An $\alpha$-particle and a proton are accelerated from rest by a potential difference of 100 V. After this, their de-Broglie wavelengths are $\lambda_{\alpha}$ and $\lambda_{p}$ respectively. The ratio $\frac{\lambda_{p}}{\lambda_{\alpha}}$, to the nearest integer, is

Question

Dr. Abubacker · Accepted Answer

(a) $\lambda = \frac{h}{p} = \frac{h}{\sqrt{2qVm}}\ \ or\ \lambda \propto \frac{1}{\sqrt{qm}}$
$\frac{\lambda_{p}}{\lambda_{\propto}} = \sqrt{\frac{q_{\alpha}}{q_{p}}.\frac{m_{\alpha}}{m_{p}}} = \sqrt{\frac{(2)(4)}{(1)(1)}}$ =2.828
The nearest integer is 3.

Q. An $\alpha$-particle and a proton are accelerated from rest by a potential difference of 100 V. After this, their de-Broglie wavelengths are $\lambda_{\alpha}$ and $\lambda_{p}$ respectively. The ratio $\frac{\lambda_{p}}{\lambda_{\alpha}}$, to the nearest integer, is

Explanation

Reviewed by Dr. Abubacker

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