An -particle, a proton and an electron have the same kinetic energy. Which one of the following is correct in case of their de-Broglie wavelength [2023]

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Solution

Q.
An $α$ -particle, a proton and an electron have the same kinetic energy. Which one of the following is correct in case of their de-Broglie wavelength [2023]

1 $λ_{α} > λ_{p} > λ_{e}$

2 $λ_{α} < λ_{p} < λ_{e}$

3 $λ_{α} = λ_{p} = λ_{e}$

4 $λ_{α} > λ_{p} < λ_{e}$

Ans.
(2)

$λ_{D} = \frac{h}{p} = \frac{h}{\sqrt{2 m K}}$

$∴$ $λ \propto \frac{1}{\sqrt{m}}$

$∵$ $m_{α} > m_{p} > m_{e}$

$λ_{e} > λ_{p} > λ_{α}$

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