Using MO theory predict which of the following species has the shortest bond length ?

$$\begin{gathered} O_2^{-2}\left(18e^{-}\right):\sigma 1s^2\sigma *1s^2\sigma 2s^2\sigma *2s^2\sigma 2p_x^2\pi 2p_y^2\pi 2p_z^2\pi *2p_y^2\pi *2p_z^2 ; \\ B.O=\frac{10-8}{2}=1 \end{gathered}$$

$O_2^{+2}\left(14e^{-}\right) : \sigma 1s^2\sigma *1s^2\sigma 2s^2\sigma *2s^2\sigma 2p_x^2\pi 2p_y^2\pi 2p_z^2 ; B.O=\frac{10-4}{2}=3$

$$\begin{gathered} O_2^{+}\left(15e^{-}\right) : \sigma 1s^2\sigma *1s^2\sigma 2s^2\sigma *2s^2\sigma 2p_x^2\pi 2p_y^2\pi 2p_z^2\pi *2p_y^1 ; \\ B.O=\frac{10-5}{2}=2.5 \end{gathered}$$

$$\begin{gathered} O_2^{-}\left(17e^{-}\right):\sigma 1s^2\sigma *1s^2\sigma 2s^2\sigma *2s^2\sigma 2p_x^2\pi 2p_y^2\pi 2p_z^2\pi *2p_y^2\pi *2p_z^1 ; \\ B.O=\frac{10-7}{2}=1.5 \end{gathered}$$

$\mathrm{Bond} \mathrm{order}\propto \frac{1}{\mathrm{Bond} \mathrm{length}}$

So, ${\mathrm{O}}_2^{2+}$  has the shortest bond length.