Answer
See explanation.
Work Step by Step
a. The minimum photon energy, which corresponds to maximum wavelength, is the energy gap, 5.47 eV.
$$E= hf=h\frac{c}{\lambda} $$
$$\lambda =\frac{hc}{E}=\frac{1.24\times10^{-6}eV\cdot m}{5.47eV}=227nm$$
This lies in the ultraviolet.
b. Visible light photons do not have enough energy to excite any electrons into the conduction band, so no visible light photons are absorbed.
c. Impurity atoms can cause new energy levels to appear within the gap, which lowers the gap energy. This makes it easier for the material to absorb some longer-wavelength visible light photons, giving the diamond color.
