The correct order of magnetic moment (spin values in is .
(Atomic number `Mn=25,Fe=26,Co=27)`
(I) `[MnBr_(4)]^(2-)`(II)`[Fe(CN)_(6)]^(4-)` (III) `[CoBr_(4)]^(2-)` .

Options

A. `IIgtIIIgtI`
B. `IgtIIgtIII`
C. `IIgtIgtIII`
D. `IgtIIIgtII`

Explanation

To determine the correct order of magnetic moments for the given coordination compounds, we will analyze each complex step by step.

### Step 1: Analyze `[MnBr_(4)]^(2-)`
1. **Determine the oxidation state of Mn**:
- Let the oxidation state of Mn be \( x \).
- The charge of bromide (Br) is -1 and there are 4 bromide ions.
- The overall charge of the complex is -2.
- Therefore, the equation is:
\[ x + 4(-1) = -2 \implies x - 4 = -2 \implies x = +2 \]
- Thus, Mn is in the +2 oxidation state.

2. **Electron configuration**:
- The atomic number of Mn is 25. The electron configuration is \( [Ar] 4s^2 3d^5 \).
- For Mn in the +2 state, it loses 2 electrons from the 4s orbital:
\[ \text{Configuration: } 4s^0 3d^5 \]

3. **Count unpaired electrons**:
- There are 5 unpaired electrons in the \( 3d \) subshell.

4. **Calculate magnetic moment**:
- Using the formula \( \mu = \sqrt{n(n+2)} \), where \( n \) is the number of unpaired electrons:
\[ \mu = \sqrt{5(5+2)} = \sqrt{35} \]

### Step 2: Analyze `[Fe(CN)_(6)]^(4-)`
1. **Determine the oxidation state of Fe**:
- Let the oxidation state of Fe be \( x \).
- The charge of CN is -1 and there are 6 cyanide ions.
- The overall charge of the complex is -4.
- Therefore, the equation is:
\[ x + 6(-1) = -4 \implies x - 6 = -4 \implies x = +2 \]
- Thus, Fe is in the +2 oxidation state.

2. **Electron configuration**:
- The atomic number of Fe is 26. The electron configuration is \( [Ar] 4s^2 3d^6 \).
- For Fe in the +2 state, it loses 2 electrons from the 4s orbital:
\[ \text{Configuration: } 4s^0 3d^6 \]

3. **Count unpaired electrons**:
- CN is a strong field ligand, which causes pairing of electrons. The configuration becomes:
\[ 3d: \uparrow\downarrow \uparrow\downarrow \uparrow\downarrow \uparrow \]
- There are 4 unpaired electrons.

4. **Calculate magnetic moment**:
- Using the formula:
\[ \mu = \sqrt{4(4+2)} = \sqrt{24} \]

### Step 3: Analyze `[CoBr_(4)]^(2-)`
1. **Determine the oxidation state of Co**:
- Let the oxidation state of Co be \( x \).
- The charge of Br is -1 and there are 4 bromide ions.
- The overall charge of the complex is -2.
- Therefore, the equation is:
\[ x + 4(-1) = -2 \implies x - 4 = -2 \implies x = +2 \]
- Thus, Co is in the +2 oxidation state.

2. **Electron configuration**:
- The atomic number of Co is 27. The electron configuration is \( [Ar] 4s^2 3d^7 \).
- For Co in the +2 state, it loses 2 electrons from the 4s orbital:
\[ \text{Configuration: } 4s^0 3d^7 \]

3. **Count unpaired electrons**:
- Br is a weak field ligand, so there will be no pairing:
\[ 3d: \uparrow \uparrow \uparrow \uparrow \uparrow \uparrow \uparrow \]
- There are 3 unpaired electrons.

4. **Calculate magnetic moment**:
- Using the formula:
\[ \mu = \sqrt{3(3+2)} = \sqrt{15} \]

### Summary of Magnetic Moments
1. **[MnBr_(4)]^(2-)**: \( \mu = \sqrt{35} \) (5 unpaired electrons)
2. **[Fe(CN)_(6)]^(4-)**: \( \mu = \sqrt{24} \) (4 unpaired electrons)
3. **[CoBr_(4)]^(2-)**: \( \mu = \sqrt{15} \) (3 unpaired electrons)

### Final Order of Magnetic Moments
The correct order of magnetic moments from highest to lowest is:
1. **[MnBr_(4)]^(2-)** > **[Fe(CN)_(6)]^(4-)** > **[CoBr_(4)]^(2-)**