Electrons with maximum kinetic energy $3 \mathrm{eV}$ are ejected from a metal surface by ultraviolet radiation of wavelength $1500 Å$. Determine the work function of the metal, the threshold wavelength of metal and stopping potential difference required to stop the emission of electrons.

Energy of incident photon in $eV$ is

$E=\frac{12431}{1500} \mathrm{eV} = 8.29 \mathrm{eV}$

According to photo electric effect equation, we have

$E=\varphi +K{E}_{max}$

or $\varphi =E-K{E}_{max}$

or $=8.29-3 \mathrm{eV}$

or $=5.29 \mathrm{eV}$

Threshold wavelength for the metal surface corresponding to work function $5.29 \mathrm{eV}$ is given as

${\lambda }_{th}=\frac{12431}{5.29} Å$

     $=2349.9 Å$    Ans.

Stopping potential for the ejected electrons can be given as 

$V_0=\frac{K{E}_{max}}{e}=\frac{3 \mathrm{eV}}{e}=3 \mathrm{V}.$  Ans.