The pair of a orbitals involved in octahedral structure having `d^(2) sp^(3)` hybridization , are

Options

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

Answer

To solve the question regarding the pair of orbitals involved in an octahedral structure with \(d^2sp^3\) hybridization, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Hybridization**:
- In octahedral complexes, the central metal atom undergoes hybridization to accommodate the ligands. The \(d^2sp^3\) hybridization indicates that two \(d\) orbitals, one \(s\) orbital, and three \(p\) orbitals are involved in forming the hybrid orbitals.

2. **Identifying the Orbitals**:
- The \(d\) orbitals that are typically involved in \(d^2sp^3\) hybridization are the \(d_{x^2-y^2}\) and \(d_{z^2}\) orbitals. These orbitals are chosen because they have the right energy and orientation to interact effectively with the ligands in an octahedral arrangement.

3. **Role of Ligands**:
- In octahedral complexes, ligands approach the metal ion along the axes (x, y, z). The \(d_{x^2-y^2}\) and \(d_{z^2}\) orbitals point directly towards the ligands, which leads to maximum overlap and strong bonding interactions.

4. **Energy Considerations**:
- The \(d\) orbitals split in energy when ligands approach the central metal ion due to electrostatic repulsion. In an octahedral field, the \(d_{x^2-y^2}\) and \(d_{z^2}\) orbitals experience higher energy due to direct interaction with the ligands, while the \(d_{xy}\), \(d_{xz}\), and \(d_{yz}\) orbitals have lower energy.

5. **Conclusion**:
- Therefore, the pair of orbitals involved in \(d^2sp^3\) hybridization in an octahedral structure are \(d_{x^2-y^2}\) and \(d_{z^2}\).

### Final Answer:
The pair of orbitals involved in octahedral structure having \(d^2sp^3\) hybridization are \(d_{x^2-y^2}\) and \(d_{z^2}\).