Amongst the following ions which one of the following has the highest magnetic moment value?

\([Fe(H_2O)_6]^{2+}\)

The correct answer is option 3. \([Fe(H_2O)_6]^{2+}\).

To arrange the given complexes in the increasing order of their magnetic behaviour we have find the values of magnetic moment of each of the given complexes.

We know the value of magnetic moment can be calculated using the formula:

\(\mu = \sqrt{n (n + 2)}\); where,  n = number of unpaired electrons.

1. \(K[Co(CO)_4]\):

Here, the central metal ion, \(Co\) is in \(+3\) oxidation state. So, the configuration will be

\(Co^{3+} = [_{18}Ar] 4s^0 3d^7\)

\(CO\) is a strong field ligand and so pairing of electrons occur.

So, the number of unpaired electrons, \(n = 1\)

Thus the magnetic moment will be

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

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

or, \(\mu = 1.73 BM\)

2. \(K_4[Mn(CN)_6]\):

Here, the central metal ion, \(Mn\) is in \(+2\) oxidation state. So, the configuration will be

\(Mn^{2+} = [_{18}Ar] 4s^0 3d^5\)

\(CN\) is a strong field ligand and so pairing of electrons occur.

So, the number of unpaired electrons, \(n = 1\)

Thus the magnetic moment will be

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

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

or, \(\mu = 1.73 BM\)

3. \([Fe(H_2O)_6]^{2+}\):

Here, the central metal ion, \(Fe\) is in \(+2\) oxidation state. So, the configuration will be

\(Fe^{2+} = [_{18}Ar] 4s^0 3d^6\)

\(H_2O\) is a weak field ligand and so pairing of electrons occur does not.

So, the number of unpaired electrons, \(n = 4\)

Thus the magnetic moment will be

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

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

or, \(\mu = 4.9 BM\)

4. \([Cr(H_2O)_6]^{3+}\):

Here, the central metal ion, \(Cr\) is in \(+3\) oxidation state. So, the configuration will be

\(Cr^{3+} = [_{18}Ar] 4s^0 3d^3\)

\(H_2O\) is a weak field ligand and so pairing of electrons occur does not.

So, the number of unpaired electrons, \(n = 3\)

Thus the magnetic moment will be

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

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

or, \(\mu = 3.87 BM\)

So, the complex with the highest magnetic moment is \([Fe(H_2O)_6]^{2+}\)