When light of wavelength \(\lambda\) is incident on a photosensitive surface the stopping potential is ' \(\mathrm{V}\) '. When light of wavelength \(3 \lambda\) is incident on same surface the stopping potential is \(\frac{\mathrm{V}}{6}\). Then the threshold wavelength for the surface is

\(
\begin{aligned}
& \lambda_1=\lambda,\left(\mathrm{V}_0\right)_1=\mathrm{V} \\
& \lambda_2=3 \lambda,\left(\mathrm{V}_0\right)_2=\frac{\mathrm{V}}{6}
\end{aligned}
\)
Photo electric equation is given by \(\mathrm{eV}_0=\mathrm{hc}\left(\frac{1}{\lambda}-\frac{1}{\lambda_0}\right)....(i)\)
In first case,
\(
\mathrm{eV}=\mathrm{hc}\left(\frac{1}{\lambda}-\frac{1}{\lambda_0}\right)
\)
For second case,
\(
\frac{\mathrm{eV}}{6}=\mathrm{hc}\left(\frac{1}{3 \lambda}-\frac{1}{\lambda_0}\right).....(ii)
\)
Dividing equation (i) by equation (ii),
\(6 =\frac{\frac{1}{\lambda}-\frac{1}{\lambda_0}}{\frac{1}{3 \lambda}-\frac{1}{\lambda_0}}=\frac{3 \lambda_0-\lambda}{\lambda_0-3 \lambda}\)
\(\therefore \lambda_0 =5 \lambda\)