A proton and an electron have the same de Broglie wavelength. If and be and the kinetic energies of proton and electron respectively, then choose the correct relation

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Solution

Q.
A proton and an electron have the same de Broglie wavelength. If $K_{p}$ and $K_{e}$ be the kinetic energies of proton and electron respectively, then choose the correct relation [2024]

1 $K_{p} = K_{e}^{2}$

2 $K_{p} = K_{e}$

3 $K_{p} > K_{e}$

4 $K_{p} < K_{e}$

Ans.
(4)

De Broglie wavelength of proton and electron = $λ$

$∵ λ = \frac{h}{p} \Rightarrow p_{proton} = p_{electron}$

$K E = \frac{p^{2}}{2 m} \Rightarrow KE \propto \frac{1}{m}$

$\frac{K E_{e}}{K E_{p}} = \frac{m_{p}}{m_{e}}$

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