`[Ni(CN)_4 ]^(2-) ` is diamagnetic ,while ` [NiCl_4]^(2) - ` is paramagnetic ,explain using crystal field theory.

Explanation

(a) `[Ni(CN)_(4)]^(2-)`
`Ni=3d^(8)4S^(2)`
`Ni^(2+)=3d^(8)`

Nature of the complex - Low spin (Spin paired)
Ligand filled electronic configuration of central metal ion, `t_(2g)^(6)e_(g)^(2)`
Magnetic property : No unpaired electron (`CN^(-)` is strong filled ligand), hence it is diamagnetic.
Magnetic moment : `mu_(s)=0`
(b) `[NiCl_(4)]^(2-)`
`Ni=3d^(8)4S^(2)`
`Ni^(2+)=3d^(8)`

Nature of the complex, - high spin
Ligand filled electronic configuration of central metal ion, `t_(2g)^(6)e_(g)^(2)`
magnetic property : Two unpaired electron (`Cl^(-)` is weak field ligand). Hence it is paramagnetic
Magnetic moment : `mu_(s)=sqrt(2(2+2))`
`=sqrt(8)=2.83BM`