The magnetic moment of complex given below are in the order:
(I) `[Ni(CO)_(4)]`
(II) `[Mn(CN)_(6)]^(4-)`
(III) `[Cr(NH_(3))_(6)]^(3+)`
(IV) `[CoF_(6)]^(3-)`

Options

A. IgtIIgtIIIgtIV
B. `I lt II lt III lt IV`
C. `IV t II gt I gt III`
D. `IV lt II lt I lt III`

Answer

To determine the magnetic moments of the given coordination complexes, we will analyze each complex step by step, calculating the oxidation states, electron configurations, and the number of unpaired electrons. The magnetic moment (μ) can be calculated using the formula:

\[ \mu = \sqrt{n(n + 2)} \]

where \(n\) is the number of unpaired electrons.

### Step 1: Analyze `[Ni(CO)₄]`

1. **Determine Oxidation State**:
- CO is a neutral ligand.
- Therefore, the oxidation state of Ni in `[Ni(CO)₄]` is 0.

2. **Electron Configuration**:
- Ground state configuration of Ni: \([Ar] 4s^2 3d^8\).

3. **Hybridization**:
- CO is a strong field ligand, causing pairing of electrons.
- The configuration after pairing: \(3d^{10}\) (all d-electrons are paired).
- Hybridization: \(sp^3\).

4. **Unpaired Electrons**:
- Number of unpaired electrons = 0.

5. **Magnetic Moment**:
\[ \mu = \sqrt{0(0 + 2)} = 0 \]

### Step 2: Analyze `[Mn(CN)₆]^{4-}`

1. **Determine Oxidation State**:
- CN is a -1 ligand.
- Let the oxidation state of Mn be \(x\):
\[ x + 6(-1) = -4 \implies x - 6 = -4 \implies x = +2 \]

2. **Electron Configuration**:
- Ground state configuration of Mn: \([Ar] 4s^2 3d^5\).
- After losing 2 electrons (from 4s): \(3d^5\).

3. **Hybridization**:
- CN is a strong field ligand, causing pairing.
- Configuration after pairing: \(3d^5\) (no pairing occurs in this case).
- Hybridization: \(d^2sp^3\).

4. **Unpaired Electrons**:
- Number of unpaired electrons = 5.

5. **Magnetic Moment**:
\[ \mu = \sqrt{5(5 + 2)} = \sqrt{35} \]

### Step 3: Analyze `[Cr(NH₃)₆]^{3+}`

1. **Determine Oxidation State**:
- NH₃ is a neutral ligand.
- Let the oxidation state of Cr be \(x\):
\[ x = +3 \]

2. **Electron Configuration**:
- Ground state configuration of Cr: \([Ar] 4s^2 3d^5\).
- After losing 3 electrons: \(3d^3\).

3. **Hybridization**:
- NH₃ is a weak field ligand, so no pairing occurs.
- Configuration: \(3d^3\).
- Hybridization: \(d^2sp^3\).

4. **Unpaired Electrons**:
- Number of unpaired electrons = 3.

5. **Magnetic Moment**:
\[ \mu = \sqrt{3(3 + 2)} = \sqrt{15} \]

### Step 4: Analyze `[CoF₆]^{3-}`

1. **Determine Oxidation State**:
- F is a -1 ligand.
- Let the oxidation state of Co be \(x\):
\[ x + 6(-1) = -3 \implies x - 6 = -3 \implies x = +3 \]

2. **Electron Configuration**:
- Ground state configuration of Co: \([Ar] 4s^2 3d^7\).
- After losing 3 electrons: \(3d^6\).

3. **Hybridization**:
- F is a weak field ligand, so no pairing occurs.
- Configuration: \(3d^6\).
- Hybridization: \(sp^3d^2\).

4. **Unpaired Electrons**:
- Number of unpaired electrons = 4.

5. **Magnetic Moment**:
\[ \mu = \sqrt{4(4 + 2)} = \sqrt{24} \]

### Summary of Magnetic Moments:

1. `[Ni(CO)₄]`: \(0\)
2. `[Mn(CN)₆]^{4-}`: \(\sqrt{35}\)
3. `[Cr(NH₃)₆]^{3+}`: \(\sqrt{15}\)
4. `[CoF₆]^{3-}`: \(\sqrt{24}\)

### Order of Magnetic Moments:
- Highest: \(\sqrt{35}\) (Mn)
- Next: \(\sqrt{24}\) (Co)
- Next: \(\sqrt{15}\) (Cr)
- Lowest: \(0\) (Ni)

Thus, the order of magnetic moments is:
\[ \text{(II) > (IV) > (III) > (I)} \]