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. `IltIIltIIIlt IV`
C. `IVgtIIgtIgtIII`
D. `IVlt IIltIltIII`

Explanation

To determine the order of magnetic moments for the given complexes, we will analyze each complex one by one, focusing on the oxidation state of the central metal ion, its electronic configuration, the nature of the ligands, and the resulting number of unpaired electrons.

### Step 1: Analyze `[Ni(CO)₄]`

1. **Oxidation State**: Nickel (Ni) is in the zero oxidation state.
2. **Electronic Configuration**: The electronic configuration of Ni in the zero oxidation state is \( [Ar] 4s^2 3d^8 \).
3. **Ligand Field**: CO is a strong field ligand, which causes pairing of electrons.
4. **Electron Configuration after Pairing**: The d-orbitals will be filled as follows:
- \( 3d: \uparrow\downarrow \uparrow\downarrow \uparrow\downarrow \uparrow\downarrow \)
- All electrons are paired.
5. **Unpaired Electrons**: 0 unpaired electrons.
6. **Magnetic Moment**: \( \mu = \sqrt{n(n+2)} = \sqrt{0(0+2)} = 0 \) Bohr magneton.

### Step 2: Analyze `[Mn(CN)₆]^{4-}`

1. **Oxidation State**: Manganese (Mn) is in the +2 oxidation state.
2. **Electronic Configuration**: The electronic configuration of Mn in the +2 oxidation state is \( [Ar] 4s^2 3d^5 \).
3. **Ligand Field**: CN⁻ is a strong field ligand, which causes pairing of electrons.
4. **Electron Configuration after Pairing**: The d-orbitals will be filled as follows:
- \( 3d: \uparrow\downarrow \uparrow\downarrow \uparrow\downarrow \uparrow \)
- There is 1 unpaired electron.
5. **Unpaired Electrons**: 1 unpaired electron.
6. **Magnetic Moment**: \( \mu = \sqrt{1(1+2)} = \sqrt{3} \approx 1.73 \) Bohr magneton.

### Step 3: Analyze `[Cr(NH₃)₆]^{3+}`

1. **Oxidation State**: Chromium (Cr) is in the +3 oxidation state.
2. **Electronic Configuration**: The electronic configuration of Cr in the +3 oxidation state is \( [Ar] 4s^0 3d^3 \).
3. **Ligand Field**: NH₃ is a weak field ligand, which does not cause pairing.
4. **Electron Configuration**: The d-orbitals will be filled as follows:
- \( 3d: \uparrow \uparrow \uparrow \)
- There are 3 unpaired electrons.
5. **Unpaired Electrons**: 3 unpaired electrons.
6. **Magnetic Moment**: \( \mu = \sqrt{3(3+2)} = \sqrt{15} \approx 3.87 \) Bohr magneton.

### Step 4: Analyze `[CoF₆]^{3-}`

1. **Oxidation State**: Cobalt (Co) is in the +3 oxidation state.
2. **Electronic Configuration**: The electronic configuration of Co in the +3 oxidation state is \( [Ar] 4s^0 3d^6 \).
3. **Ligand Field**: F⁻ is a weak field ligand, which does not cause pairing.
4. **Electron Configuration**: The d-orbitals will be filled as follows:
- \( 3d: \uparrow \uparrow \uparrow \uparrow \uparrow \uparrow \)
- There are 4 unpaired electrons.
5. **Unpaired Electrons**: 4 unpaired electrons.
6. **Magnetic Moment**: \( \mu = \sqrt{4(4+2)} = \sqrt{24} \approx 4.89 \) Bohr magneton.

### Summary of Magnetic Moments

1. `[Ni(CO)₄]`: 0 Bohr magneton
2. `[Mn(CN)₆]^{4-}`: 1.73 Bohr magneton
3. `[Cr(NH₃)₆]^{3+}`: 3.87 Bohr magneton
4. `[CoF₆]^{3-}`: 4.89 Bohr magneton

### Final Order of Magnetic Moments

The order of magnetic moments from lowest to highest is:
\[ [Ni(CO)₄] < [Mn(CN)₆]^{4-} < [Cr(NH₃)₆]^{3+} < [CoF₆]^{3-} \]