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 find the number of unpaired electrons in each complex. The magnetic moment (μ) can be calculated using the formula:

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

where \( n \) is the number of unpaired electrons. The complex with the highest number of unpaired electrons will have the highest magnetic moment.

### Step-by-Step Solution:

1. **Identify the Complexes:**
We have the following complexes to analyze:
- \( \text{CoF}_6^{3-} \)
- \( \text{Co(NH}_3)_6^{3+} \)
- \( \text{Ni(NH}_3)_4^{2+} \)
- \( \text{Fe(CN)}_6^{4-} \)

2. **Calculate the Oxidation State and Electron Configuration:**
- **For \( \text{CoF}_6^{3-} \):**
- Let the oxidation state of Co be \( x \).
- \( x + 6(-1) = -3 \) → \( x - 6 = -3 \) → \( x = +3 \)
- Cobalt in +3 state has the configuration \( [Ar] 3d^6 \).
- Fluoride is a weak field ligand, so it does not cause pairing. The configuration will be \( t_{2g}^4 e_g^2 \) → 4 unpaired electrons.

- **For \( \text{Co(NH}_3)_6^{3+} \):**
- Oxidation state of Co: \( x + 6(0) = +3 \) → \( x = +3 \)
- Configuration: \( [Ar] 3d^6 \).
- Ammonia is a strong field ligand, so it causes pairing. The configuration will be \( t_{2g}^6 \) → 0 unpaired electrons.

- **For \( \text{Ni(NH}_3)_4^{2+} \):**
- Oxidation state of Ni: \( x + 4(0) = +2 \) → \( x = +2 \)
- Configuration: \( [Ar] 3d^8 \).
- Ammonia is a weak field ligand, and the configuration will be tetrahedral. The arrangement will be \( 3d^8 \) → 2 unpaired electrons.

- **For \( \text{Fe(CN)}_6^{4-} \):**
- Oxidation state of Fe: \( x + 6(-1) = -4 \) → \( x - 6 = -4 \) → \( x = +2 \)
- Configuration: \( [Ar] 3d^6 \).
- Cyanide is a strong field ligand, so it causes pairing. The configuration will be \( t_{2g}^6 \) → 0 unpaired electrons.

3. **Count the Unpaired Electrons:**
- \( \text{CoF}_6^{3-} \): 4 unpaired electrons
- \( \text{Co(NH}_3)_6^{3+} \): 0 unpaired electrons
- \( \text{Ni(NH}_3)_4^{2+} \): 2 unpaired electrons
- \( \text{Fe(CN)}_6^{4-} \): 0 unpaired electrons

4. **Determine the Complex with the Highest Magnetic Moment:**
The complex with the highest number of unpaired electrons is \( \text{CoF}_6^{3-} \) with 4 unpaired electrons.

### Conclusion:
The complex ion which has the highest magnetic moment among the given options is \( \text{CoF}_6^{3-} \).