The ratio of de-Broglie wavelength of an -particle and a proton accelerated from rest by the same potential is , the value of is [2023]

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Solution

Q.
The ratio of de-Broglie wavelength of an $α$ -particle and a proton accelerated from rest by the same potential is $\frac{1}{\sqrt{m}}$ , the value of $m$ is [2023]

1 4

2 16

3 8

4 2

Ans.
(3)

$\frac{λ_{α}}{λ_{p}} = \frac{h}{\sqrt{2 m_{α} q_{α} V}} = \frac{h}{\sqrt{2 m_{p} q_{p} V}}$

$\frac{λ_{α}}{λ_{p}} = \sqrt{\frac{1}{8}} \Rightarrow m = 8$

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