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

Answer

To solve the problem of finding the sum of axial d-orbitals used in hybridization for the species \( IF_6^- \) and \( TeF_5^- \), we will follow these steps:

### Step 1: Determine the hybridization of \( IF_6^- \)

1. **Identify the central atom**: The central atom in \( IF_6^- \) is iodine (I).
2. **Count the valence electrons**: Iodine has 7 valence electrons (Group 17). The negative charge adds 1 more electron, giving a total of 8 valence electrons.
3. **Count the bonding pairs**: There are 6 fluorine atoms bonded to iodine, contributing 6 bonding pairs.
4. **Count the lone pairs**: With 8 total electrons and 6 bonding pairs, there is 1 lone pair left.
5. **Calculate the steric number**: The steric number is the sum of bonding pairs and lone pairs, which is \( 6 + 1 = 7 \).
6. **Determine hybridization**: A steric number of 7 corresponds to \( sp^3d^3 \) hybridization.

### Step 2: Identify the d-orbitals used in \( IF_6^- \)

1. The d-orbitals involved in \( sp^3d^3 \) hybridization are:
- \( d_{xy} \)
- \( d_{x^2-y^2} \)
- \( d_{z^2} \)

### Step 3: Determine the hybridization of \( TeF_5^- \)

1. **Identify the central atom**: The central atom in \( TeF_5^- \) is tellurium (Te).
2. **Count the valence electrons**: Tellurium has 6 valence electrons (Group 16). The negative charge adds 1 more electron, giving a total of 7 valence electrons.
3. **Count the bonding pairs**: There are 5 fluorine atoms bonded to tellurium, contributing 5 bonding pairs.
4. **Count the lone pairs**: With 7 total electrons and 5 bonding pairs, there are 1 lone pair left.
5. **Calculate the steric number**: The steric number is \( 5 + 1 = 6 \).
6. **Determine hybridization**: A steric number of 6 corresponds to \( sp^3d^2 \) hybridization.

### Step 4: Identify the d-orbitals used in \( TeF_5^- \)

1. The d-orbitals involved in \( sp^3d^2 \) hybridization are:
- \( d_{x^2-y^2} \)
- \( d_{z^2} \)

### Step 5: Sum the axial d-orbitals used in both species

1. **Axial d-orbitals in \( IF_6^- \)**:
- \( d_{x^2-y^2} \) and \( d_{z^2} \) (2 axial d-orbitals).
2. **Axial d-orbitals in \( TeF_5^- \)**:
- \( d_{x^2-y^2} \) and \( d_{z^2} \) (2 axial d-orbitals).
3. **Total axial d-orbitals**: \( 2 + 2 = 4 \).

### Final Answer
The sum of axial d-orbitals used in hybridization in both species \( IF_6^- \) and \( TeF_5^- \) is **4**.

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