Photon electron interaction?!!!!!! Please explain this ambiguity.?

Question

According to Einstiens photoelectric theory, a single photon interacts with a single electron and transfers all its energy to the electron and loses all its identity.
However, according to Compton effect, a single X-Ray photon interacts with an electron and transfers only part of its energy and thus acquires a longer wavelenth.
Could anyone explain this ambiguity?

Answer 1

I can't quite agree with the previous answer. The operative difference between the two is that momentum must be conserved for the one (the Compton effect) but not the other (photoelectric effect).

It's well known that the following reaction is impossible in free space:

photon + electron --> electron

The easiest way to see this is to look at it in the center of mass frame. The outgoing electron must be at rest in this frame so the total energy is mc^2, clearly less than the total energy of the photon+electron.

Another way of putting it is that massless particles require less energy (for a given momentum) than massive particles so it's impossible for the entire momentum of the photon to be transferred to the electron without more energy than it has (regardless of how energetic it is). The only way the photon can disappear completely is if its momentum is taken up by something else: the atom or lattice, which is available in the photoelectric effect but not the Compton effect.

All other things being equal, an interaction in which there is only one photon (i.e. the photon is completely absorbed) has a much higher probability than one with "two" photons (incoming + outgoing) so in both cases the highest probability interaction allowed by energy and momentum conservation is the one which occurs.

Answer 2

In the case of the photoelectric effect, the photon is completely absorbed by the electron in order for the electron to gain enough energy to escape its confinment to the neucleus of an atom. The photon must carry the exact amount of energy, or in other words, the photon must have the right frequency for this effect to happen for a partcular type of atom with electrons in a certain orbital shell.

In the case of Compton efect, the X-ray photon is very high energy and high frequency, and it is scattering against FREE electrons (i.e. not confined to the atom); hence the photon does NOT have to give up all of its energy to the electron, but only partially. That's why the photon acquires a longer wavelength, because it only lost some of its energy to the electron.