An electron (mass m) with an initial velocity v = v₀i (v₀ > 0) is moving in an electric field E = -E₀i (E₀ > 0) where E₀ is constant. If at t = 0 de Broglie wavelength is λ₀ = h/mv₀, then its de Broglie wavelength after time t is given by (a) λ₀ (b) λ₀(1 + (eE₀t)/(mv₀)) (c) λ₀ t (d) (λ₀)/((1+(eE₀t)/(mv₀)))

Answer: (d). Force on electron = -e E = eE₀ i, along the motion. v = v₀ + (eE₀t)/(m) λ = h/mv = (λ₀)/(1+(eE₀t)/(mv₀)) So the answer is (d).

An electron (mass m) with an initial velocity v = v₀i (v₀ > 0) is… | JEE Main 2022 (27 Jul, Shift 1)

Q88JEE Main 2022 · 27 JUL · SHIFT 1Medium

Matter Waves: de Broglie Wavelength

An electron (mass $m$ ) with an initial velocity $\vec{v} = v_0\hat{i}\ (v_0 > 0)$ is moving in an electric field $\vec{E} = -E_0\hat{i}\ (E_0 > 0)$ where $E_0$ is constant. If at $t = 0$ de Broglie wavelength is $\lambda_0 = \frac{h}{mv_0}$ , then its de Broglie wavelength after time t is given by

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Answer: (d)

Force on electron $= -e\vec E = eE_0\hat i$ , along the motion.
$v = v_0 + \dfrac{eE_0t}{m}$
$\lambda = \dfrac{h}{mv} = \dfrac{\lambda_0}{1+\frac{eE_0t}{mv_0}}$
So the answer is (d).

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Matter Waves: de Broglie Wavelength question from JEE Main 2022 (27 Jul, Shift 1)

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