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Question: The ratio of the velocities of a proton and a-particle is 4 : 1. The ratio of their de-Broglie wavel...

The ratio of the velocities of a proton and a-particle is 4 : 1. The ratio of their de-Broglie wavelengths is

A

1 : 1

B

1 : 2

C

2 : 1

D

4 : 1

Answer

1 : 1

Explanation

Solution

λpλα\frac{\lambda_{p}}{\lambda_{\alpha}}=pαpp\frac{p_{\alpha}}{p_{p}} = mαvαmpvp\frac{m_{\alpha}v_{\alpha}}{m_{p}v_{p}} = 4×144 \times \frac{1}{4} = 1