Answer
See the answer below.
Work Step by Step
Energy required by the atom is the same as the one provided by the photon:
$E=h\times\nu$
$6.7\times 10^{-19}\ J=6.626\times10^{-34}\ J.s\times \nu$
$\nu=10.11\times10^{14}\ 1/s$
$c=\lambda\times\nu$
$\lambda=2.998\times10^8\ m/s\div 10.11\times10^{14}\ 1/s$
$\lambda=2.96\times10^{-7}\ m=296\ nm$
No, the maximum wavelength allowed for the switch to work is 296 nm.
