Re: a question from an AP Chem student...

[Hugh Haskell <hhaskell@mindspring.com>]

On Oct 6, Kathy Venable wrote:
> hello all...  I have enjoyed the lively debates and have had fun
> "stretching" my brain cells.  I teach high school Physics and APChem.  We
> recently studied the introductory Quantum Mechanics chapter, and a student
> question stumped me.  I love it when that happens, as we get to do some
> searching together.  This one has us stumped and I wondered if we might
> find help here.  So.....
>
> Given that an electron must absorb a photon of just the right energy to
> make a given energy level jump, what happens when a photon having the
> "wrong" amount of energy encounters the electron.  Does it get absorbed and
> rereleased when the electron fails to make the transition?  Is its
> absorbtion somehow prevented?  The actual wording of the question was "How
> does the electron "know"  whether a photon has the "right" amount of energy?"
>
> Thanks in advance.  I look forward to learning something new!
> kathy

I had written a very long-winded reply to this question, when I realized
that it really has a much simpler explanation. When a photon interacts with
an atom, it isn't like a billiard ball collision, or even a bb and bowling
ball collision. The easiest way to visualize it is to think of the photon
as being absorbed into the atom, which then seeks a new state corresponding
to its new energy content. If there is not one avaialble, then the atom has
to re-emit a (virtually identical) new photon in the same direction as the
incoming one was traveling. The reason it must do this is because the
atom-photon system cannot conserve both energy and momentum under any other
circumstances. To see why this is true, study the Compton effect in any
introductory calculus -based text. The result depends on the fact that the
photon can only travel at "c" which severely limits the range of photon
energies that can be emitted and still have momentum conserved.

So I think that the basic answer is that we don't need to assign any
anthropomorphic characteristics to either photons or atoms. They don't
"know" anything before the collision, and so they do "merge." but if a
suitable combined final state is not available then the atom must simply
"spit the photon out" and send it on its way (in the same direction). This
process takes an amount of time constrained by the uncertainty principle.

I assume that the question came up in terms of free atoms, since when atoms
are combined into solids or liquids, then their energy states are
drastically altered and the whole process is different. In solids, ordinary
Compton scattering from free electrons can occur where there are free
electrons, and even if there are not, there are many more and more
closely-spaced energy levels, and a large structure to absorb excess
momentum, so a wider variety of photons can be accomodated.

Hugh

Hugh Haskell
<mailto://hhaskell@mindspring.com>

Let's face it. People use a Mac because they want to, Windows because they
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