(a) In $\mathrm{O}_{2}^{-}$total number of electrons
$$
=16+1=17
$$
$\therefore$ Orbital arrangement
$$
\begin{aligned}
=K K^{\prime}, \sigma 2 s^{2}, \sigma 2 s^{2}, \sigma 2 p_{z}^{2}, \pi 2 p_{x}^{2}=\pi 2 p_{y}^{2}, \\
\pi 2 p_{x}^{2} &=\pi 2 p_{y}^{1}
\end{aligned}
$$
(b) In $\mathrm{O}_{2}^{+}$, total number of electrons
$$
=16-1=15
$$
$\therefore$ Orbital arrangement $=\mathrm{KK}^{\prime}, \sigma 2 \mathrm{~s}^{2}, \sigma 2 \mathrm{~s}^{2}$,
$$
\sigma 2 \mathrm{p}_{\mathrm{z}}^{2}, \pi 2 \mathrm{p}_{\mathrm{x}}^{2}=\pi 2 \mathrm{p}_{\mathrm{y}}^{2}, \stackrel{\approx}{\pi} 2 \mathrm{p}_{\mathrm{x}}^{1}
$$
(c) In $\mathrm{O}_{2}^{2-}$, total number of electrons
$$
=16+2=18
$$
$\therefore$ Orbital arrangement $=K_{K}^{\prime}, \sigma 2 \mathrm{~s}^{2}, \sigma 2 \mathrm{~s}^{2}$, $\sigma 2 \mathrm{p}_{\mathrm{z}}^{2}, \pi 2 \mathrm{p}_{\mathrm{x}}^{2}=\pi 2 \mathrm{p}_{\mathrm{y}}^{2} \pi 2 \mathrm{p}_{\mathrm{x}}^{2}=\pi 2 \mathrm{p}_{\mathrm{y}}^{2}$
(d) In $\mathrm{O}_{2}$, total number of electrons $=16$
$\therefore$ Orbital arrangement $=K K K^{\prime}, \sigma 2 s^{2}, \sigma^{*} 2 s^{2}$,
$\sigma 2 \mathrm{p}_{\mathrm{z}}^{2}, \pi 2 \mathrm{p}_{\mathrm{x}}^{2} \approx \pi 2 \mathrm{p}_{\mathrm{y}}^{2}, \stackrel{\approx}{\pi} 2 \mathrm{p}_{\mathrm{x}}^{1} \approx \pi / 2 \mathrm{p}_{\mathrm{y}}^{1}$
Hence, only $\mathrm{O}_{2}^{2-}$ has no unpaired electrons.