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Q. Among the following molecules / ions, $C _{2}^{2-}, N _{2}^{2-}, O _{2}^{2-}, O _{2}$ which one is diamagnetic and has the shortest bond length?

JEE MainJEE Main 2019Chemical Bonding and Molecular Structure

Solution:

$C_{2}^{2-}{ }^{-\sigma} 1 s^{2 \sigma *} 1 s^{2 \sigma} 2 s^{2 \sigma *} 2 s^{2}\left[{ }^{\pi} 2 p_{x}^{2}\right]^{\sigma} 2 p^{2}$
$B . O=\frac{10-4}{2}=3($ diamagnetic $)$
$N_{2}^{2--\sigma} 1 s^{2 \sigma *} 1 s^{2 \sigma *} 2 s^{2 \sigma} 2 s^{2}\left[\pi 2 p_{x}^{2}={ }^{\pi} 2 p_{y}^{2}\right]\left[{ }^{\pi} 2 p_{x}^{1}={ }^{\pi *} 2 p_{y}^{1}\right]$
$B . O=\frac{10-6}{2} 2($ paramagnetic $)$
$O_{2}^{2-}-\sigma 1 s^{2 \sigma} 1 s^{2 \sigma} 2 s^{2 \sigma} 2 s^{2 \sigma} 2 p_{z}^{2}\left[{ }^{\pi} 2 p_{x}^{2}={ }^{\pi} 2 p_{y}^{2}\right]\left[{ }^{\pi} 2 p_{x}^{2}={ }^{\pi *} 2 p_{y}^{2}\right]$
$B . O=\frac{10-8}{2}=1($ diamagnetic $)$
$O_{2}^{-\sigma} 1 s^{2 \sigma *} 1 s^{2 \sigma} 2 s^{2 \sigma *} 2 s^{2 \sigma} 2 p_{z}^{2}\left[{ }^{\pi} 2 p_{x}^{2}={ }^{\pi} 2 p_{y}^{2}\right]\left[{ }^{\pi} 2 p_{x}^{1}={ }^{\pi *} 2 p_{y}^{1}\right]$
$B . O=\frac{10-6}{2} 2($ paramagnetic $)$