# Why can't a photon transfer all of its energy to an electron?

## Homework Statement

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.

## Homework Equations

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($$\theta$$) + pecos($$\phi$$)

4) p'sin($$\theta$$) = pesin($$\phi$$)

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. $$\theta$$ is the angle of the scattered photon and $$\phi$$ 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 $$\theta$$ and $$\phi$$ 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!

$$E^2 = m^2 c^4 + p^2 c^2$$