Question
Show that it is not possible for a photon to be completely absorbed by a free electron.
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Answer
If the i undergoes an elastic collision with a photon. Then applying energy conservation to this collision.We get, $\frac{\text{hc}}{\lambda}+\text{m}_0\text{c}^2=\text{mc}^2$
and applying conservation of momentum $\frac{\text{h}}{\lambda}=\text{mv}$
Mass of e $=\text{m}=\frac{\text{m}_0}{\sqrt{1-\frac{\text{v}^2}{\text{c}^2}}}$
from above equation it can be easily shown that
V = C
V = 0
both of these results have no physical meaning hence it is not possible for a photon to be completely absorbed by a free electron.
and applying conservation of momentum $\frac{\text{h}}{\lambda}=\text{mv}$
Mass of e $=\text{m}=\frac{\text{m}_0}{\sqrt{1-\frac{\text{v}^2}{\text{c}^2}}}$
from above equation it can be easily shown that
V = C
V = 0
both of these results have no physical meaning hence it is not possible for a photon to be completely absorbed by a free electron.
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