Question

A particle with rest mass zero is moving with speed $c$. The de-Broglie wavelength associated with it

• A. zero
• B. infinity
• C. $\frac{hv}{c}$
• D. $\frac{m_{0}c}{h}$

Answer 1

Answer: (A)

The de-Broglie wavelength $(\lambda )$ is given by
$\lambda =\frac{h}{p}$ ... (i)
where $h$ is Planck's constant, $p$ the momentum.
Also, $p=mv=\frac{m_0}{\sqrt{1-\frac{v^2}{C^2}}}$ ... (ii)
where $m_0$ is rest mass, $v$ the velocity and $c$ the speed of light.
From Eqs. (i) and (ii),
we get $\lambda =\frac{h\sqrt{1-\frac{v^2}{c^2}}}{m_{0}v}$
Given: $v=c$
$\therefore \lambda =0$