Explanation

(c)
1.($N_{2} \longrightarrow (\sigma 1{s)}^{2}\ {\ (}_{\sigma}^{*}1{s)}^{2}\ (\sigma 2{s)}^{2}(\ _{\sigma}^{*}2{s)}^{2}\ (\sigma 2p_{z})^{2}\ (\pi 2p_{x})^{2}(\pi 2p_{y})^{2}\ \ \$
$N_{2}^{+} \longrightarrow (\sigma 1{s)}^{2}\ {\ (}_{\sigma}^{*}1{s)}^{2}\ (\sigma 2{s)}^{2}(\ _{\sigma}^{*}2{s)}^{2}\ (\sigma 2p_{z})^{2}\ (\pi 2p_{x})^{2}(\pi 2p_{y})^{1}\ \ \$
1.$O_{2} \longrightarrow (\sigma 1{s)}^{2}\ {\ (}_{\sigma}^{*}1{s)}^{2}\ (\sigma 2{s)}^{2}(\ _{\sigma}^{*}2{s)}^{2}\ (\sigma 2p_{z})^{2}\ (\sigma 2p_{x})^{2}(\sigma 2p_{y})^{2}\ \left( \ _{\pi}^{*}\ 2p_{x} \right)^{1}$ $\left( \ _{\pi}^{*}\ 2p_{y} \right)^{1}$
$O_{2}^{+}\ \longrightarrow (\sigma 1{s)}^{2}\ {\ (}_{\sigma}^{*}1{s)}^{2}\ (\sigma 2{s)}^{2}\ (\ _{\sigma}^{*}2{s)}^{2}\ (2p_{z})^{2}\ (\pi 2p_{x})^{2}(\pi 2p_{y})^{2}\ \left( \ _{\pi}^{*}\ 2p_{x} \right)^{1}$ $Since\ ,\ \pi 2p_{x}\ and\ \pi 2p_{y}$ are nearly same in energy, the electrons can be removed from ($\pi 2p_{y}\ or\ \pi 2p_{x}$) and ($\ _{\pi 2p_{y}}^{*}{\ or\ \ }_{\pi 2p_{x}}^{*}$) respectively.