The de Broglie wavelength of an electron having kinetic energy E is . If the kinetic energy of electron becomes , then its de-Broglie wavelength will be [2023]

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Solution

Q.
The de Broglie wavelength of an electron having kinetic energy E is $λ$ . If the kinetic energy of electron becomes $\frac{E}{4}$ , then its de-Broglie wavelength will be [2023]

1 $\frac{λ}{\sqrt{2}}$

2 $\frac{λ}{2}$

3 $2 λ$

4 $\sqrt{2} λ$

Ans.
(3)

$λ = \frac{h}{\sqrt{2 m E}}$

$λ' = \frac{h}{\sqrt{2 m (\frac{E}{4})}} = \frac{2 h}{\sqrt{2 m E}} = 2 λ$

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