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JEE Main 2022 · 27 Jul · Shift 1, Physics question 47

An electron (mass m) with an initial velocity v⃗=v0i^\vec v=v_0\hat i (v0>0)(v_0>0) is moving in an electric field E⃗=−E0i^\vec E=-E_0\hat i (E0>0)(E_0>0) where E0E_0 is constant. If at t = 0 de Broglie wavelength is λ0=hmv0\lambda_0=\dfrac h{mv_0}, then its de Broglie wavelength after time t is given by

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Answer and worked solution

Official answer: D

Force on the electron is −eE⃗=+eE0i^-e\vec E=+eE_0\hat i, so it speeds up: v=v0+eE0tmv=v_0+\frac{eE_0t}m.

λ=hmv=λ01+eE0tmv0\lambda=\frac h{mv}=\frac{\lambda_0}{1+\frac{eE_0t}{mv_0}}. (D)

Topics:de Broglie wavesMotion in magnetic and electric fields
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