Concept: Molecular Orbital Theory (MOT)

The number of unpaired electrons in a molecule can be determined by filling electrons into molecular orbitals according to Hund's rule and Pauli's exclusion principle. For diatomic molecules, the order of filling molecular orbitals depends on whether the total number of electrons is less than or equal to 14 or greater than 14.

Why (A) is correct:

1. Calculate total electrons: Carbon (C) has 6 electrons, and Oxygen (O) has 8 electrons. So, the total number of electrons in the CO molecule is $6+8=14$.

2. Molecular Orbital Configuration: For molecules with 14 or fewer electrons, the order of filling molecular orbitals is:

${\sigma }_{1s}<{\sigma }_{1s}^{\ast }<{\sigma }_{2s}<{\sigma }_{2s}^{\ast }<{\pi }_{2p_x}={\pi }_{2p_y}<{\sigma }_{2p_z}<{\pi }_{2p_x}^{\ast }={\pi }_{2p_y}^{\ast }<{\sigma }_{2p_z}^{\ast }$

3. Fill electrons: Filling 14 electrons into these orbitals:

$({\sigma }_{1s}{)}^2({\sigma }_{1s}^{\ast }{)}^2({\sigma }_{2s}{)}^2({\sigma }_{2s}^{\ast }{)}^2({\pi }_{2p_x}{)}^2({\pi }_{2p_y}{)}^2({\sigma }_{2p_z}{)}^2$

4. Count unpaired electrons: In this configuration, all electrons are paired in the molecular orbitals. Therefore, the number of unpaired electrons is zero.

Option Analysis:

• A) Zero: This is correct, as all 14 electrons in the CO molecule are paired in their respective molecular orbitals.
• B) One: Incorrect. There are no singly occupied molecular orbitals.
• C) Three: Incorrect. This would imply a highly unstable radical species.
• D) Two: Incorrect. This would imply a diradical, which is not the case for CO.

Correct Answer: (A)