Can a Free Electron Absorb All the Energy of a Photon?

[Void123]

Homework Statement

Using energy and momentum conservation requirements, show that a free electron cannot absorb all the energy of a photon.

Homework Equations

Einstein energy-momentum formula:

(E)² = (mc²)² - (cp)², where m = mass, E = energy, c = speed of light, and p = momentum vector.

The Attempt at a Solution

I expanded this by setting the initial energies of the photon and electron equal to the final. However, I am not entirely sure what significant expression I'm supposed to be looking for here in order to answer this question.

Thanks.

 

[kuruman]

Your energy equation is incorrect; the minus sign on the right side should plus. Energy conservation requires you to write

Energy before = Energy after

So you need to find expressions for the "before" and "after" energy and set them equal. Finally, you have not considered momentum conservation. This requires you to find expressions for the "before" and "after" momentum and to write

Momentum before = Momentum after

Do all this and you might be able to see where this is going.