Step 1: Understanding the Concept:
The hybridization and geometry of a complex depend on the oxidation state of the metal and the nature of the ligand (strong field vs. weak field).
Step 3: Detailed Explanation:
1. Oxidation State: In \([CoF_6]^{3-}\), Cobalt is in the +3 state (\(Co^{3+}\)).
2. Electronic Configuration: \(Co^{3+}\) is \(3d^6\).
3. Ligand Nature: Fluoride (\(F^-\)) is a weak field ligand. It cannot cause the pairing of \(3d\) electrons.
4. Orbital Availability: Since \(3d\) electrons are not paired, the metal uses outer orbitals (\(4s, 4p, 4d\)) for bonding.
5. Hybridization: It uses one \(4s\), three \(4p\), and two \(4d\) orbitals to form six \(sp^3d^2\) hybrid orbitals.
This forms an outer orbital, high-spin complex.
Step 4: Final Answer:
The hybridization is \(sp^3d^2\).