Homework Help: Photon absorbtion by free electron

1. Jul 24, 2010

AshsZ

About a year ago a member here made a post regarding this subject title - I found this post/forum through a google search looking for this very bit of information.... this is my *first* post, so please forgive my ignorance with forum etiquette. :)

Firstly, I am not a physics major, doctorate, bachelor, or even associate. I simply have a strong affinity to "figure things out" and the physical world is the medium of focus. Hopefully I dont make a fool of myself here. :)

From what I have gathered, quantum mechanics dictates what energy states a given electron can take on through the absorption of a photon. If the energy of the photon is specific to a given electron's quantum state, it will absorb the photon and consequently move to a higher energy orbital around its native atom.

Now, depending on what atom a particular electron is mated with, and where it lay within the shells, it is locked into a specific state that only allows photons of a given energy level to be absorbed.

There are over a hundred different elements each with their own unique electron configuration. Adding further, since each atom possesses a differing number of protons within the nuclear core, each electron within every element is unique in and of itself. Emission/absorption spectra illustrate this fact.

An electron is an electron, fundamentally. There is no distinction between any two electrons other than perhaps how fast they are moving relative to another charged particle or field, but still an electron just the same.

Because there is such a large variety of elements each with their own configurations of proton/electron arrangements, producing conditions that force electrons to be selective in what they absorb, it seems intuitive to conclude that an electron must be capable of absorbing any photon of any frequency/energy. The only condition which specifies discrete behaviour is what atom is it a part of and where does it sit in the electron configuration around said atom.

Perhaps a statistical approach can be taken to define exactly every possible energy state for every electron that exists in all of the elements. This approach would not yield an infinite number of states - this would completely undermine the foundation of quantum mechanics if it did.

It appears to me that an electron free from the grip of an atom is a sort of "free agent" - what it does is no longer dictated by the conditions surrounding an organized atomic structure. Going one step further in this logic, a free electron should be capable of absorbing any photon of any energy.

In the post I previously referred to that brought me here, I noticed that the perspective taken on the photon and electron was that of a particle nature - billiard balls moving in directions and collisions, etc etc. The question here is are these "things" particles at all? What is an electron - photon collision where their relative vectors were opposing such that the collision produces a net zero energy? That makes no sense - where's conservation? What if they were considered as waves instead?

If the photon and free electron were traveling along a direct head-on collision, represented both as a wave function, at the point of intersection there would be a net constructive interference interaction, but as waves they simply pass directly through each other - the very instant after intersection, they both continue on their relative paths containing exactly what they possessed before the intersect.

You could think of this as the particle electron absorbed the electromagnetic wave energy only for a blink and the wave passed right through it - shivering the electron for that small moment but leaving and continuing on its path thereafter.

Either way you look at this, the photon and electron interacted with each other at a fundamental level. Whether or not the electron absorbed and retained the photon during the interaction or if the photon passed through the electron like a wave through a wave, they still were affected by each other.

In the quantum mechanical model of atomic structure, an impressive slew of quantified qualities can be calculated and understood. We can calculate what photon energy any given electron can absorb. Forgive my ignorance here, but I fail to recognize how the quantum model accomodates for either wave-wave, wave-particle, or particle-particle interactions occur without accounting for how waves interact dependent on relative phase or how the particles interact dependent on position probability. Is there a probability map which states just how often a given electron around a particular atom will absorb a photon within a stream of photons of a given intensity or density?

I dont know if you guys/gals run into this same problem but I continually get tripped up on these thought experiments at the same hurdle - do you consider the components in question as a wave or a particle?

Despite the apparent misdirected diarrhea of the thought process here, I really do have a purpose behind the question. All of this comes down to producing electrical power. Sunlight is composed of a wide range of frequencies of which not all of them that reach the ground can be harnessed to produce electrical potential. This limitation is due to the fact that the elements you produce your photovoltaic cell from cannot absorb all of those frequencies and convert to electrical power. This is a restriction explained by quantum mechanics. However, if one were to use lone electrons to absorb the light, every last bit of the light energy would be converted into electrical power, therby improving the efficiency of a "photovoltaic cell" from a measly 15% or so up to something within the 90+% range.

There are obviously many other aspects to be addressed in order to build a fully functional device like this, but the entire foundation of such a device is dependent on whether or not a free electron can absorb a photon of any frequency.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Jul 25, 2010

AJ Bentley

Free electrons cannot absorb EM energy for the same reason that a cork floating in the ocean cannot absorb wave energy. There is simply nowhere for the energy to go.

This is not a homework question and shouldn't be posted here.

If you do post in the discussion forums you'll get a better response if you keep your question short and to the point. (You don't need to explain basic Physical principles - assume we already know)

3. Aug 9, 2010

AshsZ

My deepest apologies - didn't realize this forum was intended for that specific purpose. :) I'll trim it down and put it up in the discussion forum. :)

Thanks!