Among the following, the molecule expected to be stabilized by anion formation is: C 2 ,   O 2 ,  …

According to molecular orbital theory the configuration is like that
${\mathrm{C}}_2\Rightarrow \mathrm{\sigma }1{\mathrm{s}}^2<{\mathrm{\sigma }}^{\mathrm{*}}1\mathrm{s}<\mathrm{\sigma }2\mathrm{s}<{\mathrm{\sigma }}^{\mathrm{*}}2\mathrm{s}\mathrm{ }$ $\mathrm{\pi }2{\mathrm{P}}_{\mathrm{x}}^2=\mathrm{\pi }2{\mathrm{P}}_{\mathrm{y}}^2<\mathrm{ }\mathrm{\sigma }2{\mathrm{P}}_{\mathrm{z}}^0\mathrm{ }\left(\mathrm{B}\mathrm{M}\mathrm{O}\right)$

$\mathrm{B}\mathrm{O}=\frac{8-4}{2}=2$
${\mathrm{C}}_2^{-}=\mathrm{\sigma }1{\mathrm{s}}^2<{\mathrm{\sigma }}^{\mathrm{*}}1{\mathrm{s}}^2<\mathrm{\sigma }2{\mathrm{s}}^2<{\mathrm{\sigma }}^{\mathrm{*}}2{\mathrm{s}}^2<\mathrm{\pi }2{\mathrm{p}}_{\mathrm{x}}^2=\mathrm{\pi }2{\mathrm{p}}_{\mathrm{y}}^2<2{\mathrm{p}}_{\mathrm{z}}^1=\frac{9-4}{2}=2.5$
${\mathrm{C}}_2\to {\mathrm{C}}_2^{-}$ bond order increases so it is more favourable.
For $\mathrm{ }{\mathrm{F}}_2,\mathrm{ }{\mathrm{O}}_2\mathrm{ }\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{ }\mathrm{N}\mathrm{O}$
${\mathrm{F}}_2=\mathrm{\sigma }1{\mathrm{s}}^2<{\mathrm{\sigma }}^{\mathrm{*}}1{\mathrm{s}}^2<\mathrm{\sigma }2{\mathrm{s}}^2<{\mathrm{\sigma }}^{\mathrm{*}}2{\mathrm{s}}^2<\mathrm{\sigma }2{\mathrm{P}}_{\mathrm{z}}^2<\mathrm{\pi }2{\mathrm{P}}_{\mathrm{x}}^2=\mathrm{\pi }2{\mathrm{P}}_{\mathrm{y}}^2<{\mathrm{\pi }}^{\mathrm{*}}2{\mathrm{P}}_{\mathrm{x}}^2=\mathrm{ }{\mathrm{\pi }}^{\mathrm{*}}2{\mathrm{P}}_{\mathrm{y}}^2<\mathrm{\sigma }\mathrm{*}2{\mathrm{P}}_{\mathrm{z}}$ $\mathrm{B}\mathrm{O}=\frac{10-8}{2}=1$
${\mathrm{F}}_2^{-}=\mathrm{\sigma }1{\mathrm{s}}^2<{\mathrm{\sigma }}^{\mathrm{*}}1{\mathrm{s}}^2<\mathrm{\sigma }2{\mathrm{s}}^2<{\mathrm{\sigma }}^{\mathrm{*}}2{\mathrm{s}}^2<\mathrm{\sigma }2{\mathrm{P}}_{\mathrm{z}}^2<\mathrm{\pi }2{\mathrm{P}}_{\mathrm{x}}^2=\mathrm{\pi }2{\mathrm{P}}_{\mathrm{y}}^2<{\mathrm{\pi }}^{\mathrm{*}}2{\mathrm{P}}_{\mathrm{x}}^2=\mathrm{ }{\mathrm{\pi }}^{\mathrm{*}}2{\mathrm{P}}_{\mathrm{y}}^2<\mathrm{\sigma }\mathrm{*}2{\mathrm{P}}_{\mathrm{z}}^1$ $\mathrm{B}\mathrm{O}=\frac{10-9}{2}=0.5$
Bond order decreases ${\mathrm{F}}_2\to {\mathrm{F}}_2^{-}$ so not favourable.
${\mathrm{O}}_2=\mathrm{\sigma }1{\mathrm{s}}^2<{\mathrm{\sigma }}^{\mathrm{*}}1{\mathrm{s}}^2<\mathrm{\sigma }2{\mathrm{s}}^2<{\mathrm{\sigma }}^{\mathrm{*}}2{\mathrm{s}}^2<\mathrm{\sigma }2{\mathrm{P}}_{\mathrm{z}}^2<\mathrm{\pi }2{\mathrm{P}}_{\mathrm{y}}^2=\mathrm{\pi }2{\mathrm{P}}_{\mathrm{x}}^2<{\mathrm{\pi }}^{\mathrm{*}}2{\mathrm{P}}_{\mathrm{y}}^1=\mathrm{ }{\mathrm{\pi }}^{\mathrm{*}}2{\mathrm{P}}_{\mathrm{z}}^1$
$\mathrm{B}\mathrm{O}=\frac{10-6}{2}=2$
${\mathrm{O}}_2^{-}=\mathrm{\sigma }1{\mathrm{s}}^2<{\mathrm{\sigma }}^{\mathrm{*}}1{\mathrm{s}}^2<\mathrm{\sigma }2{\mathrm{s}}^2<{\mathrm{\sigma }}^{\mathrm{*}}2{\mathrm{s}}^2<\mathrm{\sigma }2{\mathrm{P}}_{\mathrm{z}}^2<\mathrm{\pi }2{\mathrm{P}}_{\mathrm{y}}^2=\mathrm{\pi }2{\mathrm{P}}_{\mathrm{x}}^2<{\mathrm{\pi }}^{\mathrm{*}}2{\mathrm{P}}_{\mathrm{y}}^2=\mathrm{ }\mathrm{\pi }2{\mathrm{P}}_{\mathrm{z}}^1$
$\mathrm{B}\mathrm{O}=\frac{10-7}{2}=1.5$
Bond order decreases ${\mathrm{O}}_2\to {\mathrm{O}}_2^{-}$ so not favourable
$\mathrm{N}\mathrm{O}=\mathrm{\sigma }1{\mathrm{s}}^2<{\mathrm{\sigma }}^{\mathrm{*}}1{\mathrm{s}}^2<\mathrm{\sigma }2{\mathrm{s}}^2<{\mathrm{\sigma }}^{\mathrm{*}}2{\mathrm{s}}^2<\mathrm{\sigma }2{\mathrm{P}}_{\mathrm{z}}^2<\mathrm{\pi }2{\mathrm{P}}_{\mathrm{x}}^2=\mathrm{\pi }2{\mathrm{P}}_{\mathrm{y}}^2<{\mathrm{\pi }}^{\mathrm{*}}2{\mathrm{P}}_{\mathrm{x}}^1=\mathrm{ }{\mathrm{\pi }}^{\mathrm{*}}2{\mathrm{P}}_{\mathrm{y}}^0$
$\mathrm{B}\mathrm{O}=\frac{10-5}{2}=2.5$
$\mathrm{N}{\mathrm{O}}^{-}=\mathrm{\sigma }1{\mathrm{s}}^2<{\mathrm{\sigma }}^{\mathrm{*}}1{\mathrm{s}}^2<\mathrm{\sigma }2{\mathrm{s}}^2<{\mathrm{\sigma }}^{\mathrm{*}}2{\mathrm{s}}^2<\mathrm{\sigma }2{\mathrm{P}}_{\mathrm{z}}^2<\mathrm{\pi }2{\mathrm{P}}_{\mathrm{x}}^2=\mathrm{\pi }2{\mathrm{P}}_{\mathrm{y}}^2<{\mathrm{\pi }}^{\mathrm{*}}2{\mathrm{P}}_{\mathrm{x}}^1=\mathrm{ }{\mathrm{\pi }}^{\mathrm{*}}2{\mathrm{P}}_{\mathrm{y}}^1$
$\mathrm{B}\mathrm{O}=\frac{10-6}{2}=2$
BO $\mathrm{N}\mathrm{O}\to \mathrm{N}{\mathrm{O}}^{-}$ decreases so not favourable

In case of only ${\mathrm{C}}_2,$ incoming electron will enter the boding molecular orbital which increases the bond order and stability.

Whereas rest of all takes incoming electron in their antibonding molecular orbital which decreased stability.