A small perfectly absorbing photocathode is illuminated by an isotropic monochromatic point source. Initially the source has total optical power P, wavelength λ and is at distance r from the photocathode. The frequency is above threshold. The experiment is modified so that the optical power remains P, the wavelength becomes λ ÷ 2, and the source-cathode distance becomes 2r. Assume photocathode area, orientation and quantum efficiency remain unchanged. Which statements are correct?
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Question

A small perfectly absorbing photocathode is illuminated by an isotropic monochromatic point source. Initially the source has total optical power P, wavelength λ and is at distance r from the photocathode. The frequency is above threshold. The experiment is modified so that the optical power remains P, the wavelength becomes λ ÷ 2, and the source-cathode distance becomes 2r. Assume photocathode area, orientation and quantum efficiency remain unchanged. Which statements are correct?

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G1 Physics · Accepted Answer

For an isotropic point source, incident optical power on the small photocathode is proportional to P ÷ r². Photon rate is incident power divided by photon energy. Since Eγ = hc ÷ λ, photon rate is proportional to Pλ ÷ r². After the changes: P is unchanged, λ becomes λ ÷ 2, r becomes 2r. Therefore, Ṅγ(new) ÷ Ṅγ(old) = (1 ÷ 2)×[r² ÷ (2r)²] = (1 ÷ 2)×(1 ÷ 4) = 1 ÷ 8. Thus A is correct. With unchanged quantum efficiency, saturation current is proportional to photon rate, so it also becomes 1 ÷ 8.…