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The work function of a certain metal is h c λ 0 . When a monochromatic light of wavelength, λ < λ 0 is incident such that the plate gains a total power P . If the efficiency of photoelectric emission is η   % and all the emitted photoelectrons are captured by a hollow conducting sphere of radius R , already charged to potential V , then neglecting any interaction between the plate and the

Options

  1. AV + 100 η λ P e t 4 π ε 0 R h C
  2. BV - η λ P e t 400 π ε 0 R h C
  3. CV
  4. Dλ P e t 4 π ε 0 R h C

Correct answer

B. V - η λ P e t 400 π ε 0 R h C

Step-by-step solution

The total energy of light incident = P t . Number of photons emitted in time t = Energy   incident Energy   of   1   photon Number of photons emitted in time t = P t h c λ If the efficiency is η   % So, number of photoelectrons emitted in time t , n = η   % P t λ h c Number of photoelectrons emitted in time t , n = η P t λ 100 h c These n number of photoelectrons having a total charge η e P t λ 100 h c are added to sphere, hence, its potential is

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