strain and birefringence motivates the use of polarization in characterizing the distribution of stress and strain in prototypes

Navigation

• Sky polarization was used in the 1950s when navigating near the poles of the Earth's magnetic field when neither the sun nor stars were visible

History

The two scientists accredited with first coming up with the electron cloud model of the atom, on which atom polarization is based upon, are Ernest Rutherford, a New Zealand born British scientist, and Niels Bohr, a Danish physicist. Both of these gentlemen's atom models included the electron cloud. Rutherford released his model in 1911, and Bohr came out with his model shortly thereafter in 1913. Rutherford's model however, suggested that all atoms were unstable. Bohr corrected this by suggesting that the electrons in the atom could only have certain classical motions. Without these two men, we could never have discovered how the polarization of an atom works.

See also

Polarization

Further reading

• Polarization Functions for First and Second Row Atoms in Gaussian type MO-SCF Calculations by B. Roos and P. Siegbahn
• General Contraction of Gaussian Atomic Orbitals: Core, Valence, Polarization, and Diffuse Basis Sets by Richard C. Raffenetti
• Polarization Propagator Methods in Atomic and Molecular Calculations by Jens Oddershede, Poul Jørgensen, and Danny L. Yeager
• Phase of the Atomic Polarization in High-Order Harmonic Generation by Maciej Lewenstein, Pascal Salières, and Anne L’Huillier

External links

http://www.physicsclassroom.com/class/estatics/Lesson-1/Polarization

http://academics.smcvt.edu/abrizard/EM/dielectric_I.pdf

http://budker.berkeley.edu/papers/pdfs/QBvisualisationPreprint.pdf

http://ocw.mit.edu/resources/res-6-001-electromagnetic-fields-and-energy-spring-2008/chapter-6/06.pdf

http://www.hho4free.com/electrical_polarization.htm

References

https://www.webassign.net/ebooks/mi4/toc.html?page=14.3

http://www.slideshare.net/pabitadhungel321/polarization-and-its-application

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