`dz^2` orbital is involvedr in which of the following hybridisastion?

Options

A. `sp^3d`
B. `dsp^3`
C. `sp^3d^2`
D. `d^2sp^3`

Answer

To determine in which hybridization the `dz^2` orbital is involved, we need to analyze the different types of hybridization and their geometries.

### Step-by-Step Solution:

1. **Understanding Hybridization**:
Hybridization is the mixing of atomic orbitals to form new hybrid orbitals that can accommodate the bonding pairs of electrons in a molecule.

2. **Identifying the Relevant Hybridizations**:
- **d²sp³ Hybridization**: This hybridization occurs in octahedral geometry. It involves two `d` orbitals, one `s` orbital, and three `p` orbitals. The `dz²` orbital is one of the `d` orbitals used in this hybridization.

- **sp³d² Hybridization**: This is another form of octahedral hybridization that also involves the `dz²` orbital. It consists of one `s` orbital, three `p` orbitals, and two `d` orbitals.

- **dsp³ Hybridization**: This hybridization is typically seen in trigonal bipyramidal geometries. It involves one `d` orbital, one `s` orbital, and three `p` orbitals. The `dz²` orbital can be involved in this hybridization as well.

3. **Conclusion**:
The `dz²` orbital is involved in:
- d²sp³ hybridization (octahedral)
- sp³d² hybridization (octahedral)
- dsp³ hybridization (trigonal bipyramidal)

Therefore, the answer is that the `dz²` orbital is involved in all of the mentioned hybridizations.

### Final Answer:
The `dz²` orbital is involved in:
- d²sp³ hybridization
- sp³d² hybridization
- dsp³ hybridization

Thus, all options (A, B, C, and D) are correct.