Question

A silver ball of radius 4.8 cm is suspended by a thread in a vacuum chamber. Ultraviolet light of wavelength 200 nm 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 every ten thousand is able to eject a photo electron, find the electric potential at the surface of the ball assuming zero potential at infinity. What is the potential at the center of the ball ?

Answer 1

Given $\lambda =200nm=2\times {10}^{-7}$

'E' of one photon

$\frac{hc}{\lambda }=\frac{6.63\times {10}^{-34}\times 3\times {10}^8}{2\times {10}^{-7}}$

$=9.945\times {10}^{-18}$

Number of photons

$=\frac{1\times {10}^7}{9.945\times {10}^{-19}}$

$=1\times {10}^{11}\text{no.s}$

Hence Number of photo electrons

$=\frac{1\times {10}^{11}}{{10}^4}=1\times {10}^7$

Net amount of +ve charge 'q' developed due to the outgoing electrons

$=1\times 107\times 1.6\times {10}^{-19}$

$=1.6\times {10}^{-12}C$

Now potential developed at the centre as well as at the surface due to these charge.

$=\frac{Kq}{r}$

$=\frac{9\times {10}^9\times 1.6\times {10}^{-12}}{4.8\times {10}^{-2}}$

$=3\times {10}^{-1}V=0.3V$