Answer the question on basis of passage given below:

Transition metals form a large number of complexes or coordination compounds in which the metal atoms are bound to a number of anions or neutral molecules. The valence bond theory explain the formation, magnetic behaviour and geometrical shapes while the crystal field theory explains the effect of different crystal fields on the degeneracy of d-orbitals energies of the central metal atom/ion. This provides for the quantitative estimation of orbital separation energies, magnetic moments and spectral and stability parameters.

Amongst the following ions which should have the highest magnetic moment value?

\([CoF_6)]^{3-}\)

The correct answer is option 4. \([CoF_6)]^{3-}\).

We know Magnetic moment, \((\mu ) =\, \ \sqrt{n(n + 2)} BM\); where \(n = \text{ number of unpaired electrons}\)

Now, let us look at each of the given complexes:

1. \([NiCl_4]^{2-}\):

Here, \(Ni\) is in \(+2\) oxidation state with \(d^8\) electronic configuration. \(Cl^-\) is a weak field ligand so pairing of electrons does not occur. Thus, \(Ni^{2+}\) will have 2 unpaired electrons. Hence, the magnetic moment will be :

\((\mu ) =\, \ \sqrt{2(2 + 2)} BM\)

or, \((\mu ) =\, \ \sqrt{8} BM\)

2. \([Mn(CN)_6]^{4-}\):

Here, \(Mn\) is in \(+2\) oxidation state with \(d^5\) electronic configuration. \(CN^-\) is a strong field ligand so pairing of electrons occur. Thus, \(Mn^{2+}\) will have 1 unpaired electrons. Hence, the magnetic moment will be :

\((\mu ) =\, \ \sqrt{1(1 + 2)} BM\)

or, \((\mu ) =\, \ \sqrt{3} BM\)

3. \([Cr(NH_3)_6]^{3+}\):

Here, \(Cr\) is in \(+3\) oxidation state with \(d^3\) electronic configuration. \(NH_3\) is a weak field ligand so pairing of electrons does not occur. Thus, \(Cr^{3+}\) will have 3 unpaired electrons. Hence, the magnetic moment will be :

\((\mu ) =\, \ \sqrt{3(3 + 2)} BM\)

or, \((\mu ) =\, \ \sqrt{15} BM\)

4. \([CoF_6)]^{3-}\):

Here, \(Co\) is in \(+3\) oxidation state with \(d^6\) electronic configuration. \(F^-\) is a weak field ligand so pairing of electrons does not occur. Thus, \(Co^{3+}\) will have 4 unpaired electrons. Hence, the magnetic moment will be :

\((\mu ) =\, \ \sqrt{4(4 + 2)} BM\)

or, \((\mu ) =\, \ \sqrt{24} BM\)

It is clear from the above values that option 4. \([CoF_6)]^{3-}\) has the highest magnetic moment value.