Scattering theories

[kenhung123]

I don't understand Comptom scattering and photoelectric absorption..because I thought energy can be fully absorbed or not absorbed at all so why does Comptom's partially energy absorption exist?

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In Compton scattering, you have a free electron, which is not bound to an atom. If the photon was absorbed by the electron, I think it can be shown that this will violate conservation of energy/momentum:

Say you have a free electron at rest, and an incoming photon, and the electron absorbs the photon. Then,
. (1)
. (2)

(1) becomes (initial energy: photon, final energy: electron)

(2) becomes (initial momentum: photon, final momentum: electron)

Dividing (1) by (2),

.

This is a contradiction, since particles with mass cannot travel at the speed of light.
So photons cannot be absorbed by free electrons, but they can be scattered.

For the photoelectric effect, the electrons are bound to atoms. Electrons can fully absorb photons because the mass of the atom is there to conserve momentum (it absorbs the recoil).

To be honest I can't quite remember why the whole photon must be absorbed, I would have thought that as long as enough energy is given to the electron to free it, the rest can be scattered away as a photon of a lower frequency.

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I just did a bit of research about this and it seems that for very high energy photons, it is possible for compton scattering to occur for bound electrons. However in VCE you likely won't encounter this so you can assume that the whole photon is absorbed.