What are the energy gaps of semiconductors used in CD, DVD, and Blu-ray lasers?

[pka]

The lasers used to "read" CDs, DVDs, and Blu-ray discs operate at 780 nm, 650 nm, and 405 nm, respectively. These are produced through semiconductors. Find the energy gap needed for each laser. (Blue-ray discs can have higher information density because of the shorter wavelength).

Ok. I don't know how to even begin to solve this problem. So I was wondering if anyone could point me in the right direction. I know that for a semiconductor the fermi energy is in the energy gap (midway between the conduction band and the valence band. With that said...I could try to find the fermi energy and multiply by two in order to find the value of the energy gap? I wouldn't know how to find the energy gap without knowing what the electron density is...and a few other variables. So, what is confusing me in this problem is the fact that there seems to be too many variables in order to solve this problem. If anyone could offer any help, I would greatly appreciate it! Many thanks in advance.

 

[Kurdt]

For this problem all you need to do is find the energy of the peak wavelength photons.