Among the following complexes , how many have 'spin only' magnetic moment of 2.83 B.M. ?
`[Ni(CO)_4],[Ni(CN)_4]^(2-),[NiCl_2( P Ph_3)_2], [NiCl_4]^(2-),[NiF_6]^(2-),[NiF_6]^(4-),[Ni(NH_3)_6]^(2+),[Ni(en)_3]^(2+),[Ni(H_2O)_6]^(2+)`

Explanation

To determine how many of the given complexes have a spin-only magnetic moment of 2.83 Bohr Magneton (B.M.), we need to analyze each complex to find the number of unpaired electrons. The formula for calculating the spin-only magnetic moment (μ) is:

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

where \(n\) is the number of unpaired electrons. A magnetic moment of 2.83 B.M. corresponds to \(n = 2\) because:

\[ \sqrt{2(2 + 2)} = \sqrt{8} = 2.83 \]

Now, let's analyze each complex step by step:

1. **[Ni(CO)₄]**:
- Nickel is in the 0 oxidation state.
- Electronic configuration: [Ar] 3d⁸ 4s².
- CO is a strong field ligand, causing pairing of all electrons.
- Unpaired electrons: 0.
- Magnetic moment: 0 B.M. (not applicable).

2. **[Ni(CN)₄]²⁻**:
- Nickel is in the +2 oxidation state.
- Electronic configuration: [Ar] 3d⁸.
- CN⁻ is a strong field ligand, causing pairing of all electrons.
- Unpaired electrons: 0.
- Magnetic moment: 0 B.M. (not applicable).

3. **[NiCl₂(PPh₃)₂]**:
- Nickel is in the +2 oxidation state.
- Electronic configuration: [Ar] 3d⁸.
- PPh₃ is a weak field ligand, so no pairing occurs.
- Unpaired electrons: 2.
- Magnetic moment:
\[ \mu = \sqrt{2(2 + 2)} = \sqrt{8} = 2.83 \text{ B.M.} \quad \text{(valid)} \]

4. **[NiCl₄]²⁻**:
- Nickel is in the +2 oxidation state.
- Electronic configuration: [Ar] 3d⁸.
- Cl⁻ is a weak field ligand, so no pairing occurs.
- Unpaired electrons: 2.
- Magnetic moment:
\[ \mu = \sqrt{2(2 + 2)} = \sqrt{8} = 2.83 \text{ B.M.} \quad \text{(valid)} \]

5. **[NiF₆]²⁻**:
- Nickel is in the +2 oxidation state.
- Electronic configuration: [Ar] 3d⁸.
- F⁻ is a weak field ligand, so no pairing occurs.
- Unpaired electrons: 2.
- Magnetic moment:
\[ \mu = \sqrt{2(2 + 2)} = \sqrt{8} = 2.83 \text{ B.M.} \quad \text{(valid)} \]

6. **[NiF₆]⁴⁻**:
- Nickel is in the +4 oxidation state.
- Electronic configuration: [Ar] 3d⁶.
- F⁻ is a weak field ligand, but in this case, pairing occurs due to the higher oxidation state.
- Unpaired electrons: 0.
- Magnetic moment: 0 B.M. (not applicable).

7. **[Ni(NH₃)₆]²⁺**:
- Nickel is in the +2 oxidation state.
- Electronic configuration: [Ar] 3d⁸.
- NH₃ is a weak field ligand, so no pairing occurs.
- Unpaired electrons: 2.
- Magnetic moment:
\[ \mu = \sqrt{2(2 + 2)} = \sqrt{8} = 2.83 \text{ B.M.} \quad \text{(valid)} \]

8. **[Ni(en)₃]²⁺**:
- Nickel is in the +2 oxidation state.
- Electronic configuration: [Ar] 3d⁸.
- Ethylenediamine (en) is a bidentate ligand and a weak field ligand, so no pairing occurs.
- Unpaired electrons: 2.
- Magnetic moment:
\[ \mu = \sqrt{2(2 + 2)} = \sqrt{8} = 2.83 \text{ B.M.} \quad \text{(valid)} \]

9. **[Ni(H₂O)₆]²⁺**:
- Nickel is in the +2 oxidation state.
- Electronic configuration: [Ar] 3d⁸.
- H₂O is a weak field ligand, so no pairing occurs.
- Unpaired electrons: 2.
- Magnetic moment:
\[ \mu = \sqrt{2(2 + 2)} = \sqrt{8} = 2.83 \text{ B.M.} \quad \text{(valid)} \]

### Summary:
The complexes with a spin-only magnetic moment of 2.83 B.M. are:
- [NiCl₂(PPh₃)₂]
- [NiCl₄]²⁻
- [NiF₆]²⁻
- [Ni(NH₃)₆]²⁺
- [Ni(en)₃]²⁺
- [Ni(H₂O)₆]²⁺

Thus, **6 complexes** have a spin-only magnetic moment of 2.83 B.M.