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)

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