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

JEE Main · 2019 · 08 Apr 2019 · Shift 2 · Chemical Bonding and Molecular Structure

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?

Answer: (B)

By molecular orbital theory we look for the species that is both diamagnetic and has the highest bond order.

C X_{2} X^{2 -}

has 14 electrons filling up to

σ_{2 p}^{2}

with every electron paired, so it is diamagnetic, and its bond order is

\frac{10 - 4}{2} = 3

O X_{2} X^{2 -}

(18 electrons) is also diamagnetic, but with the antibonding levels filled its bond order is only 1. Both

N X_{2} X^{2 -}

and

O X_{2}

carry unpaired electrons in the

π^{*}

orbitals, so they are paramagnetic and ruled out. Among the diamagnetic ones the higher bond order means the shorter, tighter bond, so

C X_{2} X^{2 -}

has the shortest bond length.

JEE Main · 2019 · 08 Apr 2019 · Shift 2 · Single correct option