Question

A silver ball of radius $48\text{cm}$ is suspended by a thread in a vacuum chamber. Ultraviolet light of wavelength $200\text{nm}$ is incident on the ball for some time, during which a total light energy of $10\times {10}^{-7}\text{J}$ falls on the surface. Assuming that on the average for every ten thousand photons is able to eject a photoelectron, find the electric potential at the surface of the ball assuming zero potential at infinity.

• A. $300\text{V}$
• B. $3000\text{V}$
• C. $3\text{V}$
• D. $0.3\text{V}$

Answer 1

The correct option is D $0.3\text{V}$

Given,

$\lambda =200\text{nm}=2\times {10}^{-7}m{E}_{incident}=10\times {10}^{-7}\text{J}r=48\text{cm}=48\times {10}^{-2}\text{m}$

The energy $\left(E\right)$ of a photon is,

$E=\frac{hc}{\lambda }=\frac{6.63\times {10}^{-34}\times 3\times {10}^8}{2\times {10}^{-7}}=9.945\times {10}^{-19}\text{J}$

No.of photons emitted is,

$n=\frac{\text{Total Energy}}{\text{Energy of a photon}}$

$=\frac{1\times {10}^{-7}}{9.945\times {10}^{-19}}\approx 1\times {10}^{11}$

Hence, No. of photo electrons emitted is,

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

The net amount of positive charge $q$ developed due to the outgoing electrons is,

$q=1\times {10}^7\times 1.6\times {10}^{-19}=1.6\times {10}^{-12}\text{C}$

Now potential developed at the centre as well as at the surface due to these charges is,

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

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

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(D\right)$ is the correct answer.