In `IF_(6)^(-) and TeF_(5)^(-)`, sum of axial d-orbitals which are used in hybridisation in both species.

Answer

To find the sum of axial d-orbitals used in hybridization for the species IF₆⁻ and TeF₅⁻, we will follow these steps:

### Step 1: Determine the hybridization of IF₆⁻
- **Identify the central atom**: The central atom in IF₆⁻ is iodine (I).
- **Count the valence electrons**: Iodine has 7 valence electrons.
- **Count the number of monovalent atoms attached**: There are 6 fluorine (F) atoms attached.
- **Account for the charge**: Since IF₆⁻ is an anion, we add 1 to the total count.

Using the formula for hybridization:
\[ \text{Hybridization} = \frac{1}{2} \left( V + M + \text{Charge} \right) \]
Where:
- \( V = 7 \) (valence electrons of I)
- \( M = 6 \) (monovalent F atoms)
- Charge = +1 (for the anion)

Calculating:
\[ \text{Hybridization} = \frac{1}{2} \left( 7 + 6 + 1 \right) = \frac{14}{2} = 7 \]

This indicates sp³d³ hybridization.

### Step 2: Identify the d-orbitals used in hybridization for IF₆⁻
- The d-orbitals involved in sp³d³ hybridization are:
- \( d_{x^2-y^2} \)
- \( d_{z^2} \)
- \( d_{xy} \) (not used in axial positions)

The axial d-orbitals are \( d_{x^2-y^2} \) and \( d_{z^2} \).

### Step 3: Determine the hybridization of TeF₅⁻
- **Identify the central atom**: The central atom in TeF₅⁻ is tellurium (Te).
- **Count the valence electrons**: Tellurium has 6 valence electrons.
- **Count the number of monovalent atoms attached**: There are 5 fluorine (F) atoms attached.
- **Account for the charge**: Since TeF₅⁻ is an anion, we add 1 to the total count.

Using the same formula:
\[ \text{Hybridization} = \frac{1}{2} \left( V + M + \text{Charge} \right) \]
Where:
- \( V = 6 \) (valence electrons of Te)
- \( M = 5 \) (monovalent F atoms)
- Charge = +1 (for the anion)

Calculating:
\[ \text{Hybridization} = \frac{1}{2} \left( 6 + 5 + 1 \right) = \frac{12}{2} = 6 \]

This indicates sp³d² hybridization.

### Step 4: Identify the d-orbitals used in hybridization for TeF₅⁻
- The d-orbitals involved in sp³d² hybridization are:
- \( d_{x^2-y^2} \)
- \( d_{z^2} \)
- \( d_{xy} \) (not used in axial positions)

The axial d-orbitals are \( d_{x^2-y^2} \) and \( d_{z^2} \).

### Step 5: Sum the axial d-orbitals used in both species
- For IF₆⁻: 2 axial d-orbitals ( \( d_{x^2-y^2} \) and \( d_{z^2} \) )
- For TeF₅⁻: 2 axial d-orbitals ( \( d_{x^2-y^2} \) and \( d_{z^2} \) )

Total axial d-orbitals used = 2 (from IF₆⁻) + 2 (from TeF₅⁻) = 4.

### Final Answer
The sum of axial d-orbitals used in hybridization in both species is **4**.

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