An electron of mass ' m ' with an initial velocity v = v 0 i ^ ( v 0 > 0 ) enters an electric field E = − E o k ^ . If the initial de Broglie wavelength is λ 0 , the value after time t would be

v = v 0 i ^ − m E 0 e t k ^ ∣ v ∣ = v 0 2 + m 2 E 0 2 e 2 t 2 λ 0 = mv 0 h λ ′ = mv 0 1 + v 0 2 m 2 E 0 2 e 2 t 2 h λ ′ = 1 + v 0 2 m 2 E 0 2 e 2 t 2 λ 0

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PhysicsModern PhysicsPhotoelectric effectMedium2 minPYQ_2025

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An electron of mass ' m ' with an initial velocity $v = v_{0} \hat{i} (v_{0} > 0)$ enters an electric field $E = - E_{o} \hat{k}$ . If the initial de Broglie wavelength is $λ_{0}$ , the value after time t would be

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Solution:

$v = v_{0} \hat{i} - \frac{E _{0} e}{m} t \hat{k} ∣ v ∣ = v_{0}^{2} + \frac{E _{0}^{2} e ^{2} t ^{2}}{m ^{2}} λ_{0} = \frac{h}{mv _{0}} λ^{'} = \frac{h}{mv _{0} 1 + \frac{E _{0}^{2} e ^{2} t ^{2}}{v _{0}^{2} m ^{2}}} λ^{'} = \frac{λ _{0}}{1 + \frac{E _{0}^{2} e ^{2} t ^{2}}{v _{0}^{2} m ^{2}}}$

Stream:JEESubject:PhysicsTopic:Modern PhysicsSubtopic:Photoelectric effect

⏱ 2mℹ️ Source: PYQ_2025

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