Two isolated metallic spheres A and B are made of different photosensitive materials and are illuminated with the same monochromatic radiation of wavelength 310 nm. Sphere A has radius 5 cm and work function 2.0 eV. Sphere B has radius 10 cm and work function 2.5 eV. Both spheres are initially neutral and are illuminated long enough for positive self-charging to stop further photoemission. Take hc = 1240 eV·nm. What is the ratio of the final positive charges Q(B): Q(A)?
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Question

Two isolated metallic spheres A and B are made of different photosensitive materials and are illuminated with the same monochromatic radiation of wavelength 310 nm. Sphere A has radius 5 cm and work function 2.0 eV. Sphere B has radius 10 cm and work function 2.5 eV. Both spheres are initially neutral and are illuminated long enough for positive self-charging to stop further photoemission. Take hc = 1240 eV·nm. What is the ratio of the final positive charges Q(B): Q(A)?

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G1 Physics · Accepted Answer

Photon energy: Eγ = 1240 ÷ 310 = 4.0 eV. For sphere A: Kₘₐₓ(A) = 4.0−2.0 = 2.0 eV. Therefore the final stopping potential of sphere A is V(A) = 2.0 V. For sphere B: Kₘₐₓ(B) = 4.0−2.5 = 1.5 eV. Therefore V(B) = 1.5 V. For an isolated sphere, Q = 4πε₀RV, so Q is proportional to RV. Therefore, Q(B) ÷ Q(A) = [10×1.5] ÷ [5×2.0] = 15 ÷ 10 = 3 ÷ 2. Hence, Q(B):Q(A) = 3:2. Correct option: B.