Question

A material particle with a rest mass $m_o$ is moving with a velocity of light $c$. Then, the wavelength of the de Broglie wave associated with it is

• A. $\left(h/m_{o}c\right)$
• B. zero
• C. $\infty$
• D. $\left(m_{o}c/h\right)$

Answer 1

Answer: (B)

zero

The wavelength of de Broglie wave is given by, $\lambda =\frac{h}{p}$ where $h=$ Planck's constant and $p=$ momentum of the particle.

Now, $p=mv$, here $m=\frac{m_0}{\sqrt{1-v^2/c^2}}$, relativistic mass of the particle.

Given, $v=c$ so $m=\infty$

Thus, $p=\infty$

Hence, $\lambda =\frac{h}{\infty }=0$