Explanation

(a)
Peroxide ion in $O_{2}^{2 -}$
$O_{2}^{2 -}(18) =$ $\sigma 1s^{2},\ \ _{\sigma}^{*}1s^{2},\ \ _{\sigma}2s^{2},\ \ _{\sigma}^{*}2s^{2},\ \sigma 2p_{z}^{2}$
$\pi 2p_{x}^{2} = \pi 2p_{y}^{2},\ _{\pi}^{*}2p_{x}^{2} = \ _{\pi}^{*}2p_{y}^{2}$
Bond order = $\frac{N_{b} - N_{a}}{2} = \frac{10 - 8}{2}$=1
It contains four completely filled antibonding molecular orbitals. Since, all the electrons are paired, $O_{2}^{2 -}$ is diamagnetic.
Peroxide ion is isoelectronic with argon, not with neon.