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MHT CET202522 Apr 2025Morning ShiftPhysicsDual Nature of MatterActual

When a photosensitive metal surface is illuminated with radiation of wavelength ' ₁ ', the stopping potential is ' V ₁ ' . If the same surface is illuminated with radiation of wavelength ' 3 ₁ ', the stopping potential is V ₁ 6 . The threshold wavelength for the photosensitive metal surface is

Options

  1. A3 2 ₁
  2. B2 ₁
  3. C5 ₁
  4. D6 ₁

Correct answer

C. 5 ₁

Step-by-step solution

The photoelectric equation h = + eV_s relates the incident frequency to the stopping potential V_s , with work function . Substituting = c/ and = hc/ ₀ gives: hc = hc ₀ + eV_s For wavelength ₁ with stopping potential V₁ : hc ₁ = hc ₀ + eV₁ For wavelength 3 ₁ with stopping potential V₁/6 : hc 3 ₁ = hc ₀ + eV₁ 6 Eliminating eV₁ between these equations: hc ₁ - hc ₀ = 2hc ₁ - 6hc ₀ Dividing through by hc and simplifying yields: 5 ₀ = 1 ₁ Thus the threshold wavelength is ₀ = 5 ₁ , which corresponds to option C. Answer:

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