Explanation

(a)
$N_{2}$ molecule has 14 electrons. The molecular orbital electronic configuration of the molecule is as
$N_{2}:KK\ (\sigma 2s)^{2}\left( \ _{\sigma}^{*}2s \right)^{2}\left( \pi 2p_{x} \right)^{2}$
$= \left( \pi 2p_{y} \right)^{2}\left( \pi 2p_{z} \right)^{2}$
$N_{2}^{-}$ ion is formed when $N_{2}$ accept an electron hence it has15 electrons. The molecular orbital electronic configuration of the molecule is as
$N_{2}^{-}:KK\ (\sigma 2s)^{2}\left( \ _{\sigma}^{*}2s \right)^{2}\left( \pi 2p_{x} \right)^{2}\left( \pi 2p_{y} \right)^{2}$
$\left( \sigma 2p_{z} \right)^{2}\left( \ _{\pi}^{*}2p_{x} \right)^{1}$
Hence, this electron goes to antibonding $\pi$ molecular orbital.