Compare the bond length, bond energy of CN and CN ^- species.

We will calculate the bond length, bond energy of CN and CN ^- species with the help of molecular orbital theory.
Hence we first need the electronic configuration of the given species.
For CN:

CN has 13 electrons and its electronic configuration will be:
CN: KK σ (2s)² σ^*(2s)²π (2py)²σ (2pz)¹

As, Bond order = [number of bonding electrons – number of anti-bonding electrons]/ 2

Hence, Bond order = 1/2(7–2) =2.5

For CN^-, the one electron is added to the σ(2pz) ¹

Molecular orbital so its electronic configuration will be:

CN^-: KKσ(2s)²σ^*(2s)²π(2py)²σ (2pz)²

Hence, Bond order = 1/2 (8–2) = 3

From above it is concluded that CN^- has higher bond order. We know that higher bond order larger will be the bond energy and smaller will be the bond length. Hence CN^- has higher bond order larger will be the bond energy and smaller will be the bond length than CN.