Question

Which of the following ion has a greater bond order than its parent molecule
A.\[{C_2}^ + \]
B.\[{O_2}^ + {\text{ }}\]
C.\[{N_2}^ + \]
D.\[{B_2}^ + \]

Answer 1

Hint:To answer this question, you should recall the concept of molecular orbital theory. After a combination of atomic orbitals fill each molecular orbital in order of their energies. Now check whether there is the existence of unpaired or paired electrons.
 The formula used:
 \[\dfrac{{{N_b} - {N_a}}}{2}\] for bond order
 where ${N_b}$ is no. of electrons in bonding atomic orbital and ${N_a}$ is the no. of electrons in an anti-bonding atomic orbital

Complete step by step answer:
The filling of these orbitals takes place in the order of increasing energy and is governed by the following rules:
The molecular orbitals are arranged in the increasing order of their energies. The molecular orbital with the lowest energy is filled first as per the Aufbau principle.
Each molecular orbital can accommodate a maximum of two electrons with opposite spins as per Pauli's exclusion principle.
If there are two or more molecular orbitals of the same energy, these are the first singly filled and then pairing starts as per the Hund's rule.
Let us analyse each of the options systematically:
The bond order of \[{C_2}^ + {\text{ }} = {\text{ }}1/2{\text{ }}\left( {5{\text{ }} - {\text{ }}2} \right){\text{ }} = {\text{ }}3/2{\text{ }} = {\text{ }}1.5\]. While bond order of \[{C_2}\] = 2
The bond order of \[{O_2}^ + {\text{ }} = {\text{ }}(10 - 5)/2 = 5/2 = 2.5\]. While bond order of \[{O_2}\] = 2
The bond order of \[{N_2}^ + {\text{ }} = {\text{ }}1/2{\text{ }}\left( {{\text{7 }} - {\text{ }}2} \right){\text{ }} = 2.5\]. While bond order of \[{N_2}\] = 3
The bond order of \[{B_2}^ + {\text{ }} = {\text{ }}(5 - 4)/2 = 1/2 = 0.5\]. While bond order of \[{B_2}\] = 1
The bond order \[{O_2}^ + {\text{ }} = 2.5\] is greater than the bond order of its parent molecule \[{O_2}\] = 2.

Hence, we conclude that the correct answer to this question is option B.

Note:
While drawing MOT diagrams the important points to be kept in mind are:
Law of conservation of orbitals: The number of molecular orbitals generated is equal to the number of creating atomic orbitals.
As the overlap between two atomic orbitals increases, the difference in energy between the resulting bonding and antibonding molecular orbitals increases with the increase in overlap of the atomic orbitals
The interaction between atomic orbitals is greatest when they have the same energy.