An electron is released from rest near an infinite non-conducting sheet of uniform charge density ' -σ '. The rate of change of de-Broglie wave length associated with the electron varies inversely as n th power of time. The numerical value of n is .

Physics · Atomic Physics

JEE Main 2025 — 8 April, Evening Shift — Question 67

An electron is released from rest near an infinite non-conducting sheet of uniform charge density ' $-\sigma$ '. The rate of change of de-Broglie wave length associated with the electron varies inversely as $n^{\text {th }}$ power of time. The numerical value of $n$ is $\qquad$ .

Answer: 2

Numerical answer — enter this value.

Step-by-step solution

$F=q E=q\left(\frac{\sigma}{2 \epsilon_{0}}\right)=\frac{\Delta p}{\Delta t}$

$\lambda=\frac{h}{p} \quad \frac{d \lambda}{d t}=\frac{h}{p^{2}} \times \frac{\Delta p}{\Delta t}=\frac{h}{p^{2}} \times \frac{q \sigma}{2 \epsilon_{0}}$

$\frac{d \lambda}{d t} \propto \frac{1}{p^{2}} \propto \frac{l}{t^{2}} \propto \frac{1}{t^{n}}$

$p=\frac{q \sigma}{2 \epsilon_{0}} t$ $n=2$

Answer key and solution verified before publishing.

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Exam: JEE Main 2025
Paper: 8 April, Evening Shift
Subject: Physics
Chapter: Atomic Physics
Topic: Dual Nature of Matter