Answer
longest possible wavelength of light is approximately
$\lambda=355 nm$
Work Step by Step
metal has a work function $\phi_{0}=3.50eV$=$5.6\times10^{-19}J$
since $ 1 eV$ is equal to $1.6\times10^{-19}J$
so $3.50eV$ will be equal to $3.50\times1.6\times10^{-19}J=5.6\times10^{-19}J$
work function is threshold energy for which electron is just emitted from the surface with zero kinetic energy.
from equation 27.8
cutoff , threshold or minimum frequency $ f_{0}=\frac{\phi_{0}}{h}$
putting the values $\phi_{0}=5.6\times10^{-19}J$ and $h=6.63\times10^{-34} J.s$
$ f_{0}=\frac{5.6\times10^{-19}J}{6.63\times10^{-34} J.s}=0.8446\times10^{15}/s$
$ f_{0}=8.446\times10^{14}Hz$
corresponding longest wavelength will be
$\lambda=\frac{c}{f}=\frac {3\times10^{8}m/s}{8.446\times10^{14}Hz}=0.355197\times10^{-6}m$
$\lambda=355.197\times10^{-9}m=355.197nm$
so longest possible wavelength is approximately
$\lambda=355 nm$
