# Calculating the number of quantum states in the valence and conduction bands

• Engineering

## Homework Statement:

Calculate the number of quantum states per cm cube in GaP in the valence and conduction band, given that the mass density is 4.13g/cm^3

## Relevant Equations:

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Hi all,
This question asks me to calculate the number of quantum states, as well as electrons per cm^3 of the crystal in the room temperature.
The problem is I only dealt with a single element before without any calculation for 1cm^3 whatsoever. For example for a Silicon semiconductor, I can determine that a-Si atom share four valence electrons (2 from its 3s and 2 from 3p states) to form a stable configuration, hence only the 3s and 3p states are involved, whereby the number of states, in this case, is 8N (2+6) from the 3s and 3p state, whereby the upper band contains 4N states and lower band aka the valence band contain 4N states.

So in the question I presented, I will need to calculate the number of atoms/cm^3 to find what is N first. Hence, first, amt of GaP = mass/Mr. Hence in 1cm^3, I can find that the amount = 4.13/(69.72+30.974) = 0.0410 mol = 2.469*10^22 atoms. So N = 2.469*10^22

Now here comes the problem, how many N states are there? Since now there are 2 elements, how do I combine them together to form a lattice if GaP does not have any spare valence electrons to bond with other GaP atoms to form the crystal lattice? How can I find what are the states involved in GaP for bonding with other GaP atoms?

Thanks