Question

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

• A. both
• B. neither
• C. photon only
• D. electron only

Answer 1

The correct option is C photon only

Energy is given by
$E=\frac{m_0{c}^2}{\sqrt{1-\frac{v^2}{c^2}}}$
$\Rightarrow E^2=\frac{m_0^2{c}^6}{c^2-v^2}$
Momentum $P$ is given by
$P=\frac{m_{0}v}{\sqrt{1-\left(\frac{v^2}{c^2}\right)}}$
$P^2{c}^2=\frac{m_0^2{c}^4{v}^2}{c^2-v^2}$
$\therefore E^2-P^2{c}^2=m_0^2{c}^4$
$\Rightarrow E^2=P^2{c}^2+m_0^2{c}^4$
For photon, rest mass
$m_0=0$, so $E=Pc$
For electron, $m_0\ne 0$, so $E\ne Pc$