The correct order of the calculated spin - only magnetic moments of complexes (A) to (D) is :
(A) `Ni(CO)_(4)`
(B) `[Ni(H_(2)O)_(6)]Cl_(2)`
(C) `Na_(2)[Ni(CN)_(4)]`
(D) `PdCl_(2)(PPh_(3))_(2)`

Options

A. `(c )lt(d)lt(b) lt(a)`
B. `(a)~~(c ) lt (b) ~~ (d)`
C. `(a) ~~(c )~~(d) lt (b)`
D. `(c )~~(d)lt(b)lt(a)`

Answer

To determine the correct order of the calculated spin-only magnetic moments of the complexes (A) to (D), we need to analyze each complex step by step.

### Step 1: Analyze Complex (A) `Ni(CO)_(4)`
- **Ligand Type**: CO is a strong field ligand.
- **Nickel Oxidation State**: In `Ni(CO)_(4)`, nickel is in the zero oxidation state (Ni^0).
- **Electronic Configuration**: Nickel (atomic number 28) has the configuration: 3d^8 4s^2.
- **Electron Pairing**: Since CO is a strong field ligand, it causes pairing of electrons. The configuration becomes 3d^10, resulting in:
- **Number of Unpaired Electrons**: 0
- **Magnetic Moment**: Using the formula \( \mu = \sqrt{n(n + 2)} \):
- \( n = 0 \)
- \( \mu = \sqrt{0(0 + 2)} = 0 \, \text{BM} \)

### Step 2: Analyze Complex (B) `[Ni(H_(2)O)_(6)]Cl_(2)`
- **Ligand Type**: H2O is a weak field ligand.
- **Nickel Oxidation State**: In `[Ni(H2O)6]Cl2`, nickel is in the +2 oxidation state (Ni^2+).
- **Electronic Configuration**: For Ni^2+, the configuration is 3d^8 4s^0.
- **Electron Filling**: In an octahedral field, the 3d orbitals split into T2g and Eg. The filling will be:
- T2g: 6 electrons
- Eg: 2 electrons
- **Number of Unpaired Electrons**: 2
- **Magnetic Moment**:
- \( n = 2 \)
- \( \mu = \sqrt{2(2 + 2)} = \sqrt{8} = 2.83 \, \text{BM} \)

### Step 3: Analyze Complex (C) `Na_(2)[Ni(CN)_(4)]`
- **Ligand Type**: CN^- is a strong field ligand.
- **Nickel Oxidation State**: In `Na2[Ni(CN)4]`, nickel is in the +2 oxidation state (Ni^2+).
- **Electronic Configuration**: For Ni^2+, the configuration is 3d^8 4s^0.
- **Electron Pairing**: CN^- causes pairing of electrons, leading to:
- Configuration: 3d^10
- **Number of Unpaired Electrons**: 0
- **Magnetic Moment**:
- \( n = 0 \)
- \( \mu = \sqrt{0(0 + 2)} = 0 \, \text{BM} \)

### Step 4: Analyze Complex (D) `PdCl_(2)(PPh_(3))_(2)`
- **Ligand Type**: Cl^- and PPh3 are considered strong field ligands.
- **Palladium Oxidation State**: In `PdCl2(PPh3)2`, palladium is in the +2 oxidation state (Pd^2+).
- **Electronic Configuration**: Palladium (atomic number 46) has the configuration: 4d^10. For Pd^2+, it becomes 4d^8.
- **Electron Pairing**: The strong field ligands cause pairing:
- Configuration: 4d^8 (with all electrons paired)
- **Number of Unpaired Electrons**: 0
- **Magnetic Moment**:
- \( n = 0 \)
- \( \mu = \sqrt{0(0 + 2)} = 0 \, \text{BM} \)

### Final Order of Magnetic Moments
- Complex (A) `Ni(CO)_(4)`: 0 BM
- Complex (B) `[Ni(H2O)6]Cl2`: 2.83 BM
- Complex (C) `Na2[Ni(CN)4]`: 0 BM
- Complex (D) `PdCl2(PPh3)2`: 0 BM

Thus, the order of magnetic moments is:
\[ A = C = D < B \]

### Conclusion
The correct order of the calculated spin-only magnetic moments of complexes (A) to (D) is:
**(A) = (C) = (D) < (B)**