The total magnetic moment of any atom, ion or molecule is the sum of the following two values:

(i) Magnetic moment due to the orbital motion of the electron. It is equal to B.M. where is the azimuthally or orbital quantum number for that electron.

(ii) Magnetic moment due tot e spin motion of the electron. It is equal to B.M. where s is the spin quantum number having value equal to .

If ions or molecules are considered instead of free atoms, it is expected that the orbital motions of the electrons are tied into the nuclear configuration of the molecule or the ion so tightly that they are unable to line up with the applied magnetic field. Hence the magnetic moment contribution due to the orbital motion is negligible. Thus the magnetic moment of the molecule or the ion is mainly due to the spin motion of the electrons.(Hence it is called spin magnetic moment. Thus we have
                                                   
Here s represented spin quantum number for one unpaired electron. For a molecule or ion containing a number of unpaired electrons, the expression is usually written as
                                                                                                 
Where S represented spin quantum number.

Thus for one unpaired electrons,    

For two unpaired electrons,           

For three unpaired electron  and so on.

In general, for n unpaired electron, . Hence eqn. becomes

                                        

Thus knowing he number of unpaired electrons present, the magnetic moment can be calculated or vice versa.

For more help in Relationship Between Magnetic Moment and the Number of Unpaired Electrons click the button below to submit your homework assignment