A plane photocathode of area 4.0 cm² is illuminated by a parallel monochromatic beam of intensity 100 W·m⁻². The beam makes an angle 60° with the surface normal. The radiation wavelength is 400 nm and the quantum efficiency is 25%. Take hc = 1240 eV·nm and e = 1.6×10⁻¹⁹ C. If the saturation current is approximately (N ÷ 100) mA, find N.
Physics · Photoelectric effect and dual nature of matter · question based on photoelectric effect
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Question

A plane photocathode of area 4.0 cm² is illuminated by a parallel monochromatic beam of intensity 100 W·m⁻². The beam makes an angle 60° with the surface normal. The radiation wavelength is 400 nm and the quantum efficiency is 25%. Take hc = 1240 eV·nm and e = 1.6×10⁻¹⁹ C. If the saturation current is approximately (N ÷ 100) mA, find N.

Physics · Photoelectric effect and dual nature of matter · question based on photoelectric effect

G1 Physics · Accepted Answer

Photocathode area: A = 4.0 cm² = 4.0×10⁻⁴ m². For oblique incidence, the intercepted power is P = IA cosθ. Thus, P = 100×4.0×10⁻⁴×cos60° = 100×4.0×10⁻⁴×0.5 = 0.020 W. Photon energy: Eγ = 1240 ÷ 400 = 3.10 eV = 4.96×10⁻¹⁹ J. Photon arrival rate: Ṅγ = 0.020 ÷ 4.96×10⁻¹⁹ ≈ 4.03×10¹⁶ s⁻¹. With 25% quantum efficiency: Ṅe = 0.25×4.03×10¹⁶ ≈ 1.01×10¹⁶ s⁻¹. Saturation current: Iₛ = eṄe ≈ 1.6×10⁻¹⁹×1.01×10¹⁶ ≈ 1.61×10⁻³ A = 1.61 mA. Therefore, Iₛ ≈ 161 ÷ 100 mA. Hence N = 161.