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Question: A proton and ana-particle are accelerated through the same potential difference. The ratio of de-Bro...

A proton and ana-particle are accelerated through the same potential difference. The ratio of de-Broglie wavelength of the proton to that of the a-particle will be-

A

2 : 1

B

1 : 1

C

1 : 2

D

222\sqrt{2}: 1

Answer

222\sqrt{2}: 1

Explanation

Solution

lp = h2mpeV\frac{h}{\sqrt{2m_{p}eV}}; la = h2mα(2e)V\frac{h}{\sqrt{2m_{\alpha}(2e)V}}

la=h2(4mp)(2e)V\frac{h}{\sqrt{2(4m_{p})(2e)V}}; λpλα\frac{\lambda_{p}}{\lambda_{\alpha}}=8\sqrt{8} or λpλα\frac{\lambda_{p}}{\lambda_{\alpha}}=222\sqrt{2}