Calculating Material Bandgap Using Quantum Theory

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Quantum theory says that the energy, E , (in eV) of a photon of wavelength λ is E = hc/eλ, where h is Planck's Constant, c is the velocity of light and e is the charge on an electron. Calculate the bandgap of a material which absorbs electrons shorter than 500nm.
 
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What are your thoughts on this?
 
This one's easy. Just plug in all the numbers and you have your bandgap. Then use the values for the next two parts to the question.
 
To solve this, I first used the units to work out that a= m* a/m, i.e. t=z/λ. This would allow you to determine the time duration within an interval section by section and then add this to the previous ones to obtain the age of the respective layer. However, this would require a constant thickness per year for each interval. However, since this is most likely not the case, my next consideration was that the age must be the integral of a 1/λ(z) function, which I cannot model.
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