Concept: Molecular Orbital Theory (MOT)

Molecular Orbital Theory describes the bonding in molecules by considering the combination of atomic orbitals to form molecular orbitals. These molecular orbitals can be bonding (lower energy, increased electron density between nuclei) or anti-bonding (higher energy, decreased electron density between nuclei, with a nodal plane).

Why (A) is correct:

1. Determine total electrons: Each Helium atom (He) has 2 electrons. So, for ${\mathrm{He}}_2$, the total number of electrons is $2\times 2=4$.

2. Fill molecular orbitals: According to MOT, the electrons are filled into molecular orbitals in order of increasing energy, following Hund's rule and Pauli's exclusion principle. The electronic configuration for ${\mathrm{He}}_2$ is $({\sigma }_{1s}{)}^2({\sigma }_{1s}^{\ast }{)}^2$.

3. Identify bonding and anti-bonding electrons:

• The ${\sigma }_{1s}$ orbital is a bonding molecular orbital. It contains 2 electrons.
• The ${\sigma }_{1s}^{\ast }$ orbital is an anti-bonding molecular orbital. It also contains 2 electrons.

Therefore, the number of electrons in bonding orbitals is 2, and in anti-bonding orbitals is 2.

Option Analysis:

• A) 2,2: This is correct, as there are 2 electrons in the bonding ${\sigma }_{1s}$ orbital and 2 electrons in the anti-bonding ${\sigma }_{1s}^{\ast }$ orbital.
• B) 4,2: Incorrect. The total number of electrons is 4, but they are distributed as 2 bonding and 2 anti-bonding.
• C) 4,0: Incorrect. This would imply all 4 electrons are in bonding orbitals, which is not possible for ${\mathrm{He}}_2$ as the anti-bonding orbital must be filled.
• D) 2,4: Incorrect. This would imply 2 bonding and 4 anti-bonding electrons, which exceeds the total number of electrons.

Correct Answer: (A)