In an octahedral structure , the pair of d orbitals involved in `d^(2)sp^(2)` hybridization is
(a)`d_(x^2-y^2), d_z^2`
(b)`d_(xz), d_(x^2-y^2)`
(c)`d_(xz), d_(x^2-y^2)`
(d)`d_(xy),d_(yz)`

Options

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

Explanation

To determine the pair of d orbitals involved in `d^(2)sp^(2)` hybridization in an octahedral structure, we can follow these steps:

### Step 1: Understand the Hybridization
In an octahedral geometry, the central atom is surrounded by six ligands. The hybridization that typically occurs in this geometry is `d^(2)sp^(3)` rather than `d^(2)sp^(2)`. However, if we consider `d^(2)sp^(2)` hybridization, it suggests that two d orbitals are hybridized with two s orbitals and two p orbitals.

### Step 2: Identify the d Orbitals
In octahedral hybridization, the d orbitals that are involved are typically the ones that can effectively overlap with the orbitals of the surrounding ligands. The relevant d orbitals in an octahedral field are:
- `d_(x^2-y^2)`
- `d_(z^2)`

These orbitals are oriented along the axes and are positioned to interact with the ligands.

### Step 3: Analyze the Options
Now, let's analyze the given options:
- (a) `d_(x^2-y^2), d_z^2` - This option includes the correct d orbitals for octahedral hybridization.
- (b) `d_(xz), d_(x^2-y^2)` - This option includes `d_(xz)`, which is not typically involved in octahedral hybridization.
- (c) `d_(xz), d_(x^2-y^2)` - This option is identical to (b) and also incorrect.
- (d) `d_(xy), d_(yz)` - This option includes orbitals that are not aligned with the axes in an octahedral field.

### Step 4: Conclusion
The correct answer is (a) `d_(x^2-y^2), d_z^2`, as these are the two d orbitals involved in `d^(2)sp^(2)` hybridization in an octahedral structure.

### Final Answer:
(a) `d_(x^2-y^2), d_z^2`

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