Parallel beam of photons of light intensity I and frequency f are incident on a conducting sphere A of radius r which is connected to another conducting sphere B of radius R at a large distance by a highly conducting wire through an ideal ammeter as shown. Work function of sphere A is w[w<hf] & radiation is incident only on A. If the photo electric efficiency is k/100 and all the incident photons are absorbed by the sphere then choose correct options

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The number of electrons emitted per unit time by sphere A is $\frac{{Iπr}^{2} k}{100hf}$

Reading of the ammeter initially is $(\frac{R}{R+r}) (\frac{ek}{100}) (\frac{{Iπr}^{2}}{hf})$

Ammeter stops reading after sometime

Ammeter reading is constant at all instants

answer is A, B, C.

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Detailed Solution

Number of photons incident over time t $N_{i} = \frac{{IπR}^{2} t}{hf}$
Number of electrons emitted in time t $N_{e} = \frac{k}{100} \frac{{IπR}^{2} t}{hf}$
Total charge on A & B in a time t $Q_{A} {+Q}_{B} {=N}_{e} e= \frac{ek}{100} \frac{{IπR}^{2} t}{hf}$ $A μ O \frac{Q_{A}}{r} = \frac{Q_{3}}{R}; Q_{B} = \frac{R}{R + r} N_{e} e$
Reading of ammeter is $\frac{{dQ}_{3}}{dt} = \frac{R}{R+r} \frac{{ekIπR}^{2}}{100hf}$

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