The de Broglie wavelengths of a proton and an particle are and respectively. The ratio of the velocities of proton and particle will be

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Solution

Q.
The de Broglie wavelengths of a proton and an $α$ particle are $λ$ and $2 λ$ respectively. The ratio of the velocities of proton and $α$ particle will be [2024]

1 1 : 8

2 1 : 2

3 4 : 1

4 8 : 1

Ans.
(4)

$λ = \frac{h}{p} = \frac{h}{m v} \Rightarrow v = \frac{h}{m λ}$

$\frac{v_{p}}{v_{α}} = \frac{m_{α}}{m_{p}} \times \frac{λ_{α}}{λ_{p}} = 4 \times 2 = 8$

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