Question

A small metal plate of area $2\, cm ^{2}$ is placed at a distance of $2 \,m$ from a monochromatic light source of $\lambda=1000\,\mathring{A}$, power rating of $100\,W$, light energy conversion efficiency of $10 \%$ and emitting light uniformly in all directions. Light falls normally on the plate having work function, $\phi=10 \,eV )$. Assuming one out of $10^{6}$ photons is able to eject a photoelectron, the saturation current is $n \times 10^{-12}$ ampere. Find $n$.

Answer 1

$P_{\text {output }}$ of bulb $=10 W$
$I=\frac{10}{4 \pi(2)^{2}}$
Power incident on plate $=\frac{10}{4 \pi(2)^{2}} \times \frac{2}{10^{4}}$.
Energy of each photon $=\frac{12400}{1000}\, eV =12.4 \,eV$
Total number of photons falling on plate per second
$=\frac{\left[\frac{10 \times 2}{4 \pi(2)^{2} \times 10^{4}}\right]}{12.4 \times 1.6 \times 10^{-19}}=n$
Number of photoelectrons ejected per second $=\frac{n}{10^{6}}$
Saturation current
$=\frac{n}{10^{6}} \times e=\frac{\left[\frac{10 \times 2}{4 \pi(2)^{2} \times 10^{4}}\right]}{12.4 \times 10^{6}}$
$=3.2 \times 10^{-12} \,A$