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JEE Main 2025 (2 Apr, Shift 1) · Photoelectric Effect: Einstein's Equation

Photoelectric Effect: Einstein's Equation question from JEE Main 2025 (2 Apr, Shift 1)

Q48JEE Main 2025 · 2 APR · SHIFT 1Difficult

Photoelectric Effect: Einstein's Equation

A monochromatic light is incident on a metallic plate having work function ϕ\phi. 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 BB. The distance between AA and BB is: (Given: The magnitude of charge of an electron is e and mass is m,hm, h is Planck's constant and c is velocity of light. Take the magnetic field exists throughout the path of electron)

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Answer: (b)

ABvrAB = 2rB ⊗
  1. Kmax=hcλ−ϕK_{max} = \frac{hc}{\lambda} - \phi, momentum p=2mKmaxp = \sqrt{2mK_{max}}.
  2. Leaving normally with BB perpendicular, the electron moves on a semicircle of radius r=peBr = \frac{p}{eB} and lands back on the plate.
  3. AB=2r=22m(hc/λ−ϕ)eB=8m(hc/λ−ϕ)eBAB = 2r = \frac{2\sqrt{2m(hc/\lambda - \phi)}}{eB} = \frac{\sqrt{8m(hc/\lambda - \phi)}}{eB}
  4. So the answer is (b).
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