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

Explanation

In `[CoF_(6)]^(3)`, the cobalt ion is in +3 oxidation state and has the electronic configuration `[Ar]3d^(6)4s^(0)`.

Since `F^(-)` ion aligand , one 4s-orbital, three 4p-orbitals and two outer 4d-orbitals, undergo `sp^(3)d^(2)` hybridization to form six `sp^(2)d^(2)` hybridized orbitals directed towards the six corners of an octahedron. The hybridization scheme is as shown below.
`sp^(3)d^(2)` hybridised orbitals of `Co^(3+)` :

Six pairs of electrons, one from each `F^(-)` ion, occupy the six hybrid orbitals & form six coordinate bonds.
`[CoF_(4)]^(3-)` (outer orbital or high spin complex) :

Thus, the complex has octahedral geometry and is paramagnetic due to the presence of four unpaired electrons.