Question

A proton and an alpha particle are accelerated through the same potential difference. The ratio of their de Broglie wavelengths ( p ) is :

• A. 1
• B. 2
• C. $\sqrt{8}$
• D. $\frac{1}{\sqrt{8}}$

Answer 1

The correct option is C $\sqrt{8}$

We know, $\lambda =\frac{h}{\sqrt{2mqV}}$

Since protons and $\alpha$ particles are accelerated through same potential .$V$ is same.

$\frac{{\lambda }_p}{{\lambda }_{\alpha }}=\frac{\sqrt{2\left(4m\right)\left(2q\right)V}}{\sqrt{2mqV}}=\sqrt{8}$