Question

Is p − E/c valid for electrons?

Answer 1

From Einstein's mass- energy equation,
E = mc²
$\Rightarrow E=\frac{m_0{c}^2}{\sqrt{1-{\displaystyle \frac{v^2}{c^2}}}}$
Relativistic momentum,
$$\begin{gathered} p=mv \\ \Rightarrow p=\frac{m_0{c}^2}{\sqrt{1-{\displaystyle \frac{v^2}{c^2}}}} \end{gathered}$$
Combining the above equations, we get:
$E^2={m_0}^2{c}^4+p^2{c}^2$
From the above equation, it is clear that for p = E/c to be valid, the rest mass of the body should be zero. As electrons do not have zero rest mass, this equation is not valid for electrons.