Answer
See answers.
Work Step by Step
a. For the silicon to be transparent, the photon’s energy must be less than 1.12 eV. In other words, the photon’s wavelength is longer than the wavelength corresponding to a 1.12 eV photon.
$$\lambda=\frac{c}{f}=\frac{hc}{hf}=\frac{hc}{\Delta E}$$
$$=\frac{1240 eV \cdot nm}{1.12 eV}=1110nm$$
The minimum wavelength is in the infrared region of the spectrum. The silicon is opaque to visible light.
b. The minimum possible band gap value for glass, given that it is transparent to light, is the wavelength of the most energetic visible photon. That photon has the shortest wavelength, which we take to be 400 nm.
$$E_{band\;gap}\gt E_{min}$$
$$ E_{min}=\frac{hc}{\lambda_{min}}$$
$$=\frac{1240 eV \cdot nm}{400nm}=3.1\;eV$$
