An electron is travelling with a velocity in free space and when it enters a medium, its velocity is reduced by 20%

Question

An electron is travelling with a velocity $v$ in free space and when it enters a medium, its velocity is reduced by 20%. The de-Broglie wavelength of electron in the medium is $α λ_{0}$ , where $λ_{0}$ is its de-Broglie wavelength in the free space. The value of $α$ is _______. [2026]

Smart Achievers · Accepted Answer

(3)

$λ_{0} = \frac{h}{m v_{0}}$

$λ = \frac{h}{m v} = \frac{h}{m (0.8 v_{0})} = \frac{1}{0.8} \frac{h}{m v_{0}} = 1.25 λ_{0}$

$∴$ $α = 1.25$

Solution

Q.
An electron is travelling with a velocity $v$ in free space and when it enters a medium, its velocity is reduced by 20%. The de-Broglie wavelength of electron in the medium is $α λ_{0}$ , where $λ_{0}$ is its de-Broglie wavelength in the free space. The value of $α$ is _______. [2026]

1 1.20

2 1.0

3 1.25

4 0.75

Ans.
(3)

$λ_{0} = \frac{h}{m v_{0}}$

$λ = \frac{h}{m v} = \frac{h}{m (0.8 v_{0})} = \frac{1}{0.8} \frac{h}{m v_{0}} = 1.25 λ_{0}$

$∴$ $α = 1.25$

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