First slide

Wave nature of matter

Question

A material particle with a rest mass m₀ is moving with a velocity of light c. Then, the wavelength of the de Broglie wave associated with it is

Moderate

A

$(h / m_{o} c)$
B

$z e r o$
C

$\infty$
D

$(m_{o} c / h)$

Solution

We know that mass m in motion and the rest mass m₀ is related through the equation
$\begin{array}{l} m = \frac{m_{0}}{\sqrt{1 - \frac{v^{2}}{c^{2}}}} \\ As v = c, m = \frac{m_{0}}{\sqrt{1 - 1}} = \frac{m_{0}}{0} = \infty \end{array}$
Therefore, de Broglie wavelength is
$λ = \frac{h}{m v} = \frac{h}{(\infty) (c)} = 0$

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