Which of the following has the highest magnetic moment?

Question

Accepted Answer

The question asks which of the given complexes has the highest magnetic moment. The correct answer is Option 3: $[FeF_{6}]^{3-}$. Let's provide a detailed explanation to justify why this is the correct choice and why the other options are incorrect.

1. **Explanation for Option 3: $[FeF_{6}]^{3-}$**
   - The magnetic moment of a complex is determined by the number of unpaired electrons present in the metal ion. In $[FeF_{6}]^{3-}$, the central metal ion is Fe(III), which has an electronic configuration of $3d^5$. Fluoride (F-) is a weak field ligand, which means it does not cause significant splitting of the d-orbitals. As a result, all five d-electrons remain unpaired. The magnetic moment can be calculated using the formula $\mu = \sqrt{n(n+2)}$, where n is the number of unpaired electrons. For $[FeF_{6}]^{3-}$, n = 5, so the magnetic moment is $\mu = \sqrt{5(5+2)} = \sqrt{35}$, which is relatively high.

2. **Explanation for Option 1: $[Mn(CN)_{6}]^{3-}$**
   - In $[Mn(CN)_{6}]^{3-}$, the central metal ion is Mn(III), which has an electronic configuration of $3d^4$. Cyanide (CN-) is a strong field ligand, which causes significant splitting of the d-orbitals and leads to pairing of electrons. As a result, the number of unpaired electrons is reduced, typically resulting in a lower magnetic moment compared to complexes with weak field ligands.

3. **Explanation for Option 2: $[Fe(CN)_{6}]^{3-}$**
   - In $[Fe(CN)_{6}]^{3-}$, the central metal ion is Fe(III), with an electronic configuration of $3d^5$. Cyanide (CN-) is a strong field ligand, causing significant splitting and pairing of electrons. This results in fewer unpaired electrons compared to $[FeF_{6}]^{3-}$, leading to a lower magnetic moment.

4. **Explanation for Option 4: $[CoF_{6}]^{3-}$**
   - In $[CoF_{6}]^{3-}$, the central metal ion is Co(III), which has an electronic configuration of $3d^6$. Fluoride (F-) is a weak field ligand, but with six d-electrons, some pairing occurs even with weak field ligands. This results in fewer unpaired electrons compared to $[FeF_{6}]^{3-}$, leading to a lower magnetic moment.

In conclusion, $[FeF_{6}]^{3-}$ has the highest magnetic moment due to the presence of five unpaired electrons, which is more than any of the other complexes listed. This is why Option 3 is the correct answer.