Q164 / 170 · Manipal (MET) 2015 · Physics

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

  • A
    both
  • B
    neither
  • Correct answer
    C
    photon only
  • D
    electron only

Solution

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

Hence, the correct answer is option: 'C'.

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