An isotropic monochromatic source emits 10 W of optical power at wavelength 400 nm. A small photocathode of area 2.0 cm² is placed 1.0 m from the source with its surface normal directed toward the source. The quantum efficiency is 20%. Take hc = 1240 eV·nm and e = 1.6×10⁻¹⁹ C. If the saturation current is approximately (N ÷ 10) μA, find N.
Physics · Photoelectric effect and dual nature of matter · question based on photoelectric effect
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Question

An isotropic monochromatic source emits 10 W of optical power at wavelength 400 nm. A small photocathode of area 2.0 cm² is placed 1.0 m from the source with its surface normal directed toward the source. The quantum efficiency is 20%. Take hc = 1240 eV·nm and e = 1.6×10⁻¹⁹ C. If the saturation current is approximately (N ÷ 10) μA, find N.

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

G1 Physics · Accepted Answer

The source spreads its power uniformly over a sphere of area 4πr². At r = 1.0 m, the intensity is I = 10 ÷ (4π) W·m⁻². Photocathode area: A = 2.0 cm² = 2.0×10⁻⁴ m². Because the surface normal points toward the source, the full projected area is A. Therefore the incident power is P(hit) = 10×2.0×10⁻⁴ ÷ (4π) ≈ 1.59×10⁻⁴ W. Photon energy: Eγ = 1240 ÷ 400 = 3.10 eV. In joules: Eγ = 3.10×1.6×10⁻¹⁹ = 4.96×10⁻¹⁹ J. Photon arrival rate: Ṅγ = 1.59×10⁻⁴ ÷ 4.96×10⁻¹⁹ ≈ 3.21×10¹⁴ s⁻¹. With 20% quantum eff…