The set of d-orbitlas which do not contain any d-orbital which is involved in involved in hybridization of central atom in `ICl_(4)^(-)`

Options

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

Explanation

To solve the question regarding the set of d-orbitals that do not contain any d-orbitals involved in the hybridization of the central atom in \( ICl_4^- \), we will follow these steps:

### Step 1: Determine the Hybridization of \( ICl_4^- \)

1. **Count the Valence Electrons**:
- Iodine (I) has 7 valence electrons.
- Each chlorine (Cl) has 7 valence electrons, and there are 4 chlorine atoms contributing \( 4 \times 7 = 28 \) electrons.
- The overall charge of the ion is -1, which means we add 1 more electron.
- Total valence electrons = \( 7 + 28 + 1 = 36 \) electrons.

2. **Draw the Lewis Structure**:
- Iodine is the central atom and forms 4 bonds with 4 chlorine atoms.
- After forming 4 bonds, 4 pairs of electrons are used, leaving 2 lone pairs on iodine.

3. **Determine the Steric Number**:
- Steric number = Number of bonded atoms + Number of lone pairs = 4 (from Cl) + 2 (lone pairs) = 6.

4. **Identify Hybridization**:
- A steric number of 6 corresponds to \( sp^3d^2 \) hybridization.

### Step 2: Identify the d-Orbitals Involved in Hybridization

1. **Identify the d-Orbitals**:
- The \( sp^3d^2 \) hybridization involves the following orbitals:
- 1 s orbital
- 3 p orbitals
- 2 d orbitals

2. **Determine Which d-Orbitals are Involved**:
- The d-orbitals involved in \( sp^3d^2 \) hybridization are typically \( d_{x^2-y^2} \) and \( d_{z^2} \).

### Step 3: Identify the d-Orbitals Not Involved in Hybridization

1. **List the d-Orbitals**:
- The five d-orbitals are:
- \( d_{xy} \)
- \( d_{xz} \)
- \( d_{yz} \)
- \( d_{x^2-y^2} \) (involved)
- \( d_{z^2} \) (involved)

2. **Identify the Non-Involved d-Orbitals**:
- The d-orbitals that are **not** involved in the hybridization are:
- \( d_{xy} \)
- \( d_{xz} \)
- \( d_{yz} \)

### Final Answer

The set of d-orbitals which do not contain any d-orbitals involved in the hybridization of the central atom in \( ICl_4^- \) is:
- \( \{ d_{xy}, d_{xz}, d_{yz} \} \)

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