Question

The de-Broglie wavelength ‘$λ$’ 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)

$de$ -Broglie wavelength $(\lambda)$ of a particle is related to its momentum $(p)$ as, $\lambda=\frac{h}{p}$
where, $h$ is Planck's constant.
or $\,\,\, \lambda=\frac{h}{m v} \,\,\,\,[\because p=m v]$
or $\,\,\, \lambda=\frac{h}{m \frac{v}{t} \cdot t}=\frac{h}{m a \cdot t}=\frac{h}{F \cdot t} \,\,\,[\because F=m a]$
$\Rightarrow \lambda$ is inversely proportional to impulse $(F)$