SOLUTION :
$\mathrm{O}_2: \sigma 1 s^2, \sigma^{\star} 1 s^2, \sigma 2 s^2, \sigma^{\star} 2 s^2, \sigma 2 p_z^2\left\{\begin{array}{l}\pi 2 p_y^2 \\ \pi 2 p_x^2\end{array}\left\{\begin{array}{l}\pi^{\star} 2 p_y^1 \\ \pi^* 2 p_x^1\end{array}\right.\right.$
Bond order $=\frac{10-6}{2}=2.0$
Two unpaired electrons in antibonding molecular orbital.
$\mathrm{O}_2^{+}: \sigma 1 s^2, \sigma^{\star} 1 s^2, \sigma 2 s^2, \sigma^{\star} 2 s^2, \sigma 2 p_z^2$
${ \pi 2 p _ { y } ^ { 2 } }$
${ \pi 2 \dot { p } _ { x } ^ { 2 } }$
$\pi^{\star} 2 p_y^0$
$\pi^* 2 p_x^1$
Bond order $=\frac{10-5}{2}=2.5$
One unpaired electron in antibonding molecular orbital so it is paramagnetic.
