Pretty straight forward, I just have to show why a photon can't transfer all of its energy to an electron. I understand this in theory but I'm stuck at how to show it.
1) Ep + mec2 = Ep' + Ee
Where Ep is the energy of the photon, Ep' is the energy of the scattered photon, and the rest is obvious.
2) E = hf
3) p = p'cos([tex]\theta[/tex]) + pecos([tex]\phi[/tex])
4) p'sin([tex]\theta[/tex]) = pesin([tex]\phi[/tex])
p is the initial momentum of the photon, p' is the final momentum of the photon, pe is the momentum of the electron after scattering. [tex]\theta[/tex] is the angle of the scattered photon and [tex]\phi[/tex] is the angle of the scattered electron.
The Attempt at a Solution
I figure I have to use conservation of momentum and energy to show that it's a contradiction. I was going to assume [tex]\theta[/tex] and [tex]\phi[/tex] were 0, but I'm not sure if I can do that. I've hit a roadblock, I'm not sure how to go about this. A hint in the right direction would be much appreciated!