Question

The de-Broglie wavelength $\lambda$ of a particle

• A. is proportional to mass.
• B. is proportional to impulse.
• C. is inversely proportional to impulse.
• D. does not depend on impulse.

Answer 1

Answer: (C)

is inversely proportional to impulse.

De-Broglei wavelength, $\lambda =\frac{h}{p}$ where, $h$ is Planck's constant

Impulse, $I=\Delta p=p$

$\therefore$ $\lambda =\frac{h}{I}$

$⟹$$\lambda \propto \frac{1}{I}$

Thus, De-Broglei wavelength is inversely proportional to the impulse.

Also, $p=mv$

$\therefore$ $\lambda =\frac{h}{mv}$$⟹\lambda \propto \frac{1}{m}$