Understanding N-Atom Levels & Band Filling in C2

[roeb]

This first one is ok and I understand it:

1) Say that n =2 and l = 0. How many 'levels' does it have for N atoms?

Ans: So I can easily draw a line for 1s and 2s and say that there will be 2N levels. But I am having problems with some more complex situations.

But:
2) Say n = 2. How many levels does it have for N atoms?

Ans: According to my book it's 8N.
So for 1s and 2s there are 2N levels.
For 2p there are 3N levels.
Which would make me think 5N...

I'm not really sure why this is. Is it because there is a loss of the m-degeneracy? (Why would that occur?) Or is there something else? (2s-2p coupling?)------------------------------------------------------------
A second related question is again on the 'levels' of a C₂ atom.1) Say we have many C₂ atoms (N units). How are the bands filled?

My professor uses a nonstandard labeling system - (2pb = 2p pi (bonding) and 2pan = 2p pi* (antibonding))
This picture is from my notes and it shows a single C2 atom (without the electrons drawn in)
http://img367.imageshack.us/img367/5725/bandtheoryuj3.th.png

My question is: Why are there 3 2pb levels? The only reason I can think of is if the m-degeneracy goes away, but why would it go away? I know that when wavefunctions overlap they cause splitting. So it this just because of the wavefuction overlap?
If anything I would think 2pzb would be a separate level and 2pxb / 2pyb would be on the same level (2N)

I realize that m_l = -1, 0, 1 when l = 2 (p orbital) but since we are dealing with antibonding and bonding, I still would think 2N and not 3N...

 

[BigJDubs]

Ans: The 3 2pb levels are created due to the wavefunction overlap between the two C2 atoms. The bonding and antibonding orbitals have different energies, so this causes a splitting of the energy levels into bonding and antibonding sets. This splitting is known as the "Ligand Field Splitting". The ml degeneracy is kept intact within each set, but the higher energy antibonding orbitals are slightly shifted away from the lower energy bonding orbitals. Thus, the three 2pb levels you see in your diagram.