What can be inferred from the magnetic moment values of the following complex species?
`{:("Example","Magnetic moment(BM)"),(K_(4)[Mn(CN)_(6)],2.2),([Fe(H_(2)O)_(6)]^(2+),5.3),(K_(2)[MnCl_(4)],5.9):}`

Explanation

The magnetic moment of a compound is given by th relation `(mu)=sqrt(n(n+2))B.M`, where n is the number of unpaired electrons.
For one unpaired electron (n=1), `mu=sqrt(1(1+2))=sqrt(3)=1.73 B.M.`
For two unpaired electron (n=2), `mu=sqrt(2(2+2))=sqrt(8)=2.83 B.M.`
For three unpaired electron (n=3), `mu=sqrt(3(3+2))=sqrt(15)=3.87 B.M.`
For four unpaired electron (n=4), `mu=sqrt(4(4+2))=sqrt(24)=4.9 B.M.`
For five unpaired electron (n=5), `mu=sqrt(5(5+2))=sqrt(35)=5.92 B.M.`
In the light of the above value, let us gather the desired information about the complex species that are mentioned.
(i) `K_(4)[Mn(CN)_(6)]`
Oxidation state of Mn `,[Mn(CN)_(6)]^(4-)` , x=6(-1)=-4 or x = -4+6=+2
The magnetic value of 1.73 B.M. indicates teh presence of one unpaired electron in the complex. When six, `CN^(-)` ions ( or ligands ) approach `Mn^(2+)` ion, electrons in 3d orbitals pari up to make available six vacant orbitals involving ` d^(2)sp^(3)` hybridation.

The complex is octahedral and is paramagnetic due to one unpaired electron.
(ii) `[Fe(H_(2)O)_(6)]^(2+)`
Oxidation state of Fe : `[Fe(H_(2)O)_(6)]^(2+), x+6(0)=+2`
The magnetic moment value of 5.3 .M. indicates that there are four unpaired electrons in the complex. This means that the electrons in `Fe^(2+)` ion do not pari up when six `H_(2)O` molecules ( or ligands) approach it . Since the desired number of vacant orbital (six) are available, the complex formed in `sp^(3)d^(2)` hybridised.

The complex is octahedral and is paramagnetice] due to four unpaired electrons. It is also called outer orbital complex because 4d(n=4) orbitals are involved.
(iii) `K_(2)MnCl_(4)]`
Oxidation state of Mn :`[MnCl_(4)]^(2-), x+4(-1)= -2 or x=-2 +4 =+2`
The magnetic moment value of 5.9 B.M indicate that there are five unpaired electrons in the complex. This means that all the five 3d orbitals in `Mn^(2+)` ion are involved in the bond formation. The complex is `sp^(3)` hybridised in which one vacant 4s and three vacant 4p orbitals participate.

The complex is , therefore, tetrahedral in nature.