The correct order of magnetic moments (spin values in B.M.) among is:

Options

A. `[Fe(CN)_(6)]^(4-) gt [ClCl_(4)]^(2-) gt [MnCl_(4)]^(2-)`
B. `[MnCl_(4)]^(2-) gt [Fr(CN)_(6)]^(4-) gt [CoCl_(4)]^(2-)`
C. `[Fe(CN)_(6)]^(4-) gt [MnCl_(4)]^(2-) gt {CoCl_(4)]^(2-)`
D. `[MnCl_(4)]^(2-) gt [CoCl_(4)]^(2-) gt [Fe(CN)_(6)]^(4-)`

Answer

To determine the correct order of magnetic moments among the given coordination compounds, we will follow these steps:

### Step 1: Identify the Coordination Compounds
We have three coordination compounds to analyze:
1. \( \text{[Fe(CN)}_6]^{4-} \)
2. \( \text{[CoCl}_4]^{2-} \)
3. \( \text{[MnCl}_4]^{2+} \)

### Step 2: Determine the Oxidation States and Electron Configurations
1. **For \( \text{[Fe(CN)}_6]^{4-} \)**:
- Oxidation state of Fe: \( x + 6(-1) = -4 \) → \( x = +2 \)
- Electron configuration of \( \text{Fe}^{2+} \): \( [Ar] 3d^6 \)

2. **For \( \text{[CoCl}_4]^{2-} \)**:
- Oxidation state of Co: \( x + 4(-1) = -2 \) → \( x = +2 \)
- Electron configuration of \( \text{Co}^{2+} \): \( [Ar] 3d^7 \)

3. **For \( \text{[MnCl}_4]^{2+} \)**:
- Oxidation state of Mn: \( x + 4(-1) = +2 \) → \( x = +2 \)
- Electron configuration of \( \text{Mn}^{2+} \): \( [Ar] 3d^5 \)

### Step 3: Determine the Number of Unpaired Electrons
1. **For \( \text{[Fe(CN)}_6]^{4-} \)**:
- \( \text{CN}^- \) is a strong field ligand, leading to pairing of electrons.
- Configuration: \( 3d^6 \) → All electrons are paired.
- Unpaired electrons = 0.

2. **For \( \text{[CoCl}_4]^{2-} \)**:
- \( \text{Cl}^- \) is a weak field ligand, resulting in unpaired electrons.
- Configuration: \( 3d^7 \) → 3 unpaired electrons.
- Unpaired electrons = 3.

3. **For \( \text{[MnCl}_4]^{2+} \)**:
- \( \text{Cl}^- \) is also a weak field ligand.
- Configuration: \( 3d^5 \) → 5 unpaired electrons.
- Unpaired electrons = 5.

### Step 4: Calculate the Magnetic Moments
The magnetic moment (\( \mu \)) can be calculated using the formula:
\[ \mu = \sqrt{n(n + 2)} \text{ B.M.} \]
where \( n \) is the number of unpaired electrons.

1. **For \( \text{[Fe(CN)}_6]^{4-} \)**:
- \( n = 0 \)
- \( \mu = \sqrt{0(0 + 2)} = 0 \text{ B.M.} \)

2. **For \( \text{[CoCl}_4]^{2-} \)**:
- \( n = 3 \)
- \( \mu = \sqrt{3(3 + 2)} = \sqrt{15} \approx 3.87 \text{ B.M.} \)

3. **For \( \text{[MnCl}_4]^{2+} \)**:
- \( n = 5 \)
- \( \mu = \sqrt{5(5 + 2)} = \sqrt{35} \approx 5.92 \text{ B.M.} \)

### Step 5: Arrange the Compounds in Increasing Order of Magnetic Moments
Based on the calculated magnetic moments:
1. \( \text{[Fe(CN)}_6]^{4-} \): 0 B.M.
2. \( \text{[CoCl}_4]^{2-} \): \( \sqrt{15} \approx 3.87 \) B.M.
3. \( \text{[MnCl}_4]^{2+} \): \( \sqrt{35} \approx 5.92 \) B.M.

### Final Order
The correct order of magnetic moments is:
\[ \text{[Fe(CN)}_6]^{4-} < \text{[CoCl}_4]^{2-} < \text{[MnCl}_4]^{2+} \]