Question

The de-Broglie wavelength of proton travelling at velocity $v$ is same as the wavelength of an alpha particle. What is the velocity of the alpha particle ?

• A. $2v$
• B. $\frac{v}{2}$
• C. $\frac{v}{4}$
• D. $4v$

Answer 1

The correct option is C $\frac{v}{4}$

Given : ${\lambda }_{proton}={\lambda }_{alpha}$

$\Rightarrow \frac{h}{mv}=\frac{h}{\left(4m\right)v_{\alpha }}$
$\Rightarrow v_{\alpha }=\frac{v}{4}$

Hence, $\left(C\right)$ is the correct answer.