Conservation of Energy/momentum in Photoelectric process

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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?
 
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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.
 
How/where then should I start?
 
Start by writing the equations for the conservation of energy and momentum the electron and photon would have to satisfy.
 

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