The d-orbitals involved in `sp^(3)d^(2) or d^(2)sp^(3)` hybridization of the central metal ion are:

Options

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

Answer

To determine the d-orbitals involved in \( sp^3d^2 \) or \( d^2sp^3 \) hybridization of the central metal ion, we can follow these steps:

### Step 1: Understand the Hybridization
In \( sp^3d^2 \) or \( d^2sp^3 \) hybridization, we need to identify the orbitals involved. The notation indicates that we are using one s orbital, three p orbitals, and two d orbitals.

### Step 2: Identify the Orbitals
- The **s orbital** involved is the \( 1s \) orbital.
- The **p orbitals** involved are \( p_x \), \( p_y \), and \( p_z \).
- The **d orbitals** involved are from the d subshell, which consists of five orbitals: \( d_{xy} \), \( d_{yz} \), \( d_{zx} \), \( d_{x^2-y^2} \), and \( d_{z^2} \).

### Step 3: Determine Which d-Orbitals Participate
In \( sp^3d^2 \) hybridization, the two d orbitals that participate in the hybridization are typically:
- \( d_{x^2-y^2} \)
- \( d_{z^2} \)

These orbitals are involved because they can effectively overlap with the s and p orbitals to form hybrid orbitals suitable for bonding.

### Step 4: Conclusion
Thus, the d-orbitals involved in \( sp^3d^2 \) or \( d^2sp^3 \) hybridization of the central metal ion are:
- \( d_{x^2-y^2} \)
- \( d_{z^2} \)

### Final Answer
The d-orbitals involved in \( sp^3d^2 \) or \( d^2sp^3 \) hybridization are \( d_{x^2-y^2} \) and \( d_{z^2} \).

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