Using crystal field theory, draw energy level diagram, write electronic configuration of the central metal atom/ion and determine the magnetic moment value in the following
(a) `[CoF_(6)]^(3-), [Co(H_(2)O)_(6)]^(2+), [Co(CN)_(6)]^(3-)`
(b) `FeF_(6)^(3-), [Fe(H_(2)O)_(6)]^(2+), [Fe(CN)_(6)]^(4-)`

Explanation

`[CoF_(6)]^(3-)`.
`F^(-)` is a weak field ligand.

Configuration of `Co^(3+)=3 d^(6) ("or "t_(2g)^(4)e_(g)^(2))`
Number of unpaired electrons `(n)=4`
Magnetic moment `(mu) =sqrt(n(n+2))=sqrt(4(4+2))=sqrt(24)=4.9 BM`
`[Co(H_(2)O)_(6)]^(2+)`,
`H_(2)O` is a weak field ligand.

Configuration of `Co^(2+)=3d^(7) ("or "t_(2g)^(5) e_(g)^(2))`
Number of unpaired electrons `(n)=3`
`mu=sqrt(3(3+2))=sqrt(15)=3.87 BM`
`[Co(CN)_(6)]^(3-)` i.e., `Co^(3+)`
`:.` CN is strong field ligand.

`Co^(3+)=3d^(6) ("or "t_(2g)^(6) e_(g)^(0))`
there is no unpaired electron, so it is diamagnetic.
`mu=0`
(b) `[FeF_(6)]^(3-)`,

`Fe^(3+)=3d^(5) ("or "t_(2g)^(3)e_(g)^(2))`
Number of unpaired electrons, `n=5`
`mu = sqrt(5(5+2))`
`=sqrt(35)=5.92 BM`
`[Fe(H_(2)O)_(6)]^(2+)`

`Fe^(2+)=3d^(6) ("or "t_(2g)^(4)e_(g)^(2))`
Number of unpaired electrons, `n=4`
`mu = sqrt(4(4+2))`
`Z=sqrt(24)`
`= 4.98 BM`
`[Fe(CN)_(6)]^(4-)`

since, `CN^(-)` is a strong field ligand, all the electrons get paired.
`Fe^(2+)=3d^(6) ("or "t_(2g)^(6) e_(g)^(0))`
Because there is no unpaired electron, so it is diamagnetic in nature.