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JEE Main 2025 (8 Apr, Shift 2) · Matter Waves: de Broglie Wavelength

Matter Waves: de Broglie Wavelength question from JEE Main 2025 (8 Apr, Shift 2)

Q47JEE Main 2025 · 8 APR · SHIFT 2Difficult

Matter Waves: de Broglie Wavelength

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 nth power of time. The numerical value of n is _____.

Numerical answer type. Work it out, then open the answer.

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Answer: 2

Infinite sheet: uniform field $E = \dfrac{\sigma}{2\varepsilon_0}$ , so constant force $eE$ .
From rest: $p = eEt$ , $\lambda = \dfrac{h}{eEt}$ .
$\dfrac{d\lambda}{dt} = -\dfrac{h}{eEt^2} \propto t^{-2}$
Answer: $n = 2$

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