Question

A silver sphere of radius $1 \, cm$ and work function $\text{4.7} \, eV$ is suspended from an insulating thread in free-space. It is under continuous illumination of $200 \, nm$ wavelength electromagnetic waves. As photoelectrons are emitted, the sphere gets charged and acquires a potential. The maximum number of photoelectrons emitted from the sphere is $A\times 10^{Z}$ (where $1 < A < 10$ ). The value of $Z$ is

Answer 1

Photo emission will stop when potential on silver sphere becomes equal to the stopping potential.
Stopping potential
$= \frac{\text{hc}}{\lambda } - \text{w}$
$=\text{6.2}-\text{4.7}=\text{1.5}eV$
$\text{V} = \frac{\text{Kq}}{\text{r}} = 1 \text{.} 5 = \frac{\text{K} \times \text{n} \times \text{e}}{\text{r}}$
$\Rightarrow \text{n} = \frac{1 \text{.} 5 \times 1 0^{- 2}}{1 \text{.} 6 \times 1 0^{- 1 9} \times 9 \times 1 0^{9}} = 1 \text{.} 0 5 \times 1 0^{7}$
$\Rightarrow $ $z=7$
Therefore answer is $7$ .