The glass panels of a sky roof need to be coated in order to screen out ultraviolet radiation (10-400 nm wavelength) but without color distortion in the visible spectrum. Candidate coating materials are gallium nitride (GaN) with a band gap,Eg, of 3.2 eV, or gallium arsenide (GaAs) with a band gap, Eg, of 1.34 eV. Choose the best explanation for which of these materials, if either, will work.

DATA: representative wavelengths associated with different colors in the visible spectrum:
violet 425 nm
blue 475 nm
green 535 nm
yellow 590 nm
orange 610 nm
red 700 nm

GaAs is the best choice, it has a band gap low enough to block out UV radiation while allowing visible light to pass.

GaN is the best choice, it has a band gap low enough to block out UV radiation while allowing visible light to pass.

Neither will work, due to the electromagnetic spectrum any material that blocks out UV radiation will also block out visible light, this is why sunscreen and sunglasses tend to be somewhat opaque.

Neither will work, UV light will be able to pass through both of them if visible light is able to pass through as well.

Neither will work, visible light has energy greater than 3 eV and the semiconductors will be opaque.

Both will work, visible light has energy lower than 1 eV and is able to pass through both materials unaltered.

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To determine which material, if either, will work for coating the glass panels of a sky roof, we need to consider the band gap of each material and compare it to the wavelengths of UV radiation and visible light.

The band gap is the energy difference between the valence band and the conduction band in a material. If the band gap is smaller than the energy of the incoming photons, the material will absorb the photons and become opaque to that particular energy of light.

In this case, GaN has a band gap, Eg, of 3.2 eV and GaAs has a band gap, Eg, of 1.34 eV. The energy of a photon can be calculated using the equation E = hc/λ, where E is the energy, h is Planck's constant, c is the speed of light, and λ is the wavelength.

The UV radiation range mentioned is 10-400 nm. Using the equation E = hc/λ, the energy range of UV radiation is approximately 3.1-124 eV.

Comparing the band gaps of GaN and GaAs to the energy range of UV radiation, we can see that both materials' band gaps are larger than the energy of UV radiation. Therefore, neither material will absorb UV radiation effectively.

Next, let's consider the visible spectrum. Given representative wavelengths associated with different colors, we can calculate the corresponding energies using the equation E = hc/λ.

For the visible spectrum, the energy range is approximately 1.6-2.9 eV, which is below the band gaps of both GaN and GaAs. This means that both materials will allow visible light to pass through without significant absorption or color distortion.

Based on this analysis, neither GaN nor GaAs will effectively block out UV radiation while allowing visible light to pass. The statement that says "Neither will work, due to the electromagnetic spectrum any material that blocks out UV radiation will also block out visible light, this is why sunscreen and sunglasses tend to be somewhat opaque" is the correct explanation.

Therefore, other coating materials or combinations of materials would need to be considered to achieve the desired result of blocking UV radiation without color distortion in the visible spectrum.