Question

A silver ball of radius $4.8cm$ is suspended by a thread in a vacuum chamber. Ultraviolet light of wavelength $200nm$ is incident on the ball for some time during which a total light energy of $1.0\times {10}^{-7}$ J falls on the surface. Assuming that on the average, one photon out of ten thousand photons is able to eject a photoelectron, find the electric potential (in terms of ${10}^{-1}V$) at the surface of the ball assuming zero potential at infinity.

Answer 1

Let us first find the number of photons falling on the sphere.
$E=n\frac{hC}{\lambda }$
$n=\frac{E\lambda }{hC}$ = $\frac{{10}^{-7}\times 200\times {10}^{-9}}{2\times {10}^{-25}}$ = ${10}^{11}$
Given that one in ten thousand eject an electron .
Therefore total number of electrons ejected = $\frac{{10}^{11}}{{10}^4}$ = ${10}^7$
Total charge on sphere = ${10}^7\times 1.6\times {10}^{-19}$ = $1.6\times {10}^{--12}$ C
Potential = $\frac{KQ}{R}$ = $\frac{9\times {10}^9\times 1.6\times {10}^{-12}}{4.8\times {10}^{-2}}$ = 3$\times {10}^{-1}V$