Question

How many antibonding electrons are there in ${O_2}$ molecule?
(A) 10
(B) 8
(C) 6
(D) 4

Answer 1

To find out the number of antibonding electrons first write down the electronic configuration of ${O_2}$ molecule according to MOT. The electrons should be filled in the molecular orbitals according to their increasing order of energy. Now calculate the total number of antibonding electrons.

Complete step by step solution:
-The concept of bonding and antibonding electrons comes under the Molecular Orbital theory and so first we shall talk about the theory.
According to the molecular orbital theory, the idea of quantum mechanics is used for the explanation of electronic configuration or structure of the molecules. When 2 atoms bond, their atomic orbitals combine and form new molecular orbitals. This theory says that:
(1)The number of atomic and molecular orbitals will always be equal.
(2)The resultant molecular orbitals are basically of 3 types: bonding molecular orbitals, non-bonding molecular orbitals and anti-bonding molecular orbitals. The electrons filled in the bonding orbitals are known as bonding electrons and those in the antibonding orbitals are known as antibonding electrons. The different types of molecular orbitals also differ in their energy levels as the anti-bonding molecular orbitals are at higher energy than the parent atomic orbital, while the bonding molecular orbitals are at lower energy than the parent atomic orbitals.
(3)The sequence of filling electrons in the molecular orbitals is always according to the increasing order of energy of the orbitals.
(4)The formed molecular orbitals are most effective only when the combining atomic orbitals are similar in their energies.
-According to the MOT (point 3) the electrons should be filled in the molecular orbitals according to their increasing order of energy as shown below:
$\sigma 1s,{\sigma ^*}1s,\sigma 2s,{\sigma ^*}2s,\sigma 2{p_z},\pi 2{p_x} = \pi 2{p_y},{\pi ^*}2{p_x} = {\pi ^*}2{p_y},{\sigma ^*}2{p_z}$ and so on.
Where the orbitals with ‘*’ are the anti-bonding orbitals and electrons in them are the antibonding electrons.
-Now coming back to the question, we need to find out the number of antibonding electrons present in ${O_2}$. For this, we need to first write down the electronic configuration of ${O_2}$ according to the MOT.
For ${O_2}$: total number of electrons = 16
Configuration: ${\sigma}$ $1$ $s^2$ ${\sigma ^*}$ $1$ $s^2$ ${\sigma }$ $2$ $s^2$ ${\sigma ^*}$ $2$ $s^2$ ${\sigma}$ $2$ ${p_z^2}$ $\pi$ $2$ ${p_x^2}$ $\pi$ $2$ ${p_y^2}$ ${\pi ^*}$ $2$ ${p_x^1}$ ${\pi ^*}$ $2$ ${p_y^1}$
From this configuration we can see that: The number of bonding electrons = 10 and the number of antibonding electrons = 6.
So, we can finally conclude that the number of antibonding electrons in ${O_2}$ are = 6

Hence, the correct option will be: (C) 6.

Note: The electrons should always be filled according to the increasing energy level of the molecular orbitals. Also, the MOT uses the concept of bond order to explain the existence of a molecule on the basis of bond order, but this method can neither be feasible nor appropriate to explain about the molecular existence of polyatomic molecules. Also, MOT does not say anything about the geometry and shape of the molecule. So, this theory also has some drawbacks.