Question

A silver ball of radius 4.8 cm is suspended by a thread in the vacuum chamber. UV light of wavelength 200 nm is incident on the ball for some times during which a total energy of $1\times {10}^{-7}J$ falls on the surface. Assuming on an average one out of ${10}^3$ photons incident is able to eject electron. The potential on sphere will be

• A. 1 V
• B. 2 V
• C. 3 V
• D. Zero

Answer 1

The correct option is C 3 V

$n=\frac{E\lambda }{hc}=\frac{1\times {10}^{-7}\times 200\times {10}^{-9}}{6.6\times {10}^{-34}\times 3\times {10}^8}=1\times {10}^{11}$
Number of electrons ejected = $\frac{{10}^{11}}{{10}^3}={10}^8$
$\therefore V=\frac{q}{4\pi {ϵ}_{0}r}=\frac{({10}^8\times 1.6\times {10}^{-19})\times 9\times {10}^9}{4.8\times {10}^{-2}}=3V$