Electrons ejected from a metal surface by a beam of incident light are fully stopped by a retarding potential of $3V$. The photo electric effect begins in this metal at frequency of $6\times {10}^{14}se{c}^{-1}$. Find the work function for this metal and frequency of incident light.

The threshold frequency for the given metal surface is

${\nu }_{th}=6\times {10}^{14} \mathrm{Hz}$

Thus the work function for metal surface is

$\varphi =h{\nu }_{th}=6.63\times {10}^{-34}\times 6\times {10}^{14}$$=3.978\times {10}^{-19} \mathrm{J}$  Ans.

As stopping potential for the ejected electrons is $3V$, the maximum kinetic energy of ejected electrons will be

$K{E}_{max}=3eV=3\times 1.6\times {10}^{-19}J=4.8\times {10}^{-19}J$

According to photo electric effect equation, we have

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

or frequency of incident light is

$\nu =\frac{\varphi +K{E}_{max}}{h}=\frac{3.978\times {10}^{-19}+4.8\times {10}^{-19}}{6.63\times {10}^{-34}}$

    $=1.32\times {10}^{15} Hz$ Ans.