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.

 

[paranormal]

Your argument is correct. In the photoelectric process, a photon is absorbed by an electron, causing it to be ejected from the atom. In order for this process to occur, both energy and momentum must be conserved. However, since the electron has a non-zero rest energy, it cannot absorb the photon and conserve both energy and momentum. This is because the photon has energy, but no momentum, while the electron has both energy and momentum. Therefore, a bound electron, which has a lower energy and can absorb the photon without violating conservation laws, is necessary for the photoelectric process to occur. This is one of the key observations that led to the development of the quantum theory of light and the understanding of the particle-like nature of photons.