The question is quite confusing because you are asking about the bond order of the N- N bond in the C2 molecule, you see that there is no N-N bond because it is only composed of C and C atoms. The bond order is based on the number of bonds on the atoms, so if there is double bond, so the order is 2. When it is triple bond the order is 3. For N-N alone for N2 molecule, the order is 3.
Bond order= Bonding electrons-antibonding electrons/2
In H2, there are two bonding electrons and no antibonding electrons. In H2+ there is only one bonding electron and no antibonding electron while in H22- there are two bonding and two antibonding electrons respectively.
The bond order for C2 molecule is 2.
Bond order can be defined as the half of the difference between the number of electrons in the bonding orbital and the number of electrons in the antibonding orbitals. It can be represented mathematically by; .
Bond order,n= [number of electrons in the bonding molecular orbitals(BMO) - the number or electrons in the anti-bonding molecular orbitals(AMO) ] / 2.
The electronic configuration of the C2 molecule is given below;
C2 = (1sσ)^2 (1s^*σ)^2 (2sσ)^2 (2s^*σ)^2 (2pπ)^4.
The ones with the (*) are known as the Anti-bonding molecular orbitals while the ones without (*) are known as the bonding molecular orbitals. Hence, we have 8 Electrons from the bonding molecular orbitals and 4 Electrons from the anti-bonding molecular orbitals.
So, from the formula given above, the bond order of C2 molecule is;
===> 8-4/2= 4/2.