With the help of Valence Bond theory account for hybridisation, geometry and magnetic property of `[Ni(CN)_(4)]^(2-)` complex ion `[Z" for "Ni=28]`

Explanation

In the given complex ion central metal is nickel with electronic configuration `[Ar]^(18)3d^(8)4s^(2)`
Nickel is in `+2` oxidation state thereofre electronic configurations is `Ni^(+2)`

In the given complex, `CN^(-)` is a strong ligand. On the approach of strong ligand the unpaired 3d electron will get pair up. As a result one d - orbital becomes vacant.

The one vacant 3d orbital, one vacant 4s orbital and two vacant 4p orbitals hybridize to give four hybrid orbitals.

Four pairs of electrons one from each `CN-` molecule occupy the four hybridized orbitals.

Due to `dsp^(2)` hybridization the complex ion is square planar in shape. There are no unpaired electrons in the complex so it is diamagnetic.
Hybridisation `-dsp^(2)`
Geometrical shape - Square planar
Magnetic property - Diamagnetic