Question

Show that it is not possible for a photon to be completely absorbed by a free electron.

Answer 1

Explanation:

To Show that it is not possible for a photon to be completely absorbed by a free electron:

Step 1:

If an electron experiences an inelastic collision with a photon, on this collision we can apply the principle of energy conservation.

$p c+m_{e} c^{2}=\sqrt{p^{2} c^{2}+m_{e}^{2} c^{4}} \ldots(i)$

where, h is the Planck constant

           c is the light speed  

           $m_e$ is  rest electron mass  

           pc is photon energy  

Step 2:

Equation (i) squaring on both sides

$\left(p c+m_{e} c^{2}\right)^{2}=p^{2} c^{2}+m_{e}^{2} c^{4}$

$p^{2} c^{2}+m_{e}^{2} c^{4}+2(p c)\left(m_{e} c^{2}\right)=p^{2} c^{2}+m_{e}^{2} c^{4}$

$2(p c)\left(m_{e} c^{2}\right)=0 \text { or } p c=0\left(a s^{\prime} m^{\prime} \text { and }^{\prime} c^{\prime} \text { are non zero }\right)$

It gives photon energy disappearing which is not possible.