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 their de-Broglie wavelengths when both move with equal velocities.

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

Answer 1

The correct option is A $1:4$

We know,

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

At constant velocity ($v$),

$\lambda \propto \frac{1}{m}$

$\frac{{\lambda }_{\alpha }}{{\lambda }_p}=\frac{m_p}{m_{\alpha }}$

Mass of $\alpha$ particle is 4 times mass of a proton.

$\frac{m_p}{m_{\alpha }}=\frac{1}{4}$

Hence,

$\frac{{\lambda }_{\alpha }}{{\lambda }_p}=\frac{1}{4}$

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