Max Energy Transfer Relativistic Collision: Electron & Photon

[Eric_meyers]

Homework Statement

"A photon of energy E collides with an electron at rest. Calculate the maximum amount of Energy E_k that may be transferred to the electron. Make a graph of E_k versus E, labeling the scale in electronvolts.

Homework Equations

Transfer = E_k = E - mc^2*E/(mc^2 + 2E)

The Attempt at a Solution

So, I'm not sure if I have the correct equation, the reason why is:

I take the derivative of the function and set it equal to 0

E = -mc^2

and then I plug that value into my function of E_k and I get 0.. but how can the max value for energy transfer be 0? I understand the -mc^2 conceptually saying perfect back scattering but I'm not sure.

 

[vela]

The energy of the outgoing photon in Compton scattering is a function of the angle. Your formula doesn't depend on the angle, so it's not a general formula for this type of scattering. Wherever you got this expression, it should explain any assumptions that went into deriving it. You need to know what those assumptions are before you use the formula. For all you know, it may not even be valid for this situation.