Question

A small metal plate of area $2c{m}^2$ is placed at a distance of $2m$ from a monochromatic light source of $\lambda =1000\mathring{A}$, power rating of $100W$, light energy conversion efficiency of $10\%$ and emitting light uniformly in all directions. Light falls normally on the plate having work function, $\varphi =10eV)$. 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

Answer: 3.20

$P_{\text{output }}$ of bulb $=10W$
$I=\frac{10}{4\pi (2{)}^2}$
Power incident on plate $=\frac{10}{4\pi (2{)}^2}\times \frac{2}{10^4}$.
Energy of each photon $=\frac{12400}{1000}eV=12.4eV$
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
$=\frac{n}{10^6}\times e=\frac{\left[\frac{10\times 2}{4\pi (2{)}^2\times 10^4}\right]}{12.4\times 10^6}$
$=3.2\times 10^{-12}A$