In compton scattering, a photon may deliver only some of its energy to an electron.
But when dealing with photon electron interaction in an atom, it's all or nothing.
Why the difference?
Also, within compton scattering, given the initial wavelength of the photon, we get a relationship between scattering angle, and wavelength of the scattered photon. But we can't know the scattering angle without knowing the wavelength of the scattered photon. So there's a free variable. What determines the wavelength of the scattered photon? Is it some type of random process?
Thanks in advance.
Best Answer
A free electron does not have any potential to which it is constraint so it can have any energy possible. i.e. it's energy states are continuum much like a free particle in classical mechanics. So scattering of such a particle is possible.
On the other hand, when in an atom, the electron is subjected to coulomb potential and this potential dictates the energy levels accessible to the electron. It's no more continuous. This means that the electron can only absorb or emit energies in steps. Thus it's an all-or-nothing phenomena. What are the energy states accessible is dictated by solving Schrodinger's equation. Thus any photon cannot pluck out the electron only a specific protons can do that(for whom the energy matches the energy difference of states).
For the second part of your question, In Compton effect the change of wavelength is determined by the scattering angle. The more the angle the more is the change. And you can treat the initial wavelength as the free parameter in this case.