Concept: Hybridization and Molecular Geometry

The shape of a molecule is determined by the hybridization of its central atom. For a trigonal bipyramidal geometry, the central atom undergoes sp³d hybridization. This hybridization involves one s orbital, three p orbitals (p_x, p_y, p_z), and one d orbital.

Why (C) is correct:

For a trigonal bipyramidal geometry, the hybridization is sp³d. The orbitals involved in sp³d hybridization are one s orbital, three p orbitals (p_x, p_y, p_z), and one d orbital. The d orbital involved in sp³d hybridization is typically the d_z² orbital because its lobes are directed along the z-axis, which aligns with the axial bonds in a trigonal bipyramidal structure, and it can effectively overlap with the p orbitals.

Option Analysis:

• A) d_x²-y², d_z², s, p_x, p_y: This set includes two d orbitals and only two p orbitals, which would correspond to sp²d² hybridization, leading to a square planar or octahedral geometry, not trigonal bipyramidal.
• B) d_xy, s, p_x, p_y, p_z: This set includes the d_xy orbital instead of d_z². While it's sp³d, the d_xy orbital is not typically involved in forming the axial bonds of a trigonal bipyramidal structure. The d_z² orbital is the correct d orbital for sp³d hybridization leading to trigonal bipyramidal geometry.
• C) s, p_x, p_y, p_z, d_z²: This set correctly represents the orbitals involved in sp³d hybridization, which results in a trigonal bipyramidal geometry.
• D) d_x²-y², s, p_x, p_y, p_z: This set includes the d_x²-y² orbital instead of d_z². While it's sp³d, the d_x²-y² orbital is not typically involved in forming the axial bonds of a trigonal bipyramidal structure.

Correct Answer: (C)