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Q.
A material particle with a rest mass $m_{0}$ is moving with a velocity of light $c$. Then, the wavelength of the de Broglie wave associated with it is
Dual Nature of Radiation and Matter
Solution:
We know that mass $m$ in motion and the rest mass $m_{0}$ is related through the equation
$m=\frac{m_{0}}{\sqrt{1-\frac{v^{2}}{c^{2}}}}$
As $v=c, m=\frac{m_{0}}{\sqrt{1-1}}=\frac{m_{0}}{0}=\infty$
Therefore, de Broglie wavelength is
$\lambda=\frac{h}{m v}=\frac{h}{(\infty)(c)}=0$