Given following complexes
`(I) Na_4[Fe(CN)_6] (II) [Cr(H_2O)_6] Cl_2 (III) (NEt_4)_2 [CoCl_4] (IV) Na_3[Fe(C_2O_4)_3] (Delta_0 gt P)`
Correct order of spin only magnetic moment for the above complexes is

Options

A. `(II) gt (III) gt (IV) gt I`
B. `(II) gt (IV) gt (III) gt (I)`
C. `(I) gt (IV) gt (III) gt (II)`
D. `(II) gt (I) gt (IV) gt (III)`

Answer

To determine the correct order of spin-only magnetic moments for the given complexes, we will analyze each complex step by step, find the oxidation states, electronic configurations, and then calculate the magnetic moments.

### Step 1: Analyze Complex (I) Na₄[Fe(CN)₆]

1. **Determine the oxidation state of Iron (Fe)**:
- Sodium (Na) has a +1 charge, so 4 Na contributes +4.
- The complex ion [Fe(CN)₆] has an overall charge of -4.
- Let the oxidation state of Fe be \( x \):
\[ x + 6(-1) = -4 \implies x - 6 = -4 \implies x = +2 \]

2. **Electronic configuration of Fe²⁺**:
- Fe (atomic number 26) has the configuration [Ar] 3d⁶ 4s².
- For Fe²⁺, it loses two electrons (from 4s), resulting in 3d⁶.

3. **Determine the geometry and field strength**:
- CN⁻ is a strong field ligand, leading to pairing of electrons.
- The electron filling in the d-orbitals will be:
\[ \text{t}_{2g}^6 \text{e}_g^0 \]
- **Number of unpaired electrons**: 0.

4. **Calculate magnetic moment**:
\[ \mu = \sqrt{n(n+2)} = \sqrt{0(0+2)} = 0 \]

### Step 2: Analyze Complex (II) [Cr(H₂O)₆]Cl₂

1. **Determine the oxidation state of Chromium (Cr)**:
- Water (H₂O) is neutral, and Cl⁻ has a -1 charge.
- Let the oxidation state of Cr be \( x \):
\[ x + 6(0) + 2(-1) = 0 \implies x - 2 = 0 \implies x = +2 \]

2. **Electronic configuration of Cr²⁺**:
- Cr (atomic number 24) has the configuration [Ar] 3d⁵ 4s¹.
- For Cr²⁺, it loses one 4s and one 3d electron, resulting in 3d⁴.

3. **Determine the geometry and field strength**:
- H₂O is a weak field ligand, leading to no pairing.
- The electron filling in the d-orbitals will be:
\[ \text{t}_{2g}^3 \text{e}_g^1 \]
- **Number of unpaired electrons**: 4.

4. **Calculate magnetic moment**:
\[ \mu = \sqrt{n(n+2)} = \sqrt{4(4+2)} = \sqrt{24} \approx 4.9 \, \mu_B \]

### Step 3: Analyze Complex (III) (NEt₄)₂[CoCl₄]

1. **Determine the oxidation state of Cobalt (Co)**:
- The complex ion [CoCl₄] has a -2 charge.
- Let the oxidation state of Co be \( x \):
\[ x + 4(-1) = -2 \implies x - 4 = -2 \implies x = +2 \]

2. **Electronic configuration of Co²⁺**:
- Co (atomic number 27) has the configuration [Ar] 3d⁷ 4s².
- For Co²⁺, it loses two electrons (from 4s), resulting in 3d⁷.

3. **Determine the geometry and field strength**:
- Cl⁻ is a weak field ligand, leading to no pairing.
- The electron filling in the d-orbitals will be:
\[ \text{t}_{2g}^5 \text{e}_g^2 \]
- **Number of unpaired electrons**: 3.

4. **Calculate magnetic moment**:
\[ \mu = \sqrt{n(n+2)} = \sqrt{3(3+2)} = \sqrt{15} \approx 3.87 \, \mu_B \]

### Step 4: Analyze Complex (IV) Na₃[Fe(C₂O₄)₃]

1. **Determine the oxidation state of Iron (Fe)**:
- Oxalate (C₂O₄) has a -2 charge and there are 3 oxalate ligands.
- Let the oxidation state of Fe be \( x \):
\[ x + 3(-2) = -3 \implies x - 6 = -3 \implies x = +3 \]

2. **Electronic configuration of Fe³⁺**:
- For Fe³⁺, it loses three electrons (from 4s and 3d), resulting in 3d⁵.

3. **Determine the geometry and field strength**:
- Oxalate is a bidentate ligand and a strong field ligand (given that \( \Delta_0 > P \)).
- The electron filling in the d-orbitals will be:
\[ \text{t}_{2g}^5 \text{e}_g^0 \]
- **Number of unpaired electrons**: 1.

4. **Calculate magnetic moment**:
\[ \mu = \sqrt{n(n+2)} = \sqrt{1(1+2)} = \sqrt{3} \approx 1.73 \, \mu_B \]

### Summary of Magnetic Moments
- Complex (I): \( \mu = 0 \)
- Complex (II): \( \mu \approx 4.9 \)
- Complex (III): \( \mu \approx 3.87 \)
- Complex (IV): \( \mu \approx 1.73 \)

### Correct Order of Spin-Only Magnetic Moments
From the calculated values:
1. Complex (II) > Complex (III) > Complex (IV) > Complex (I)

Thus, the correct order of spin-only magnetic moments is:
**(II) > (III) > (IV) > (I)**