Which of the following d-orbital(s) participate in the hybridisation for `Xe` in the cationic part of `XeF_(6)(s)`?

Options

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

Explanation

To determine which d-orbitals participate in the hybridization of xenon in the cationic part of \( \text{XeF}_6 \), we can follow these steps:

### Step 1: Understand the Structure of \( \text{XeF}_6 \)
- \( \text{XeF}_6 \) is a compound where xenon (Xe) is the central atom surrounded by six fluorine (F) atoms.
- In the solid state, \( \text{XeF}_6 \) can dissociate into \( \text{XeF}_5^+ \) (cationic part) and \( \text{F}^- \) (anionic part).

### Step 2: Determine the Valence Electrons of Xenon
- Xenon is in group 18 and has 8 valence electrons.
- The cation \( \text{XeF}_5^+ \) has lost one electron due to the positive charge, leaving it with 7 valence electrons.

### Step 3: Count the Bonding and Lone Pairs
- Each fluorine atom forms a single bond with xenon. Since there are 5 fluorine atoms, xenon will form 5 bonds.
- This means 5 of the 7 valence electrons are used for bonding, leaving 2 electrons.
- These 2 remaining electrons will form 1 lone pair.

### Step 4: Determine the Hybridization
- The total number of electron pairs around xenon in \( \text{XeF}_5^+ \) is 6 (5 bond pairs + 1 lone pair).
- The hybridization corresponding to 6 electron pairs is \( \text{sp}^3\text{d}^2 \).

### Step 5: Identify the Participating d-Orbitals
- The \( \text{sp}^3\text{d}^2 \) hybridization involves one s orbital, three p orbitals, and two d orbitals.
- The d-orbitals that participate in this hybridization are typically the \( d_{xy} \), \( d_{xz} \), \( d_{yz} \), \( d_{x^2-y^2} \), and \( d_{z^2} \) orbitals.

### Conclusion
- In the case of \( \text{XeF}_5^+ \), the d-orbitals involved in the hybridization are \( d_{xy} \) and \( d_{x^2-y^2} \) (or any two of the five d-orbitals, depending on the orientation).

### Final Answer
The d-orbitals participating in the hybridization for \( \text{Xe} \) in the cationic part of \( \text{XeF}_6 \) are \( d_{xy} \) and \( d_{x^2-y^2} \).

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