Question

Assuming that Hund’s rule is violated, the bond order and magnetic nature of the diatomic molecule ${B_2}$ is
A. 1 and diamagnetic
B. 0 and diamagnetic
C. 1 and paramagnetic
D. 0 and paramagnetic

Answer 1

Hint: Since \[{B_2}\] is a diatomic molecule, we have to write down its electronic configuration according to the Molecular Orbital Theory (MOT) and then we will be able to calculate its bond order using the formula:
\[Bond{\text{ }}Order{\text{ = }}\dfrac{{Number{\text{ }}of{\text{ }}Bonding{\text{ }}electrons{\text{ }}-{\text{ }}Number{\text{ }}of{\text{ }}Antibonding{\text{ }}electrons}}{2}\]

Complete solution:
According to MOT, when the total number of electrons in a molecule is less than 14, then the filling of the molecular orbitals occurs as per the following order:
\[\]\[\]$\sigma 1s,\sigma ^*1s,\sigma 2s,\sigma ^*2s,\pi 2{p_x} = \pi 2{p_y},\sigma 2{p_z},\pi ^*2{p_x} = \pi ^*2{p_y},\sigma ^*2{p_z}$
Also, each molecular orbital (whether bonding or antibonding) can contain maximum 2 electrons, both with opposite spins, as per Hund’s rule of maximum multiplicity.
So, in \[{B_2}\] molecules, there are 10 electrons overall as each Boron atom has 5 electrons. So using the above order, the configuration of the diatomic molecule can be written as:
$\sigma 1{s^2},\sigma ^*1{s^2},\sigma 2{s^2},\sigma ^*2{s^2},\pi 2{p_x}^2$
So, from this configuration, it is pretty much clear that the total number of electrons in bonding molecular orbitals is 6 while the total number of electrons in antibonding molecular orbitals is 4. Hence, using the above mentioned formula, we can calculate the bond order as:
\[Bond{\text{ }}Order = \dfrac{{6 - 4}}{2} = \dfrac{2}{2} = 1\]
Also, we can clearly see that there are no unpaired electrons present in the molecular orbitals of this diatomic molecule. So, here, we can conclude that the magnetic nature of the molecule would be Diamagnetic due to absence of unpaired electrons.
Had there been present any unpaired electrons, the magnetic nature would have been paramagnetic then.

So, as per the given question, option (A) would be the correct answer.

Note:
Students must note here that whenever we have to write the electronic configuration of a molecule as per MOT, we need calculate the total number of electrons in the molecule first because, if the number of electrons is higher than 14, then the order of filling of electrons would change.