Bond order in ${\mathrm{O}}_2$ is ‘X’. Bond order in ${\mathrm{O}}_2^{-}$ is ‘Y’. Difference between X and Y is

${\mathrm{O}}_2^{-2}-{\mathrm{KK}}^{\text{'}}{\left({\mathrm{\sigma }}_{2\mathrm{s}}\right)}^2{\left({\mathrm{\sigma }}_{2\mathrm{s}}^{*}\right)}^2{\left({{\mathrm{\sigma }}_{2\mathrm{p}}}_{\mathrm{z}}\right)}^2{\left({\mathrm{\pi }}_{2{\mathrm{p}}_{\mathrm{x}}}\right)}^2{\left({\mathrm{\pi }}_{2{\mathrm{p}}_{\mathrm{y}}}\right)}^2{\left({\mathrm{\pi }}_{2{\mathrm{p}}_{\mathrm{x}}}^{*}\right)}^2{\left({\mathrm{\pi }}_{2{\mathrm{p}}_{\mathrm{y}}}^{*}\right)}^2$

${\mathrm{O}}_2^{-}-{\mathrm{KK}}^{\text{'}}{\left({\mathrm{\sigma }}_{2\mathrm{s}}\right)}^2{\left(\mathrm{\sigma }\stackrel{*}{{ }_{2\mathrm{s}}}\right)}^2{\left({{\mathrm{\sigma }}_{2\mathrm{p}}}_{\mathrm{z}}\right)}^2{\left({\mathrm{\pi }}_{2{\mathrm{p}}_{\mathrm{y}}}\right)}^2{\left({\mathrm{\pi }}_{2{\mathrm{p}}_{\mathrm{y}}}\right)}^2{\left({\mathrm{\pi }}_{2{\mathrm{p}}_{\mathrm{x}}}^{*}\right)}^2{\left({\mathrm{\pi }}_{2{\mathrm{p}}_{\mathrm{y}}}^{*}\right)}^1$

${\mathrm{O}}_2^{ }-{\mathrm{KK}}^{\text{'}}{\left({\mathrm{\sigma }}_{2\mathrm{s}}\right)}^2{\left({\mathrm{\sigma }}_{2\mathrm{s}}^{*}\right)}^2{\left({{\mathrm{\sigma }}_{2\mathrm{p}}}_{\mathrm{z}}\right)}^2{\left({\mathrm{\pi }}_{2{\mathrm{p}}_{\mathrm{x}}}\right)}^2{\left({\mathrm{\pi }}_{2{\mathrm{p}}_{\mathrm{y}}}\right)}^2{\left({\mathrm{\pi }}_{2{\mathrm{p}}_{\mathrm{x}}}^{*}\right)}^1{\left({\mathrm{\pi }}_{2{\mathrm{p}}_{\mathrm{y}}}^{*}\right)}^1$

${\mathrm{O}}_2^{+}-{\mathrm{KK}}^{\text{'}}{\left({\mathrm{\sigma }}_{2\mathrm{s}}\right)}^2{\left({\mathrm{\sigma }}_{2\mathrm{s}}^{*}\right)}^2{\left({\mathrm{\sigma }}_{2{\mathrm{p}}_{\mathrm{z}}}\right)}^2{\left({\mathrm{\pi }}_{2{\mathrm{p}}_{\mathrm{x}}}\right)}^2{\left({\mathrm{\pi }}_{2{\mathrm{p}}_{\mathrm{y}}}\right)}^2{\left({\mathrm{\pi }}_{2{\mathrm{p}}_{\mathrm{x}}}^{*}\right)}^1{\left({\mathrm{\pi }}_{2{\mathrm{p}}_{\mathrm{y}}}^{*}\right)}^0$

Bond order and magnetic moment :

$$\begin{gathered} {\mathrm{\mu }}_{\mathrm{s}}=\sqrt{\mathrm{n}\left(\mathrm{n}+2\right)} \mathrm{B}. \mathrm{M} ; \\ {\mathrm{O}}_2^{-2}=\frac{10-8}{2}=1; \mathrm{Diamagnetic}...{\mathrm{\mu }}_{\mathrm{s}}=0 ; \\ {\mathrm{O}}_2^{-}=\frac{10-7}{2}=1.5; \mathrm{Paramagnetic}..{\mathrm{\mu }}_{\mathrm{s}}=1.732 \mathrm{B}.\mathrm{M} ; \\ {\mathrm{O}}_2=\frac{10-6}{2}=2; \mathrm{Paramagnetic}.......{\mathrm{\mu }}_{\mathrm{s}}=2.82 \mathrm{B}.\mathrm{M} ; \\ {\mathrm{O}}_2^{+}=\frac{10-5}{2}=2.5; \mathrm{Paramagnetic}.....{\mathrm{\mu }}_{\mathrm{s}}=1.732\mathrm{B}.\mathrm{M} ; \end{gathered}$$

O $—$ O bond length in

${\mathrm{O}}_2^{-2}>{\mathrm{O}}_2^{-}>{\mathrm{O}}_2>{\mathrm{O}}_2^{+}$