Conservation of Energy/momentum in Photoelectric process

[Ambidext]

Homework Statement

Show that a free electron cannot absorb a photon and conserve both energy and momentum in the process. Hence, the photoelectric process requires a bound electron. (Eisberg and Resnick 2nd Ed)

Homework Equations

hv = E
p = K / c
E² = (pc)² + (m₀c²)²

The Attempt at a Solution

I've simply shown since
E² = (pc)² + (m₀c²)²,

rest energy of a moving electron isn't zero and thus energy and momentum cannot be conserved. Is this argument true/suffice?

 

[vela]

I don't see how the conclusion follows from the premise, and I suspect you don't either since you asked if the argument was true.

 

[Ambidext]

How/where then should I start?

 

[vela]

Start by writing the equations for the conservation of energy and momentum the electron and photon would have to satisfy.