Explanation

(a)
In $O_{2}$ molecule, the total number of electrons = 16
Electronic distribution in molecular orbital of
$O_{2} =$ $\sigma 1s^{2},\ _{\sigma}^{*}1s^{2}\ ,\sigma 2s^{2},\ _{\sigma}^{*}2s^{2}\ ,\ \sigma 2p_{x}^{2}\ \left( \pi 2p_{y}^{2},\pi 2p_{z}^{2} \right)$
$,{(\ }_{\pi}^{*}2p_{y}^{1},\ _{\pi}^{*}2p_{z}^{1})$
Bond order in $O_{2}$ $= \frac{1}{2}\lbrack N_{b - \ }N_{a\ }\rbrack = \frac{1}{2}\lbrack 10 - 6\rbrack = 2.0$
In $O_{2}^{+}\$=$\ \sigma 1s^{2},\ _{\sigma}^{*}1s^{2}\ ,\sigma 2s^{2},\ _{\sigma}^{*}2s^{2}\ ,\ \sigma 2p_{x}^{2}$
$\ \left( \pi 2p_{y}^{2} = \pi 2p_{z}^{2} \right),{(\ }_{\pi}^{*}2p_{y}^{1})$
Bond order in $O_{2}^{+}\$ $= \frac{N_{b - \ }N_{a\ }}{2} = \frac{10 - 5}{2} = 2.5$