If an electron and an α-particle are accelerated from rest through a potential difference of 100 volt. The ratio of their momenta will be MenMα the value of n is ___

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If an electron and an $α$ -particle are accelerated from rest through a potential difference of 100 volt. The ratio of their momenta will be $\sqrt{\frac{M_{e}}{n M_{α}}}$ the value of n is ____

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answer is 2.

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Detailed Solution

$\begin{aligned} \frac{1}{2} m u^{2} = e V \\ u = \sqrt{\frac{2 e V}{m}} \end{aligned}$

$\begin{aligned} P = m u = \sqrt{2 m e V} \\ \frac{P_{e}}{P_{x}} = \sqrt{\frac{M_{e}}{2 M_{α}}} \end{aligned}$

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