6a)
To check the hybridisation of the C atoms, count the number of atoms the Carbon is attached to.
If it is attached to 4 other atoms , then the hybridisation is sp3. (to remember :1s + 3p = 4 total atoms bonded to Carbon)
Similarly, it is sp2 , then it will be attached to 3 other atoms, and for sp, Carbon will be attached to 2 more atoms.
Alternatively, if a carbon has a triple bond then it will be sp hybridised, if it has a double bond, it is sp2 hybridised, and if it has only single bonds, then it will be sp3 hybridised.
However, if an allene is given : CH2=C=CH2 , then the two terminal carbons are sp2 hybridised (as expected) while the central carbon is sp hybridised.
In the given question :
C1 = sp3
C2 = sp3,
C3 = sp2
C4 = sp
C5 = sp
C6 = sp2
(b)

Bond order = (No. of bonding electrons - No. of antibonding electrons)/2
For calculating this, we can either consider all the electrons, or we can consider only the valence MOs. They both will give same result.
If we consider all electrons : No. of bonding electrons = 4 (from σ1s and 2s) , No. of antibonding electrons = 2 (from σ*1s)
So, bond order = (4-2)/2 = 1
If we consider only valence MO (here, it is σ2s and σ*2s) then bonding electrons = 2(σ2s) and antibonding electrons = 0, which gives bond order = (2-0)/2 = 1
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