Among the following, the species with one unpaired electron are:

(i) ${\mathrm{O}}_2^{+}$ and NO will have the same electrical structure since they both have the same number of electrons. Total: e = 15.

configuration:

$\begin{array}{r}{\sigma }_{1\mathrm{s}}^2,{\sigma }_{1\mathrm{s}}^{\ast 2},{\sigma }_{2\mathrm{s}}^2{\sigma }_{2\mathrm{s}}^{\ast 2},{\sigma }_{2{\mathrm{p}}_{\mathrm{z}}}^2,\left({{\mathrm{\Pi }}_{2{\mathrm{p}}_{\mathrm{s}}}}^2{{\mathrm{\Pi }}_{2{\mathrm{py}}^2}}^2\right),\left({{\mathrm{\Pi }}_{2{\mathrm{p}}_{\mathrm{s}}}}^{\ast 1}{{\mathrm{\Pi }}_{2{\mathrm{p}}_{\mathrm{y}}}}^{\ast }\right)\\ \therefore {\mathrm{O}}_2^{+}\mathrm{\&}\mathrm{NO}\end{array}$

contain 1 unpaired electron.     

(ii) ${\mathrm{O}}_2^{-}$ different e configurations are available for $17{\mathrm{e}}^{-}$

${\sigma }_{1\mathrm{s}}^2,{\sigma }_{1\mathrm{s}}^{\ast 2},{\sigma }_{2\mathrm{s}}^2,{\sigma }_{2\mathrm{s}}^{\ast 2},{\sigma }_{2{\mathrm{p}}_{\mathrm{z}}}^2,\left({{\mathrm{\Pi }}_{2{\mathrm{p}}_{\mathrm{a}}}}^2{\mathrm{\Pi }}_{2\mathrm{py}}^2\right),\left({\mathrm{\Pi }}_{2{\mathrm{p}}_{\mathrm{x}}}^{\ast 2}{\mathrm{\Pi }}_{2{\mathrm{p}}_{\mathrm{y}}}^{\ast 1}\right)$

$\therefore {\mathrm{O}}_2^{-}$contains 1 unpaired electron

(iii) Since 2 has an even number of electrons, it cannot have a single unpaired electron. Either there won't be any unpaired electrons or there will be two but only one unpaired electron is possible.