Calculate the spin only magnetic momentum µ of K3 [ Mn(CN)6] compound .

Calculate the spin only magnetic momentum  µ of K₃[ Mn(CN)₆]  compound  .

In K₃ [ Mn(CN)₆]  the metal  manganese in Mn ⁺³ oxidation state . Mn ⁺³  ion is a d ⁴ system . Cyanide ion is a very strong field ligand . 

According to crystal field theory the given complex will be of low spin type  and its electron distribution will be t_2g⁴ e_g⁰ which is shown below.

There is two unpaired electron in the complex , it will be paramagnetic and magnetic moment will correspond to two unpaired electron which is given by µ .

Why tetrahedral metal complexes are usually not of low spin ?

According to crystal field theory splitting of d-orbitals takes place during complexation and they split into two different sets of orbitals in both octahedral and tetrahedral complexes. 

The value of splitting energy depends on the nature of the metal ion ligand and the nature of the geometry of the complexes. 

Depending of the value of this splitting energy Δo ( for octahedral ) and Δt ( for tetrahedral ) high spin and low spin complexes may result. 

As for example , for an octahedral complex of d4 system the electron distribution may either be  t_2g3 e_g1 ( high spin) when Δo < p or t_2g4 e_g0 (low spin ) when Δo > p . 

Spin pairing energies of different d4-system of a given d-series of transition element are almost the same.

Therefore it is necessary to obtain high spin low spin complexes the value of  Δo should be greater than pairing energy, p ( low spin ) in some cases and also it should be less than ,p ( high spin ) in some cases. Actually these are possible in octahedral complexes.

It has been found that Δt is always very small and is about 45% of Δo in all cases and never exceeds pairing energy.

Therefore these is no possibility of formation of low spin complexes . So it can be said that all tetrahedral metal complexes are usually not of low spin.

Summary.

Calculate the spin only magnetic momentum  µ of  K₃ [ Mn(CN)₆]  compound  .

 Why tetrahedral metal complexes are usually not of low spin ?

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