First slide

Electromagnetic radiation - Dual nature of radiation and matter

Question

Out of a photon and an electron, the equation $E = p c$ , is valid for

Moderate

A

both
B

neither
C

photon only
D

electron only

Solution

Energy is given by
$E = \frac{m_{0} c^{2}}{\sqrt{1 - (v^{2} / c^{2})}} or E^{2} = \frac{m_{0}^{2} c^{6}}{c^{2} - v^{2}}$
Momentum p is given by
$\begin{array}{l} p = \frac{m_{0} v}{\sqrt{1 - (v^{2} / c^{2})}} or p^{2} c^{2} = \frac{m_{0}^{2} c^{4} v^{2}}{c^{2} - v^{2}} \\ ∴ E^{2} - p^{2} c^{2} = {m_{0}}^{2} c^{4} \\ or E^{2} = p^{2} c^{2} + {m_{0}}^{2} c^{4} \end{array}$
For photon, rest mass
$m_{0} = 0, so E = p c$
For electron, $m_{0} \neq 0, so E \neq p c$

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