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JEE Main202431 Jan 2024Morning ShiftPhysicsDual Nature of MatterActual

When a metal surface is illuminated by light of wavelength λ , the stopping potential is 8 V . When the same surface is illuminated by light of wavelength 3 λ , stopping potential is 2 V . The threshold wavelength for this surface is :

Options

  1. A5 λ
  2. B3 λ
  3. C9 λ
  4. D4 . 5 λ

Correct answer

C. 9 λ

Step-by-step solution

From photoelectric effect equation, we can write E = ϕ + K m a x and work function can be written as ϕ = h c λ 0 . Also, maximum kinetic energy K m a x = e V 0 For first case: 8 e = h c λ - h c λ 0 ... (i) For second case: 2 e = h c 3 λ - h c λ 0 ... (ii) After using equation (ii) in (i), we get 4 h c 3 λ - h c λ 0 = h c λ - h c λ 0 ⇒ λ 0 = 9 λ

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