Which of the following complex show magnetic moment = 5.91 BM

Options

A. `[Ni(CO)_4]`
B. `[FeF_6]^(3-)`
C. `[Fe(CN)_6]^(3-)`
D. `[Cr(H_2O)_6]^(3+)`

Answer

To solve the problem of determining which complex shows a magnetic moment of 5.91 BM, we will analyze each complex step by step.

### Step 1: Identify the complexes and their oxidation states

We have the following complexes to analyze:
1. Ni(CO)4
2. FeF6^3-
3. Fe(CN)6^3-
4. Cr(H2O)6^3+

#### Complex 1: Ni(CO)4
- **Oxidation State of Ni**: Since CO is a neutral ligand, the oxidation state of Ni is 0.
- **Electron Configuration of Ni**: Ni has an electron configuration of [Ar] 3d^8 4s^2.
- **Unpaired Electrons**: In the presence of CO (a strong field ligand), pairing occurs. Thus, all 8 d-electrons will pair up, resulting in 0 unpaired electrons.
- **Magnetic Moment**:
\[ \mu = \sqrt{n(n+2)} = \sqrt{0(0+2)} = 0 \text{ BM} \]

#### Complex 2: FeF6^3-
- **Oxidation State of Fe**:
\[ x + 6(-1) = -3 \implies x - 6 = -3 \implies x = +3 \]
- **Electron Configuration of Fe**: Fe has an electron configuration of [Ar] 3d^6 4s^2. In the +3 oxidation state, it loses 3 electrons (2 from 4s and 1 from 3d), resulting in 3d^5.
- **Unpaired Electrons**: F is a weak field ligand, so the 5 d-electrons will remain unpaired.
- **Magnetic Moment**:
\[ \mu = \sqrt{5(5+2)} = \sqrt{35} \approx 5.92 \text{ BM} \]

#### Complex 3: Fe(CN)6^3-
- **Oxidation State of Fe**:
\[ x + 6(-1) = -3 \implies x - 6 = -3 \implies x = +3 \]
- **Electron Configuration of Fe**: As above, Fe is in the +3 state with a configuration of 3d^5.
- **Unpaired Electrons**: CN is a strong field ligand, leading to pairing of electrons. Thus, there will be 1 unpaired electron.
- **Magnetic Moment**:
\[ \mu = \sqrt{1(1+2)} = \sqrt{3} \approx 1.73 \text{ BM} \]

#### Complex 4: Cr(H2O)6^3+
- **Oxidation State of Cr**:
\[ x + 6(0) = +3 \implies x = +3 \]
- **Electron Configuration of Cr**: Cr has an electron configuration of [Ar] 3d^5 4s^1. In the +3 state, it becomes 3d^3.
- **Unpaired Electrons**: H2O is a weak field ligand, so the 3 d-electrons will remain unpaired.
- **Magnetic Moment**:
\[ \mu = \sqrt{3(3+2)} = \sqrt{15} \approx 3.87 \text{ BM} \]

### Conclusion
From our calculations, the only complex that shows a magnetic moment of approximately 5.91 BM is **FeF6^3-**.

### Final Answer
The complex that shows a magnetic moment of 5.91 BM is **FeF6^3-**.