JEE Main · 2025 · 02 Apr 2025 · Shift 1 · Modern Physics

A monochromatic light is incident on a metallic plate having work function

ϕ

. An electron, emitted normally to the plate from a point A with maximum kinetic energy, enters a constant magnetic field, perpendicular to the initial velocity of electron. The electron passes through a curve and hits back the plate at a point B. The distance between A and B is:
(Given: The magnitude of charge of an electron is e and mass is

m, h

is Planck's constant and c is velocity of light. Take the magnetic field exists throughout the path of electron)

(A) $2 m (\frac{hc}{λ} - ϕ) / eB$
(B) $m (\frac{hc}{λ} - ϕ) / eB$
(C) $8 m (\frac{hc}{λ} - ϕ) / eB$ ✓ Correct
(D) $2 m (\frac{hc}{λ} - ϕ) / eB$

Answer: (C)

Solution

The fastest photoelectron carries

K E_{m a x} = \frac{h c}{λ} - ϕ

, so its momentum is

p = 2 m K E_{m a x} = 2 m (\frac{h c}{λ} - ϕ)

. In the transverse field it travels on a circle of radius

R = \frac{p}{e B}

, and leaving and returning to the plate places A and B a full diameter apart:

d = 2 R = \frac{2 2 m ( \frac{h c}{λ} - ϕ )}{e B} = \frac{8 m ( \frac{h c}{λ} - ϕ )}{e B}

JEE Main · 2025 · 02 Apr 2025 · Shift 1 · Single correct option

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JEE Main · 2025 · 02 Apr 2025 · Shift 1 · Modern Physics

Solution

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