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Question: If the de-Broglie wavelengths for a proton and for a \(\alpha -\)particle are equal, then the ratio ...

If the de-Broglie wavelengths for a proton and for a α−\alpha -particle are equal, then the ratio of their velocities will be.

A

4 : 1

B

2 : 1

C

1 : 2

D

1 : 4

Answer

4 : 1

Explanation

Solution

λ=hm1v1=hm2v2; 6mu 6mu∴ 6mu 6muv1v2=m2m1=41\lambda = \frac{h}{m_{1}v_{1}} = \frac{h}{m_{2}v_{2}};\mspace{6mu}\mspace{6mu}\therefore\mspace{6mu}\mspace{6mu}\frac{v_{1}}{v_{2}} = \frac{m_{2}}{m_{1}} = \frac{4}{1}