Question

A silver sphere of radius $1cm$ and work function $\text{4.7}eV$ is suspended from an insulating thread in free-space. It is under continuous illumination of $200nm$ 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

Answer: 7

Photo emission will stop when potential on silver sphere becomes equal to the stopping potential.
Stopping potential
$=\frac{\text{hc}}{\lambda }-\text{w}$
$=\text{6.2}-\text{4.7}=\text{1.5}eV$
$\text{V}=\frac{\text{Kq}}{\text{r}}=1\text{.}5=\frac{\text{K}\times \text{n}\times \text{e}}{\text{r}}$
$\Rightarrow \text{n}=\frac{1\text{.}5\times 10^{-2}}{1\text{.}6\times 10^{-19}\times 9\times 10^9}=1\text{.}05\times 10^7$
$\Rightarrow$ $z=7$
Therefore answer is $7$ .