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Q.
The correct order of increasing bond lengths of the following species is
I. $C_{2}^{-}$
II. $C_{2}^{2-}$
III. $C_{2}$
Solution:
Total number of electrons in $C_{2}$ molecule is 12
Electronic configuration is $\sigma 1 s^{2} \sigma * 1 s^{2} \sigma 2 s^{2} \sigma * 2 s^{2} \pi 2 p_{x}^{2}=\pi 2 p_{y}^{2}$
Bond order $=\frac{1}{2}(8-4)=2$
Electronic configuration of $C_{2}^{-} \sigma 1 s^{2} \sigma * 1 s^{2} \sigma 2 s^{2} \sigma * 2 s^{2}\left(\pi p_{x}^{2}=\pi 2 p_{y}^{2}\right)$
Bond order $=\frac{1}{2}(9-4)=2.5$
Electronic configuration of $C_{2}^{2-}=\sigma 1 s^{2} \sigma * 1 s^{2} \sigma 2 s^{2} \sigma * 2 s^{2} \pi 2 p_{x}^{2}=\pi 2 p_{y}^{2} \sigma 2 p_{z}^{2}$
Bond order $=\frac{1}{2}(10-4)=3$
Greater the bond order, shorter is the bond length
$\therefore $ Order of band lengths $C_{2}^{2-}