Question

The de-Broglie wavelength of a proton and $\alpha$-particle are equal. The ratio of their velocities is:

• A. $4:2$
• B. $4:1$
• C. $1:4$
• D. $4:3$

Answer 1

The correct option is B $4:1$

From de-Broglie wavelength:

$\lambda =\frac{h}{mv}$

$\Rightarrow v=\frac{h}{\lambda m}$

We get,

$\frac{v_p}{v_{\alpha }}=\frac{m_{\alpha }}{m_p}$

As we know, $m_{\alpha }=4m_p$

$\therefore \frac{v_p}{v_{\alpha }}=\frac{4m_p}{m_p}=\frac{4}{1}=4:1$