Answer
$\lambda = 226 nm $
Work Step by Step
When electron jumps from valence band to conduction band, it will release energy in form of photon. The energy released is equal to energy gap between conduction band and valence band. Hence the energy of photon
$E = \frac{hc}{\lambda}$
Where
Planck Constant, $h = 6.626\times 10^{-34} J.s$
Speed of light, $c = 2.998 \times 10^8 m/s$
$E_{Gap} = 5.5 eV $
So,
Rearrange the equation to solve for $\lambda$
$\lambda = \frac{(6.626\times 10^{-34} J.s)(2.998 \times 10^8 m/s)}{(5.5 eV)(1.602 \times 10^{-19} J/eV)}$
$\lambda = 2.26 \times 10^{-7} m$
$\lambda = 226 nm $
