In 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.

The d orbital involved in sp³d hybridization for trigonal bipyramidal geometry is the d_z² orbital. This specific d orbital is chosen because its lobes are directed along the z-axis, which aligns with the axial positions in a trigonal bipyramidal structure, and its donut-shaped electron density lies in the xy-plane, aligning with the equatorial positions. This orientation allows for effective overlap with the atomic orbitals of the surrounding atoms to form the five hybrid orbitals.

• A) d_x²-y²: This orbital is involved in square planar geometry (dsp² hybridization) or octahedral geometry (sp³d² hybridization) along with d_z².
• B) d_z²: This is the correct d-orbital involved in sp³d hybridization for trigonal bipyramidal geometry.
• C) d_xy: This orbital, along with d_xz and d_yz, are non-axial d-orbitals and are typically involved in crystal field splitting in transition metal complexes, but not directly in sp³d hybridization for trigonal bipyramidal geometry.
• D) d_xz: Similar to d_xy, this orbital is not involved in sp³d hybridization for trigonal bipyramidal geometry.

Correct Answer: (B)