JEE Main 2025 Apr 2 Shift 2, Physics Q5: Wave Nature of Matter

JEE Main2025Apr 2, Shift 2Physics

An electron with mass ' $m$ ' with an initial velocity ( $t = 0$ ) $v = v_{0} \hat{i}$ ( $v_{0} > 0$ ) enters a magnetic field $B = B_{0} \hat{j}$ . If the initial de-Broglie wavelength at $t = 0$ is $λ_{0}$ then its value after time ' $t$ ' would be :

A
$\frac{λ _{0}}{1 - \frac{e ^{2} B _{0}^{2} t ^{2}}{m ^{2}}}$
B
$\frac{λ _{0}}{1 + \frac{e ^{2} B _{0}^{2} t ^{2}}{m ^{2}}}$
C
$λ_{0} 1 + \frac{e ^{2} B _{0}^{2} t ^{2}}{m ^{2}}$
D
$λ_{0}$

Solution

The magnetic force $F = q v \times B$ is always perpendicular to the velocity, so it does no work on the electron.

Consequently the kinetic energy and the magnitude of momentum $p = m v$ remain unchanged.

Since the de Broglie wavelength $λ = \frac{h}{p}$ depends only on $∣ p ∣$ , it stays at its initial value $λ_{0}$ at all later times.

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JEE Main 2025 Apr 2 Shift 2, Physics Q5: Wave Nature of Matter

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