To determine which of the given complexes shows a magnetic moment of 5.91 Bohr Magnetons (BM), we need to find the number of unpaired electrons in each complex. A magnetic moment of 5.91 BM corresponds to 5 unpaired electrons, as the magnetic moment (μ) can be calculated using the formula:
\[
\mu = \sqrt{n(n + 2)}
\]
where \( n \) is the number of unpaired electrons. For \( n = 5 \):
\[
\mu = \sqrt{5(5 + 2)} = \sqrt{5 \times 7} = \sqrt{35} \approx 5.91 \text{ BM}
\]
Now, let's analyze each complex step by step:
### Step 1: Analyze the first complex (assumed to be Ni(CO)4)
- Nickel (Ni) has an atomic number of 28, with an electron configuration of \( [Ar] 4s^2 3d^8 \).
- In the presence of CO (a strong field ligand), the electrons will pair up in the d-orbitals.
- Thus, the configuration will be \( 4s^0 3d^{10} \) with **0 unpaired electrons**.
### Step 2: Analyze the second complex (FeF6)³⁻
- For FeF6³⁻, we calculate the oxidation state of iron:
- Let \( x \) be the oxidation state of iron. Fluorine has a charge of -1, and there are 6 fluorines, so:
\[
x + 6(-1) = -3 \implies x - 6 = -3 \implies x = +3
\]
- Iron in the +3 oxidation state has the configuration \( [Ar] 4s^0 3d^5 \).
- Since F is a weak field ligand, the electrons do not pair up, leaving us with **5 unpaired electrons**.
### Step 3: Analyze the third complex (Fe(CN)6)³⁻
- For Fe(CN)6³⁻, again calculate the oxidation state of iron:
- Let \( x \) be the oxidation state of iron. CN has a charge of -1, and there are 6 CN ligands, so:
\[
x + 6(-1) = -3 \implies x - 6 = -3 \implies x = +3
\]
- Iron in the +3 oxidation state has the configuration \( [Ar] 4s^0 3d^5 \).
- However, CN is a strong field ligand, which causes pairing of electrons. Thus, the configuration will be \( 3d^6 \) with **1 unpaired electron**.
### Step 4: Analyze the fourth complex (Cr³⁺)
- For Cr³⁺, chromium has an atomic number of 24, with an electron configuration of \( [Ar] 4s^1 3d^5 \).
- In the +3 oxidation state, the configuration becomes \( 3d^3 \).
- Since we are considering a strong field ligand, the electrons will pair up, resulting in **3 unpaired electrons**.
### Conclusion
After analyzing all complexes, we find that only the second complex (FeF6)³⁻ has 5 unpaired electrons, which corresponds to a magnetic moment of 5.91 BM. Thus, the answer is:
**Answer: FeF6³⁻ (Option 2)**
