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Question: A proton and an a-particle have K.E. in the ratio of 16 : 1. The ratio of de-Broglie wavelengths ass...

A proton and an a-particle have K.E. in the ratio of 16 : 1. The ratio of de-Broglie wavelengths associated with them is–

A

1 : 2

B

2 : 1

C

2 : 3

D

1 : 4

Answer

1 : 2

Explanation

Solution

KpKα\frac{K_{p}}{K_{\alpha}} = 161\frac{16}{1}

l = h2mE\frac{h}{\sqrt{2mE}}

λpλα\frac{\lambda_{p}}{\lambda_{\alpha}} = mαEαmpEp\sqrt{\frac{m_{\alpha}E_{\alpha}}{m_{p}E_{p}}} = 4mpmp×116\sqrt{\frac{4m_{p}}{m_{p}} \times \frac{1}{16}} = 14\sqrt{\frac{1}{4}} = 12\frac{1}{2}