The molecular geometry of \( \text{XeF}_4 \) involves the xenon atom bonded to four fluorine atoms. Xenon has 8 valence electrons, and the bonding arrangement involves four single bonds with fluorine atoms, leaving two lone pairs on the xenon atom.
The hybridization of the xenon atom in \( \text{XeF}_4 \) can be determined by considering the number of electron pairs around the central atom. In this case, there are 4 bonding pairs and 2 lone pairs, making a total of 6 electron pairs.
To accommodate 6 electron pairs, the xenon atom undergoes \( sp^3d^2 \) hybridization, which involves the mixing of one s orbital, three p orbitals, and two d orbitals to form six hybrid orbitals. These hybrid orbitals form bonds with the fluorine atoms and also accommodate the lone pairs.
Thus, the correct hybridization of \( \text{XeF}_4 \) is \( sp^3d^2 \).