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.