The work function of a certain metal is $\frac{hc}{λ_{0}} .$ 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 plate and the sphere, expression of potential of the sphere at time $t$ is

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$V + \frac{100 ηλPet}{4 {πε}_{0} Rhc}$

$\frac{λPet}{4 {πε}_{0} Rhc}$

$V$

$V - \frac{ηλPet}{400 {πε}_{0} Rhc}$

answer is B.

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Detailed Solution

Number of photons emitted per second $N = \frac{η}{100} X \frac{Pλ}{hc}$

Potential due to the captured electron, $V' = \frac{Q}{4 {πε}_{0} R}$

where, charge captured in time t is, $Q = eNt$

Potential of the sphere after time $t$ is $V^{'} = V - \frac{(Ne) t}{4 {πε}_{0} R} = V - \frac{ηPλet}{400 {πε}_{0} Rhc}$

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