Question

An $\alpha -$particle and a proton have their masses in the ratio $4:1$ and charges in the ratio $2:1$.

Find ratio of de-Broglie wavelengths when both have equal momentum.

• A. $2:1$
• B. $1:1$
• C. $4:1$
• D. $1:4$
• E. $1:4$

Answer 1

The correct option is B $1:1$

We know,
De broglie wavelength= $\lambda =\frac{h}{mv}$

At constant momentum ($mv$),
$\lambda \propto \text{constant}$

$\frac{{\lambda }_{\alpha }}{{\lambda }_p}=\frac{c}{c}$

Hence,
$\frac{{\lambda }_{\alpha }}{{\lambda }_p}=\frac{1}{1}$

Hence option $\text{B}$ is correct.