What is the wavelength of the radiation corresponding to this band gap?

Question

 What is the wavelength of the radiation corresponding to this band gap?

ZnO is a semiconductor whose band gap is 308.71  kJ/mol at room temperature.

1. I think I need to use the equation E(g) = hc/ wavelength, but I've tried every way, and it isn't working.
2. I'm also confused on how to just get joules from kJ/mol

Answer 1

First convert 308.71 kj/mole to J / atom by dividing 308.71kJ by Avogadro’s number and multiplying the result by 1000.

308.71 KJ x 1000 j/Kj / 6.022 x 10^23 atoms/mole = 5.126 x 10^-19 joules/atom.

Now put this into your formula for wavelength after solving for wavelength.

Λ = 6.63 x 10^-34 x 3.0 x 10^8 / 5.126 x 10^-19 = 3.88 x 10^-7 meters.

Change this to nm by dividing by 1.0 x 10^-9 m/nm to get 388 nm.

Check math.