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For a certain metal, when monochromatic light of wavelength is incident, the stopping potential for photoelectrons is 3V₀ . When the same metal is illuminated by light of wavelength 2 , then the stopping potential becomes V₀ . The threshold wavelength for photoelectric emission for the given metal is . The value of is _______.

Options

  1. A1
  2. B4
  3. C2
  4. D3

Correct answer

B. 4

Step-by-step solution

Using Einstein's photoelectric equation: eV_s = hc - For the first case: 3eV₀ = hc - For the second case: eV₀ = hc 2 - Multiplying the second equation by 3 and equating with the first equation: hc - = 3hc 2 - 3 2 = 3hc 2 - hc 2 = hc 2 = hc 4 Since the work function = hc ₀ , where ₀ is the threshold wavelength: hc ₀ = hc 4 ₀ = 4 Given ₀ = , we get = 4 . Answer: 4

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