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Concepts Of Physics MCQ Edition [Volume 2]PhysicsPhotoelectric Effect and Wave–Particle Duality

In a photoelectric effect experiment, the stopping potential is measured for monochromatic light beams of varying wavelengths. Find the threshold wavelength from the experimental data. wavelength (nm) 350 400 450 500 550 stopping potential (V) 1.45 1.00 0.66 0.38 0.16

Options

  1. A1170 nm
  2. B585 nm
  3. C293 nm
  4. D450 nm

Correct answer

B. 585 nm

Step-by-step solution

According to Einstein's photoelectric equation: V_s = hc e - Using the data points ₁ = 350 nm , V_ s1 = 1.45 V and ₂ = 400 nm , V_ s2 = 1.00 V : 1.45 = hc 350e - 1.00 = hc 400e - Subtracting the second equation from the first: 0.45 = hc e ( 1 350 - 1 400 ) 0.45 = hc e ( 400 - 350 350 400 ) = hc e ( 50 140000 ) hc e = 0.45 2800 = 1260 V nm Substituting this value back into the second equation to find the work function : 1.00 = 1260 400 - = 3.15 - 1.00 = 2.15 eV The threshold wavelength ₀ is given by: ₀ = hc e ₀ = 12

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