A completely absorbing photocathode receives monochromatic light of wavelength 400 nm and total optical power 10 mW. Its quantum efficiency is 20%. Assume all emitted photoelectrons are collected at saturation and neglect the mechanical recoil associated with emitted electrons when calculating radiation force. Take hc = 1240 eV·nm, e = 1.6×10⁻¹⁹ C and c = 3×10⁸ m·s⁻¹. Which pair is closest to the saturation current and the radiation force due to the incident photons?
Options

Question

A completely absorbing photocathode receives monochromatic light of wavelength 400 nm and total optical power 10 mW. Its quantum efficiency is 20%. Assume all emitted photoelectrons are collected at saturation and neglect the mechanical recoil associated with emitted electrons when calculating radiation force. Take hc = 1240 eV·nm, e = 1.6×10⁻¹⁹ C and c = 3×10⁸ m·s⁻¹. Which pair is closest to the saturation current and the radiation force due to the incident photons?

Options

G1 Physics · Accepted Answer

Photon energy: Eγ = 1240 ÷ 400 = 3.10 eV. Convert to joules: Eγ = 3.10×1.6×10⁻¹⁹ = 4.96×10⁻¹⁹ J. Incident optical power: P = 10 mW = 0.010 W. Photon arrival rate: Ṅγ = 0.010 ÷ 4.96×10⁻¹⁹ ≈ 2.02×10¹⁶ s⁻¹. With 20% quantum efficiency: Ṅe = 0.20×2.02×10¹⁶ ≈ 4.03×10¹⁵ s⁻¹. Saturation current: Iₛ = eṄe ≈ 1.6×10⁻¹⁹×4.03×10¹⁵ ≈ 6.45×10⁻⁴ A = 0.645 mA. For complete absorption, radiation force is F = P ÷ c = 0.010 ÷ (3×10⁸) = 3.33×10⁻¹¹ N. Correct option: A.