The complex ion which has the highest magnetic moment among the following is

Options

A. `[CoF_6]^(3-)`
B. `[Co(NH_3)_6]^(3+)`
C. `[Ni(NH_3)_4]^(2+)`
D. `[Fe(CN)_6]^(4-)`

Answer

To determine which complex ion has the highest magnetic moment, we need to analyze each complex and calculate the number of unpaired electrons. The magnetic moment (μ) can be calculated using the formula:

\[ \mu = \sqrt{n(n + 2)} \]

where \(n\) is the number of unpaired electrons.

### Step-by-Step Solution:

1. **Identify the Complex Ions and Their Oxidation States:**
- **CuF6^3-**:
- Let the oxidation state of Cu be \(x\).
- The equation is \(x + 6(-1) = -3\) → \(x - 6 = -3\) → \(x = +3\).
- Thus, Cu is in the +3 oxidation state.

- **Co(NH3)6^3+**:
- NH3 is a neutral ligand, so the oxidation state of Co is also +3.

- **Ni(NH3)4^2+**:
- The oxidation state of Ni is +2.

- **Fe(CN)6^4-**:
- The oxidation state of Fe is +2 (since CN is -1 and there are 6 CN ligands: \(x + 6(-1) = -4\) → \(x - 6 = -4\) → \(x = +2\)).

2. **Determine the Electronic Configuration:**
- **Cu^3+**:
- Atomic number of Cu = 29.
- Electronic configuration: [Ar] 4s^2 3d^9 → 3d^9 loses 3 electrons → 3d^9.
- In 3d^9, there are 1 unpaired electron.

- **Co^3+**:
- Atomic number of Co = 27.
- Electronic configuration: [Ar] 4s^2 3d^7 → 3d^6 after losing 3 electrons.
- NH3 is a strong field ligand, so pairing occurs → 0 unpaired electrons.

- **Ni^2+**:
- Atomic number of Ni = 28.
- Electronic configuration: [Ar] 4s^2 3d^8 → 3d^8 after losing 2 electrons.
- NH3 is a strong field ligand, so pairing occurs → 0 unpaired electrons.

- **Fe^2+**:
- Atomic number of Fe = 26.
- Electronic configuration: [Ar] 4s^2 3d^6 → 3d^6 after losing 2 electrons.
- CN is a strong field ligand, so pairing occurs → 0 unpaired electrons.

3. **Count the Number of Unpaired Electrons:**
- **CuF6^3-**: 1 unpaired electron.
- **Co(NH3)6^3+**: 0 unpaired electrons.
- **Ni(NH3)4^2+**: 0 unpaired electrons.
- **Fe(CN)6^4-**: 0 unpaired electrons.

4. **Calculate the Magnetic Moment for Each Complex:**
- **CuF6^3-**:
- \(n = 1\) → \(\mu = \sqrt{1(1 + 2)} = \sqrt{3} \approx 1.73\) Bohr magnetons.
- **Co(NH3)6^3+**:
- \(n = 0\) → \(\mu = 0\).
- **Ni(NH3)4^2+**:
- \(n = 0\) → \(\mu = 0\).
- **Fe(CN)6^4-**:
- \(n = 0\) → \(\mu = 0\).

5. **Conclusion:**
- The complex ion with the highest magnetic moment is **CuF6^3-** with a magnetic moment of approximately 1.73 Bohr magnetons.

### Final Answer:
The complex ion which has the highest magnetic moment among the following is **CuF6^3-**.