Answer
1.11 micrometers
Work Step by Step
The minimum-frequency (or maximum-wavelength) photon that enables conduction has an energy equal to the energy gap.
$$E_g=hf=\frac{hc}{\lambda}$$
$$\lambda = \frac{hc}{E_g}$$
$$=\frac{(6.63\times10^{-34}J \cdot s)(3.00\times10^8m/s)}{(1.60\times10^{-19}J/eV)(1.12eV)}$$
$$=1.11\times10^{-6}m $$