The number of paramagnetic species among the following is B _ 2 ,...

The species that contain unpaired electrons are paramagnetic.

Electronic configuration of ${Li}_{2}$ molecule is ${\left(\sigma1s\right)}^{2}{\left({\sigma}^{*}1s\right)}^{2}{\left(\sigma2s\right)}^{2}$.

The electronic configuration of ${B}_{2}$ molecule is

${\left(\sigma1s\right)}^{2}{\left({\sigma}^{⋆}1s\right)}^{2}{\left(\sigma2s\right)}^{2}{\left({\sigma}^{⋆}2s\right)}^{2}\left(\pi2{{p}_{x}}^{1} = \pi2{{p}_{y}}^{1}\right)$

The presence of unpaired electrons in the two $\pi$ bonding molecular orbitals explains its paramagnetic nature.

The electronic configuration of ${C}_{2}$ $KK\sigma2{s}^{2}{\sigma}^{*}2{s}^{2}\pi2{p}_{x}^{2}\pi2{p}_{y}^{2}$

${O}_{2}: KK{\left({\sigma}_{2s}\right)}^{2}{\left({\sigma}_{2s}\right)}^{2}{\left({\sigma}_{2{p}_{z}}\right)}^{2}{\left({\pi}_{2{p}_{x}}\right)}^{2} = {\left({\pi}_{2{p}_{y}}\right)}^{2}{\left(\pi{*}_{2{p}_{x}}\right)}^{1} = {\left(\pi{*}_{2{p}_{y}}\right)}^{1}$

Hence, ${O}_{2}$ molecule is paramagnetic.

The electronic configuration of ${C}_{2}^{-}$ is ${\left(\sigma1s\right)}^{2}{\left({\sigma}^{⋆}1s\right)}^{2}{\left(\sigma2s\right)}^{2}{\left({\sigma}^{⋆}2s\right)}^{2}\left(\pi2{{p}_{x}}^{2} = \pi2{{p}_{y}}^{2}\right)\sigma2{{p}_{z}}^{1}$

Hence, it is paramagnetic substance.

${O}_{2}^{2 -}: KK{\left({\sigma}_{2s}\right)}^{2}{\left({\sigma}_{2s}\right)}^{2}{\left({\sigma}_{2{p}_{z}}\right)}^{2}{\left({\pi}_{2{p}_{x}}\right)}^{2} = {\left({\pi}_{2{p}_{y}}\right)}^{2}{\left(\pi{*}_{2{p}_{x}}\right)}^{2} = {\left(\pi{*}_{2{p}_{y}}\right)}^{2}$

${O}_{2}^{+}: KK{\left({\sigma}_{2s}\right)}^{2}{\left({\sigma}_{2s}\right)}^{2}{\left({\sigma}_{2{p}_{z}}\right)}^{2}{\left({\pi}_{2{p}_{x}}\right)}^{2} = {\left({\pi}_{2{p}_{y}}\right)}^{2}{\left(\pi{*}_{2{p}_{x}}\right)}^{1} = \left(\pi{*}_{2{p}_{y}}\right)$

Hence, the above species is paramagnetic.