AIIMS 2005 Chemistry Molecular Orbital Theory Assertion Reason Question

To analyze the given question regarding the B₂ molecule, we need to examine both the assertion and the reason in the context of molecular orbital theory.

Assertion: B₂ molecule is diamagnetic.

Explanation of the Assertion: The B₂ molecule (diatomic boron) has a total of 10 electrons. According to molecular orbital theory, the electronic configuration of B₂ can be derived as follows:

1. The molecular orbitals for diatomic boron are filled in the following order:
   • $\sigma_{1s}^2$
   • \sigma_{1s}^*^2
   • $\sigma_{2s}^2$
   • \sigma_{2s}^*^2
   • $\sigma_{2p_z}^2$
   • $\pi_{2p_x}^1$
   • $\pi_{2p_y}^1$

The relevant filling up to 10 electrons gives us: \sigma_{1s}^2 \sigma_{1s}^*^2 \sigma_{2s}^2 \sigma_{2s}^*^2 \sigma_{2p_z}^2 \pi_{2p_x}^1 \pi_{2p_y}^1

In B₂, there are two unpaired electrons, one in each of the $\pi_{2p_x}$ and $\pi_{2p_y}$ molecular orbitals. Since there are unpaired electrons, the B₂ molecule is actually paramagnetic, not diamagnetic. Therefore, the assertion that B₂ is diamagnetic is false.

Reason: The highest occupied molecular orbital is of σ type.

Explanation of the Reason: The highest occupied molecular orbital (HOMO) of B₂ is actually of $\pi$ type, as it contains the unpaired electrons. The correct ordering of the molecular orbitals indicates that the last filled molecular orbitals for B₂ are:

• $\pi_{2p_x}$ and $\pi_{2p_y}$

Since the $\pi$ orbitals are higher in energy than the $\sigma_{2p_z}$ orbital in the case of B₂ (a characteristic that holds for lighter elements like boron), the statement that the highest occupied molecular orbital is of $\sigma$ type is also false.

Conclusion:

Since both the assertion and the reason are false, the correct answer is:

D) If both assertion and reason are false.

Clarification of Incorrect Options:

• A) If both assertion and reason are true and reason is the correct explanation of assertion: This is incorrect because both the assertion and reason are false.

• B) If both assertion and reason are true but reason is not the correct explanation of assertion: This is incorrect for the same reason as option A. Both statements are false.

• C) If assertion is true but reason is false: This is incorrect because the assertion is false (B₂ is paramagnetic).

By understanding the electronic configuration and applying the principles of molecular orbital theory, we can confidently conclude that the correct answer to the question is option D.