Which of the following facts regarding change in bond length is correct?

Bond order$=\frac{\mathrm{No}. \mathrm{of} \mathrm{electrons} \mathrm{in} \mathrm{B}.\mathrm{M}.\mathrm{O}-\mathrm{No}. \mathrm{of} \mathrm{electrons} \mathrm{in} \mathrm{A}.\mathrm{B}.\mathrm{M}.\mathrm{O}}{2}$

$$\begin{gathered} \mathrm{Bond} \mathrm{order}=\frac{1}{2}\left({\mathrm{N}}_{\mathrm{B}}-{\mathrm{N}}_{\mathrm{AB}}\right) \\ 1. {\mathrm{N}}_2: \\ \mathrm{valence} \mathrm{electrons}=5+5=10 \end{gathered}$$

(σ2s)²(σ^∗2s)²(σ2p)²(π2p)⁴

BO=1/2×(6−0)=3

$$\begin{gathered} 2.{\mathrm{N}}_2^{+}: \\ \mathrm{valence} \mathrm{electrons}=5+5-1=9 \end{gathered}$$

(σ2s)²(σ^∗2s)²(σ2p)²(π2p)³

BO=1/2×(5−0)=2.5

$$\begin{gathered} 3.{\mathrm{O}}_2: \\ \mathrm{valence} \mathrm{electrons}=6+6=12 \end{gathered}$$

(σ2s)²σ*(2s)²(σ2p)²(π2p)⁴(π^∗2p)²

BO=1/2×(6−2)=2

$$\begin{gathered} 4.{\mathrm{O}}_2^{+}: \\ \mathrm{valence} \mathrm{electrons}=6+6-1=11 \end{gathered}$$

(σ2s)²(σ*2s)²(σ2p)²(π2p)⁴(π^∗2p)¹

BO=1/2×(6−1)=2.5

Since, bond length ∝$\frac{1}{\mathrm{bond} \mathrm{order}}$​

Order of bond length is: ${\mathrm{N}}_2<{\mathrm{N}}_2^{+} \mathrm{and} {\mathrm{O}}_2>{\mathrm{O}}_2^{+}$