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
8
D
18

Solution

## The correct option is C $$\sqrt{8}$$We know, $$\lambda = \dfrac{h}{\sqrt{2mqV}}$$Since protons and $$\alpha$$ particles are accelerated through same potential .$$V$$ is same.$$\dfrac{\lambda_p}{\lambda_\alpha} = \dfrac{\sqrt{2(4m)(2q)V}}{\sqrt{2mqV}} = \sqrt{8}$$  Physics

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