The complex 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. `|Ni(CN)_(4)|^(2-)`

Explanation

To determine which complex has the highest magnetic moment, we need to analyze the number of unpaired electrons in each complex and then calculate the magnetic moment using the formula:

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

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

### Step-by-Step Solution

1. **Identify the complexes and their oxidation states:**
- Option 1: Cobalt hexafluoride \( [CoF_6]^{3-} \)
- Option 2: Cobalt ammine \( [Co(NH_3)_6]^{3+} \)
- Option 3: Nickel ammine \( [Ni(NH_3)_4]^{2+} \)
- Option 4: Nickel tetracyanide \( [Ni(CN)_4]^{2-} \)

2. **Determine the oxidation state and electronic configuration:**
- **Cobalt in \( [CoF_6]^{3-} \)**:
- Oxidation state: +3
- Electronic configuration of Co: \( [Ar] 4s^2 3d^7 \)
- For Co\(^{3+}\): Remove 2 from 4s and 1 from 3d → \( 3d^6 \)
- Fluoride is a weak field ligand, so no pairing occurs.
- Unpaired electrons: 4

- **Cobalt in \( [Co(NH_3)_6]^{3+} \)**:
- Oxidation state: +3
- Electronic configuration: \( 3d^6 \)
- Ammonia is a strong field ligand, causing pairing.
- Unpaired electrons: 0

- **Nickel in \( [Ni(NH_3)_4]^{2+} \)**:
- Oxidation state: +2
- Electronic configuration of Ni: \( [Ar] 4s^2 3d^8 \)
- For Ni\(^{2+}\): Remove 2 from 4s → \( 3d^8 \)
- Ammonia is a strong field ligand, causing pairing.
- Unpaired electrons: 0

- **Nickel in \( [Ni(CN)_4]^{2-} \)**:
- Oxidation state: +2
- Electronic configuration: \( 3d^8 \)
- Cyanide is a strong field ligand, causing pairing.
- Unpaired electrons: 0

3. **Calculate the magnetic moment for each complex:**
- For \( [CoF_6]^{3-} \):
\[ \mu = \sqrt{4(4 + 2)} = \sqrt{24} \approx 4.9 \, \text{Bohr magnetons} \]
- For \( [Co(NH_3)_6]^{3+} \):
\[ \mu = \sqrt{0(0 + 2)} = 0 \]
- For \( [Ni(NH_3)_4]^{2+} \):
\[ \mu = \sqrt{0(0 + 2)} = 0 \]
- For \( [Ni(CN)_4]^{2-} \):
\[ \mu = \sqrt{0(0 + 2)} = 0 \]

4. **Conclusion:**
- The complex with the highest magnetic moment is \( [CoF_6]^{3-} \) with a magnetic moment of approximately 4.9 Bohr magnetons.

### Final Answer:
The complex which has the highest magnetic moment among the following is \( [CoF_6]^{3-} \).