The involvement of specific d-orbitals in hybridization depends on the geometry of the molecule and the type of hybridization.

Concept:

Hybridization is the mixing of atomic orbitals to form new hybrid orbitals suitable for the pairing of electrons to form chemical bonds. The specific d-orbitals involved depend on the geometry and the number of d-orbitals participating.

Why (B) is correct:

In $s{p}^3{d}^2$ hybridization, the geometry is octahedral. The d-orbitals involved are $d_{z^2}$ and $d_{x^2-y^2}$. These two d-orbitals have lobes directed along the axes, which allows for maximum overlap with the ligand orbitals in an octahedral arrangement.

Option Analysis:

• A) $s{p}^{3}d$ (TBP): In trigonal bipyramidal (TBP) geometry, the d-orbital involved is $d_{z^2}$. This orbital has lobes along the z-axis and a donut in the xy-plane, which suits the axial and equatorial positions in TBP geometry.
• B) $s{p}^3{d}^2$: In octahedral geometry, the d-orbitals involved are $d_{z^2}$ and $d_{x^2-y^2}$. Both of these orbitals have their lobes directed along the axes, which align perfectly with the six ligands in an octahedral complex.
• C) $s{p}^3{d}^3$: In $s{p}^3{d}^3$ hybridization, which leads to pentagonal bipyramidal geometry, the d-orbitals involved are $d_{z^2}$, $d_{x^2-y^2}$, and $d_{xy}$.
• D) None of these: This is incorrect as $d_{x^2-y^2}$ orbital is involved in $s{p}^3{d}^2$ hybridization.

Correct Answer: (B)