A proton, an electron and an alpha particle have the same energies. Their de-Broglie wavelengths will be compared as

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Solution

Q.
A proton, an electron and an alpha particle have the same energies. Their de-Broglie wavelengths will be compared as [2024]

1 $λ_{e} > λ_{α} > λ_{p}$

2 $λ_{α} < λ_{p} < λ_{e}$

3 $λ_{p} < λ_{e} < λ_{α}$

4 $λ_{p} > λ_{e} > λ_{α}$

Ans.
(2)

$λ = \frac{h}{P} = \frac{h}{\sqrt{2 m K E}}$

$KE is same for all . \Rightarrow λ \propto \frac{1}{\sqrt{m}}$

$m_{e} < m_{p} < m_{α} or λ_{e} > λ_{p} > λ_{α}$

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