The calculated magnetic moment (B.M.) for the ground state of a f⁵ ion is

Concept:

The magnetic moment of coordination compounds is a property that provides insight into the magnetic behavior of these complex molecules. Coordination compounds are composed of a central metal atom or ion bonded to surrounding ligands. The magnetic moment is a measure of the magnetic strength and orientation of the electron distribution within the compound.

Explanation:

\(u = {g\sqrt{J(J+1)}}\)

The above equation is used to calculate the magnetic moment of heavier atoms. Eg. F block elements.

Where, \(g = {1+{S(S+1) - L(L+1) +J(J+1)\over 2J(J+1)}}\)

S = 1/2 +1/2 +1/2+ 1/2 +1/2

S = 5/2

L = (3 x 1) +(2 x 1) + (1 x 1) + (0 x 1) + (-1 x 1)

L = 5

J = |L - S|.  As f orbital is less than half filled

J = |5 - 5/2|

J = 5/2

Putting the values of S, L and J in the above equation of g

Hence, g = 2/7

Now, putting the value of g to calculate magnetic moment of f⁵ ion.

\(u ={ {2 \over7}}{\sqrt{{5\over2}({5 \over2}+1)}}\)

\(u = {\sqrt {35}\over 7}\)

Conclusion:

The magnetic moment of f⁵ ion is \({\sqrt {35}\over 7}\).