JEE Main 2025 Apr 8 Shift 2, Physics Q21: Wave Nature of Matter

JEE Main2025Apr 8, Shift 2Physics

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 _____.

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Solution

The electric field from an infinite sheet with density $- σ$ is $E = \frac{σ}{2 ε _{0}}$ , pushing the electron uniformly away from the sheet with acceleration $a = \frac{e E}{m} = \frac{e σ}{2 m ε _{0}}$ (a constant).

Starting from rest, the electron's speed at time $t$ is $v = a t$ , and momentum is $p = m v = ma t$ .

De Broglie wavelength: $λ = \frac{h}{p} = \frac{h}{ma t}$ , so $λ \propto \frac{1}{t}$ .

Differentiating: $\frac{d λ}{d t} = - \frac{h}{ma t ^{2}}$ , so $\frac{d λ}{d t} \propto \frac{1}{t ^{2}}$ .

Comparing with $\frac{1}{t ^{n}}$ gives $n = 2$ .

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JEE Main 2025 Apr 8 Shift 2, Physics Q21: Wave Nature of Matter

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