JEE Chemistry 2025 Question with Solution

Given: The internuclear axis is along the $z$-direction, and we must identify which listed pair of atomic orbitals can combine to form molecular orbitals in a homonuclear diatomic molecule.

Find: The correct option corresponding to the valid linear combination.

For molecular orbital formation, the two atomic orbitals must have compatible symmetry with respect to the internuclear axis and must overlap effectively.

1. $2p_z$ and $2p_x$: $2p_z$ is oriented along the $z$-axis, whereas $2p_x$ is oriented along the $x$-axis. Their symmetries do not match for overlap along the internuclear axis, so this combination does not form a molecular orbital.

2. $2s$ and $2p_x$: $2s$ is spherically symmetric, but $2p_x$ has its directional character along the $x$-axis, not along the internuclear $z$-axis. Effective overlap for the given axis is not obtained, so this combination is not suitable.

3. $3d_{xy}$ and $3d_{x^2-y^2}$: Both orbitals lie in the $xy$-plane and do not have the required symmetry for overlap along the $z$-axis. Therefore, this combination does not form molecular orbitals for the given orientation.

4. $2s$ and $2p_z$: $2s$ is spherically symmetric and $2p_z$ is aligned along the internuclear $z$-axis. Their symmetry is appropriate for overlap along this axis, so this combination can form molecular orbitals.

5. $2p_z$ and $3d_{x^2-y^2}$: $2p_z$ is oriented along $z$, but $3d_{x^2-y^2}$ lies in the $xy$-plane. Their symmetries are incompatible for overlap along the internuclear axis.

Hence, only statement (4) is correct.

Therefore, the correct option is C.

Given: The internuclear axis is along $z$.

Find: Which orbital pair has proper symmetry for molecular orbital formation.

Shortcut idea: Keep only orbitals that have suitable symmetry or directional character with respect to the $z$-axis.

• Any orbital directed along another axis, such as $2p_x$, is eliminated.
• Orbitals confined to the $xy$-plane, such as $3d_{xy}$ and $3d_{x^2-y^2}$, are also eliminated.
• The only pair left with suitable overlap along the $z$-axis is $2s$ and $2p_z$.

Therefore, the correct option is C.