unhybridized p and d orbitals

[Harsimer Bal 3K]

For trigonal bipyramidal and octahedral electron arrangements, I understand that there are 5sp3d and 6sp3d2 hybridized orbitals, respectively, but how many unhybridized p and d orbitals are present for each arrangement?

[Paul Zhang 2F]

Hello! For sp3d, we start out with 1 s orbital, 3 p orbitals, and 5 d orbitals for 9 total. Since 5 hybridized orbitals are formed, there are 4 unhybridized d orbitals (s and p are used up). For sp3d2, we also start out with 9 total orbitals (same reasoning). Since 6 hybridized orbitals are formed, there are 3 unhybridized d orbitals (ditto for s and p). Let me know if you have more questions!