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 this complex, the oxidation state of nickel is `+2` and has an electronic configuration.
`Ni:1S^(2)2S^(2)2P^(6)3S^(2)3P^(6)4S^(2)3d^(8)`
`Ni^(2+): 1S^(2)2S^(2)2P&(6)3S^(2)3P^(6)4S^(0)3d^(8)`

In this case, the two unpaired electrons of the 3d-orbital are forced to pair in the presence of a strong ligand `CN^(-)` ion. Since four ligand are to be accommodated, nickel (11) ion undergoes `dsp^(2)` hybridisation forming four equivalent `dsp^(2)` hybrid orbitals.

These four hybrid orbitals overlap with the orbitals of the ligands and ligands donate four pairs of electrons to form four co-ordinate bonds.

  Four dsp hybrid orbitals with 4 pairs of electrons of ligands
Since the complex undergoes dsp hybridisation the geometry is square planar.
It is diamagnetic complex due to the absence of unpaired elections.
Hence `[Ni(CN)_(4)]^(2-)` is having `dsp^(2)` hybridisation, with square planar and it has diamagnetic property.