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
To determine which material, GaN or GaAs, will work best for coating the glass panels of the sky roof, we need to analyze their band gaps and compare them to the wavelengths associated with different colors in the visible spectrum.
Band gap is the energy difference between the valence band and conduction band in a material. If the energy of a photon (light) is higher than the band gap, it can be absorbed by the material. In this case, we want to screen out ultraviolet radiation (wavelengths of 10-400 nm), while avoiding any color distortion in the visible spectrum.
Let's compare the band gaps of GaN and GaAs:
- GaN has a band gap, Eg, of 3.2 eV.
- GaAs has a band gap, Eg, of 1.34 eV.
To convert electron volts (eV) into wavelengths (nm), we can use the following relationship, known as the energy-wavelength equation:
λ (nm) = 1240 / E (eV)
Applying this equation to both materials:
- For GaN: λ = 1240 / 3.2 ≈ 387.5 nm
- For GaAs: λ = 1240 / 1.34 ≈ 925.4 nm
Now, let's compare these wavelengths to the 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
From the calculations, we can see that GaN has a wavelength of approximately 387.5 nm, which is within the ultraviolet range we want to screen out. Therefore, GaN would be effective in blocking ultraviolet radiation but may cause some color distortion in the visible spectrum.
On the other hand, GaAs has a wavelength of approximately 925.4 nm, which is much larger than the visible spectrum wavelengths. Therefore, GaAs is unlikely to cause any color distortion in the visible spectrum.
Based on this analysis, GaAs would be the better choice for coating the glass panels of the sky roof since it can effectively block ultraviolet radiation without causing color distortion in the visible spectrum.