Question

If Hund's rule is not applicable, then how many unpaired electrons are present in ${{B}_{2}} $molecule?

Answer 1

Hint: Use the molecular orbital theory to understand what is being asked here. Write down the molecular orbital configurations to get a better perspective.

Complete answer:
The Hund’s rule for maximum multiplicity is one of the foundational laws regarding the atomic orbitals and the nature or manner of electrons arranged in them. It states that electrons always enter all the degenerate empty orbitals of a particular subshell before pairing up in individual orbitals. In other words all the orbitals belonging to a particular subshell which have the same energy are at first filled partially. Pairing of electrons only occurs when all the orbitals have been partially filled.
It turns out this is not only applicable to atomic orbitals but also to molecular orbitals. Let us see the electronic configuration of the Boron molecule. It is as follows:
\[\sigma 1{{s}^{2}}<{{\sigma }^{*}}1{{s}^{2}}<\sigma 2{{s}^{2}}<{{\sigma }^{*}}2{{s}^{2}}<\pi 2{{p}_{x}}^{1}=\pi 2{{p}_{y}}^{1}\]
As you can see above, the molecular orbitals $\pi 2{{p}_{x}}$ and $\pi 2{{p}_{y}}$ are degenerate in nature. In other words they nearly have the same energy. So according to Hund’s rule of maximum multiplicity, the molecular orbitals will only get paired when both of them have been partially filled, as is the case this time. If another electron were to come then it would first enter the $\pi 2{{p}_{x}}$orbital, hence making a pair.
We have two unpaired electrons in this case which makes Boron molecules paramagnetic in nature. But here we have been asked what would have happened if the rule of Hund is not followed. Well, then the electronic configuration would be somewhat like this:
\[\sigma 1{{s}^{2}}<{{\sigma }^{*}}1{{s}^{2}}<\sigma 2{{s}^{2}}<{{\sigma }^{*}}2{{s}^{2}}<\pi 2{{p}_{x}}^{2}=\pi 2{{p}_{y}}\]
The $\pi 2{{p}_{x}}$ orbital is completely filled, leaving no electrons for the next orbital even if they have the same energy. In this case, the molecule is diamagnetic in nature as there are no unpaired electrons.

Note: Hund’s rule for maximum multiplicity is a foundational rule and all of the atomic and molecular structures depend on it. So there would never be a case when this rule is not followed.
While writing the electronic configurations in molecular orbitals, degenerate orbitals are only those which have an “equals to” sign between them. All other orbitals have different energies which is apparent from the “less than” sign.