Final answer:
The orbitals that can form a trigonal bipyramidal shape are one s orbital, three p orbitals, and one d orbital, combining to create sp³d hybrid orbitals. This hybridization is only feasible for atoms with d orbitals in their valence shell, excluding elements from the first and second periods.
Step-by-step explanation:
Valence Shell Orbital Clusters for Trigonal Bipyramidal Shape
The clusters of orbitals that can form a trigonal bipyramidal shape in the valence shell of an atom are comprised of five atomic orbitals: one s orbital, three p orbitals, and one d orbital. These orbitals combine to form five sp³d hybrid orbitals. In comparing this with an octahedral arrangement which uses six orbitals, i.e., one s orbital, three p orbitals, and two d orbitals to create six sp³d² hybrid orbitals, it's evident that these hybridizations are possible only for atoms that have d orbitals in their valence shell, excluding those in the first and second period.
The electron pair geometry is determined by the number of regions of electron density around the central atom. When there are five regions of electron density, the arrangement that minimizes repulsions is trigonal bipyramidal. If lone pairs are present, their placement in the structure is important; in a trigonal bipyramidal arrangement, lone pairs are most stable in the equatorial positions.