The work function of a certain metal is \( \frac{\mathrm{hC}}{\lamb...

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The work function of a certain metal is \( \frac{\mathrm{hC}}{\lambda_{0}} \). When a monochromatic light of wavelength \( \lambda\lambda_{0} \) is incident such that the plate gains a total power \( P \). If the efficiency of photoelectric emission is \( \eta \% \) and all the emitted photoelectrons are captured by a hollow conducting sphere of radius \( \mathrm{R} \) already charged to potential V, then neglecting any interaction between plate and the sphere, expression of potential of the sphere at time \( t \) is \( \left(e=1.6 \times 10^{-19} \mathrm{C}\right) \) :
\( -(\mathrm{A}) \mathrm{V}+\frac{100 \eta \lambda \mathrm{Pet}}{4 \pi \varepsilon_{0} \mathrm{RhC}} \)
(B) \( V-\frac{\eta \lambda \text { Pet }}{400 \pi \varepsilon_{0} \mathrm{RhC}} \)
(C) \( \vee \)
(D) \( \frac{\lambda \mathrm{Pe} \mathrm{t}}{4 \pi \varepsilon_{0} \mathrm{RhC}} \)
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