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

A) Zero
B) Infinity
C) $\frac{hv}{c}$
D) $\frac{m_{0}c}{h}$
Explanation

(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, $v = c\ \ \ \ \ \ \ \therefore\lambda = 0$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.