Electron/Photon Scattering

Question

Hey guys, I have a final tomorrow and I am going over some assignments. One of the questions from the assignment was:

A photon having 37 keV scatters from a free electron at rest. What is the maximum energy that the electron can obtain?

Now, I got the right answer (4.67 KeV) but I can't seem to figure it out now. Maybe I am just too tired. Any hints to where I should begin?

Answer 1

There is only one parameter in the system. You have several choices, but you might use the scattering angle, $\Theta$, of the photon in the electrons initial rest frame.

Now conserve 4-momentum, and write the final state energy of the electron as a function of $\Theta$ and maximize.