When hybridisation involving d-orbitals are considered then all the five d-orbitals are not degenerate, rather `d_(x^(2)-y^(2)),d_(s^(2)) and d_(xy),d_(zx)` form two different sets of orbitals and orbitals of appropriate set is involved in the hybridisation.
Molecule having trigonal bipyramidal geometry and `sp^(3)`d hybridisation, d-orbitals involved is :

Options

A. `d_(xy)`
B. `d_(yz)`
C. `d_(x^(2)-y^(2))`
D. `d_(z^(2))`

Answer

To determine the d-orbitals involved in sp³d hybridization for a molecule with trigonal bipyramidal geometry, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Hybridization**:
- Hybridization is the mixing of atomic orbitals to form new hybrid orbitals that are suitable for the pairing of electrons to form chemical bonds.
- In the case of sp³d hybridization, we are dealing with one s orbital, three p orbitals, and one d orbital.

2. **Identify the Orbitals**:
- The orbitals involved in sp³d hybridization are:
- 1 s orbital (1s)
- 3 p orbitals (px, py, pz)
- 1 d orbital (from the d subshell)

3. **Recognize the d-Orbitals**:
- The d subshell consists of five orbitals:
- dxy
- dyz
- dzx
- dx²-y²
- dz²

4. **Determine the d-Orbital for sp³d Hybridization**:
- In sp³d hybridization, only one d orbital is used.
- The d orbital that is typically involved in this type of hybridization is dz². This is because dz² has the appropriate orientation to form bonds in a trigonal bipyramidal geometry.

5. **Conclusion**:
- Therefore, the d-orbital involved in sp³d hybridization for a molecule with trigonal bipyramidal geometry is **dz²**.

### Final Answer:
The d-orbital involved in sp³d hybridization is **dz²**.

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