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The stopping potential when a metal surface is illuminated by light of wavelength is 15 V . The stopping potential when the same surface is illuminated by light of wavelength 4 is 3 V . The ratio of threshold wavelength to the initial incident wavelength is:

Options

  1. A15: 1
  2. B1: 16
  3. C1: 15
  4. D16: 1

Correct answer

D. 16: 1

Step-by-step solution

From Einstein's photoelectric equation, the stopping potential V_s is given by eV_s = hc - , where is the work function of the metal and ₀ is the threshold wavelength such that = hc ₀ . For the first case, eV₁ = hc - hc ₀ = 15e . Thus, hc - hc ₀ = 15e (Equation 1). For the second case, eV₂ = hc 4 - hc ₀ = 3e . Thus, hc 4 - hc ₀ = 3e (Equation 2). Subtracting Equation 2 from Equation 1: ( hc - hc 4 ) = 15e - 3e = 12e 3hc 4 = 12e hc = 16e . Substituting hc = 16e into Equation 1: 16e - hc ₀ = 15e hc ₀ = e . Since hc =

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