Which of the following outer orbital complex has the highest magnetic moment ?

Options

A. `[Mn(NH_3)_6]Cl_3`
B. `[Cr(NH_3)_6]Cl_3`
C. `[Ni(CO)_4]`
D. `[Co(CN)_6]^(4-)`

Answer

To determine which outer orbital complex has the highest magnetic moment, we need to analyze the number of unpaired electrons in each complex. The magnetic moment is directly related to the number of unpaired electrons, with more unpaired electrons resulting in a higher magnetic moment.

### Step-by-Step Solution:

1. **Identify the complexes and their oxidation states**:
- **Manganese complex**: Manganese with ammonia and 3 Cl⁻.
- Oxidation state: \( +3 \) (since ammonia is neutral and Cl⁻ contributes -3).
- **Chromium complex**: Chromium with ammonia and 3 Cl⁻.
- Oxidation state: \( +3 \).
- **Nickel complex**: Nickel with carbonyl (CO).
- Oxidation state: \( 0 \) (since CO is neutral).
- **Cobalt complex**: Cobalt with cyanide (CN⁻).
- Oxidation state: \( +2 \) (since CN⁻ contributes -6).

2. **Determine the electron configuration for each metal in its oxidation state**:
- **Manganese (Mn)**: Atomic number 25, configuration \( [Ar] 3d^5 4s^2 \).
- In \( +3 \) state: \( 3d^4 \) (removing 2 electrons from 4s and 1 from 3d).
- **Chromium (Cr)**: Atomic number 24, configuration \( [Ar] 3d^5 4s^2 \).
- In \( +3 \) state: \( 3d^3 \) (removing 2 electrons from 4s and 1 from 3d).
- **Nickel (Ni)**: Atomic number 28, configuration \( [Ar] 3d^8 4s^2 \).
- In \( 0 \) state: \( 3d^8 \) (no electrons removed).
- **Cobalt (Co)**: Atomic number 27, configuration \( [Ar] 3d^7 4s^2 \).
- In \( +2 \) state: \( 3d^7 \) (removing 2 electrons from 4s).

3. **Count the number of unpaired electrons for each complex**:
- **Manganese (Mn)**: \( 3d^4 \) → 4 unpaired electrons.
- **Chromium (Cr)**: \( 3d^3 \) → 3 unpaired electrons.
- **Nickel (Ni)**: \( 3d^8 \) → 2 unpaired electrons.
- **Cobalt (Co)**: \( 3d^7 \) → 3 unpaired electrons.

4. **Determine the magnetic moment**:
- The magnetic moment can be calculated using the formula:
\[ \mu = \sqrt{n(n+2)} \]
where \( n \) is the number of unpaired electrons.
- For **Manganese**: \( \mu = \sqrt{4(4+2)} = \sqrt{24} \).
- For **Chromium**: \( \mu = \sqrt{3(3+2)} = \sqrt{15} \).
- For **Nickel**: \( \mu = \sqrt{2(2+2)} = \sqrt{8} \).
- For **Cobalt**: \( \mu = \sqrt{3(3+2)} = \sqrt{15} \).

5. **Conclusion**:
- The complex with the highest magnetic moment is the **Manganese complex** with 4 unpaired electrons.

### Final Answer:
The outer orbital complex with the highest magnetic moment is the **Manganese complex**.