A photocathode having work function 2.0 eV is illuminated simultaneously by two monochromatic beams of wavelengths 300 nm and 400 nm. Each beam has optical power 1.0 mW incident on the cathode. Assume 100% quantum efficiency and complete collection of emitted electrons at saturation. Take hc = 1240 eV·nm and e = 1.6×10⁻¹⁹ C. Which pair is closest to the saturation current and stopping potential?
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Question

A photocathode having work function 2.0 eV is illuminated simultaneously by two monochromatic beams of wavelengths 300 nm and 400 nm. Each beam has optical power 1.0 mW incident on the cathode. Assume 100% quantum efficiency and complete collection of emitted electrons at saturation. Take hc = 1240 eV·nm and e = 1.6×10⁻¹⁹ C. Which pair is closest to the saturation current and stopping potential?

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G1 Physics · Accepted Answer

Both wavelengths are above threshold, so both contribute to the saturation current. For 300 nm: E₁ = 1240 ÷ 300 ≈ 4.133 eV. For 400 nm: E₂ = 1240 ÷ 400 = 3.10 eV. The photon rate from each beam equals power divided by energy per photon. Using 1 eV = 1.6×10⁻¹⁹ J: Ṅ₁ ≈ 1.51×10¹⁵ s⁻¹, Ṅ₂ ≈ 2.02×10¹⁵ s⁻¹. Total electron rate at 100% quantum efficiency: Ṅe ≈ 3.53×10¹⁵ s⁻¹. Therefore, Iₛ = eṄe ≈ 5.65×10⁻⁴ A = 0.565 mA. The stopping potential is determined by the fastest photoelectrons, produced b…