Question

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

• A. $1V$
• B. $2V$
• C. $3V$
• D. zero

Answer 1

Answer: (C)

The total number of photons striking the surface of the ball is
$n_p=\frac{E\lambda }{hc}=\frac{1\times 10^{-7}\times 200\times 10^{-9}}{6.6\times 10^{-34}\times 3\times 10^8}=1\times 10^{11}$
The total number of electrons ejected is
$n_e=\frac{10^{11}}{10^3}=10^8$
$\therefore V=\frac{q}{4{\left(\pi \epsilon \right)}_{0}r}=\frac{\left({\left(10\right)}^8\times 1.6\times {\left(10\right)}^{-19}\right)\times 9\times {\left(10\right)}^9}{4.8\times {\left(10\right)}^{-2}}=3V$