Using valence bond theory explain geometry, hybridisation and magnetic property of `[CoF_6]_3^-` (Atomic number of Co = 27).

Explanation

In this complex, the oxidation state of Co is +3. The electronic configuration of cobalt in +3 oxidation state is `[Ar]3d^(6) 4s^(0)`.
Orbitals of `Co^(3+)` ion are represented as

Since `F^(-)` ion provides a weak ligand field, one 4s, three 4p and two outer 4d-orbitals hybridised to yield six sp.d hybrid orbitals pointing towards the six corners of an octahedron.

These six hybridised orbitals of `Co^(3+)` overlaps with orbitals of six `F^(-)`ligands and six pairs of electrons donated by six F-to form six coordinate bonds.

Six `sp^(3)d^(2)` hybrid orbitals with six pairs of electrons from ligands.
Thus, the complex has octahedral geometry. This complex is paramagnetic because of the presence of unpaired electrons,.