Correct order of magnetic moment (spin only) for the following complexes `
(a) [Pd(PPh_(3))_(2)Cl_(2)]
(b) [Ni(CO)_(4)]
(c) [Ni(CN)_(4)]^(2-)
(d) [Ni(H_(2)O)_(6)]^(2+)`

Options

A. ` a = b = c lt d`
B. `a lt b lt c lt d`
C. `a gt b gt c gt d`
D. `a = b gt c gt d `

Explanation

To determine the correct order of magnetic moments (spin-only) for the given complexes, we will analyze each complex step by step, calculate the number of unpaired electrons, and then use the formula for magnetic moment.

### Step 1: Analyze the Complexes

1. **Complex (a) [Pd(PPh₃)₂Cl₂]**
- Palladium (Pd) is in the +2 oxidation state.
- Electronic configuration: Pd²⁺ → 4d⁸.
- Geometry: Square planar (due to strong field ligands).
- In a square planar configuration, the 4d orbitals will be filled as follows:
- dxy, dxz, dyz, dz², dx²-y².
- All electrons are paired: 4d⁸ has no unpaired electrons.
- **Unpaired Electrons (n) = 0**
- **Magnetic Moment (μ) = √(n(n + 2)) = √(0(0 + 2)) = 0**

2. **Complex (b) [Ni(CO)₄]**
- Nickel (Ni) is in the 0 oxidation state.
- Electronic configuration: Ni → 3d⁸ 4s².
- Geometry: Tetrahedral (CO is a strong field ligand).
- In tetrahedral geometry, all electrons will pair up due to strong field ligands.
- **Unpaired Electrons (n) = 0**
- **Magnetic Moment (μ) = √(0(0 + 2)) = 0**

3. **Complex (c) [Ni(CN)₄]²⁻**
- Nickel (Ni) is in the +2 oxidation state.
- Electronic configuration: Ni²⁺ → 3d⁸.
- Geometry: Square planar (CN⁻ is a strong field ligand).
- In square planar geometry, all electrons are paired.
- **Unpaired Electrons (n) = 0**
- **Magnetic Moment (μ) = √(0(0 + 2)) = 0**

4. **Complex (d) [Ni(H₂O)₆]²⁺**
- Nickel (Ni) is in the +2 oxidation state.
- Electronic configuration: Ni²⁺ → 3d⁸.
- Geometry: Octahedral (H₂O is a weak field ligand).
- In octahedral geometry, the electrons will be filled as follows:
- T₂g (3 electrons) and Eₑg (5 electrons).
- There are 2 unpaired electrons in the Eₑg orbitals.
- **Unpaired Electrons (n) = 2**
- **Magnetic Moment (μ) = √(2(2 + 2)) = √8 = 2.83**

### Step 2: Summary of Magnetic Moments
- **[Pd(PPh₃)₂Cl₂]**: μ = 0
- **[Ni(CO)₄]**: μ = 0
- **[Ni(CN)₄]²⁻**: μ = 0
- **[Ni(H₂O)₆]²⁺**: μ = 2.83

### Step 3: Correct Order of Magnetic Moments
The complexes can be ordered based on their magnetic moments:
- **[Pd(PPh₃)₂Cl₂] = 0**
- **[Ni(CO)₄] = 0**
- **[Ni(CN)₄]²⁻ = 0**
- **[Ni(H₂O)₆]²⁺ = 2.83**

Thus, the correct order of magnetic moments is:
**[Pd(PPh₃)₂Cl₂] = [Ni(CO)₄] = [Ni(CN)₄]²⁻ < [Ni(H₂O)₆]²⁺**

### Final Answer
**Correct order of magnetic moment (spin only): [Pd(PPh₃)₂Cl₂] = [Ni(CO)₄] = [Ni(CN)₄]²⁻ < [Ni(H₂O)₆]²⁺**

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