A silver sphere of radius \(1 \mathrm{~cm}\) and work function \(4.7 \mathrm{eV}\) is suspended from an insulating thread in free-space. It is under continuous illumination of \(200 \mathrm{~nm}\) wavelength light. As photoelectrons are emitted, the sphere gets charged and acquires a potential. The maximum number of photoelectrons emitted from the sphere is \(A \times 10^Z\) (where \(1 < A < 10\) ). The value of \(Z\) is

Photoemission will stop when potential on silver sphere becomes equal to the stopping potential.
\(\therefore \quad \frac{h c}{\lambda}-W=e V_0\)
Here, \(\quad V_0=\frac{1}{4 \pi \varepsilon_0} \frac{n e}{r}\)
\(
\begin{aligned}
& \therefore \quad\left(\frac{1240}{1200} \mathrm{eV}\right)-(4.7 \mathrm{eV}) \\
&=\frac{9 \times 10^9 \times n \times 1.6 \times 10^{-19}}{10^{-2}} \\
&(6.2-4.7)=\frac{9 \times 10^9 \times n \times 1.6 \times 10^{-19}}{10^{-2}} \\
& \text { or } \quad n= \frac{1.5 \times 10^{-2}}{9 \times 1.6 \times 10^{-10}}=1.04 \times 10^7
\end{aligned}
\)
\(\therefore\) Answer is 7 .
Analysis of Question
(i) Question is moderately difficult.
(ii) In \(\mathrm{eV}_0\) if we substitute the value of \(e=1.6 \times 10^{-19} \mathrm{C}\), then answer is in J. If we leave it then, answer is in \(e \mathrm{~V}\).