Question

A silver ball of radius $\text{4.8} \, cm$ is suspended by a thread in a vacuum chamber. $UV$ light of wavelength $200 \, nm$ 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. $1 \, V$
• B. $2 \, V$
• C. $3 \, V$
• D. zero

Answer 1

Answer: (C)

The total number of photons striking the surface of the ball is
$n_{p}=\frac{E \lambda }{h c}=\frac{1 \, \times \, 10^{- 7} \times 200 \times 10^{- 9}}{6 .6 \times 10^{- 34} \times 3 \times 10^{8}}=1\times 10^{11}$
The total number of electrons ejected is
$n_{e}=\frac{1 0^{11}}{1 0^{3}}=10^{8}$
$\therefore V=\frac{q}{4 \left(\pi ε\right)_{0} r}=\frac{\left(\left(10\right)^{8} \times 1 .6 \times \left(10\right)^{- 19}\right) \times 9 \times \left(10\right)^{9}}{4 .8 \times \left(10\right)^{- 2}}=3 \, V$