Answer
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Work Step by Step
The proposal is to use silicon to filter out visible light wavelengths. In other words, visible light wavelengths, shorter than those in the infrared region, should cause an electron to jump from the valence band to the conduction band. This means the photon is absorbed, and doesn’t make it through the silicon window.
As requested, find the shortest wavelength that can cause an electron to jump.
$$\lambda=\frac{c}{f}=\frac{hc}{hf}\gt\frac{hc}{E_{gap}}$$
$$=\frac{(6.626\times10^{-34}J \cdot s)(3.00\times10^8m/s)}{(1.60\times10^{-19}J/eV)(1.12eV)}=1.11\times10^{-6}m$$
This is in the infrared region of the spectrum, and visible light has wavelengths shorter than this. Photons of visible light will excite an electron in silicon, and be absorbed.
Yes, silicon can be used as a window to filter out visible light, but let through IR radiation.
