Among the following complexes `(K - P) : K_(3) [Fe(CN)_(6)] - K , [Co(NH_(3))_(6)]Cl_(3)- L , Na_(3)[Co("oxalate")_(3)]-M , [Ni(H_(2)O)_(6)]Cl_2 - N, K_(2) [Pt(CN)_(4)]-O and [Zn(H_(2)O)_(6)] (NO_(3))_(2)-P,` the diamagnetic complexes are

Options

A. K , L , M , N
B. K , M , O , P
C. L , M , O , P
D. L , M , N , O

Explanation

To determine which of the given complexes are diamagnetic, we need to analyze each complex based on the metal ion's electron configuration and the nature of the ligands involved. Diamagnetic complexes have all their electrons paired, while paramagnetic complexes have unpaired electrons.

### Step-by-Step Solution:

1. **Complex K: \( K_3[Fe(CN)_6] \)**
- Iron (Fe) in this complex is in the +3 oxidation state (Fe^3+), which has the electron configuration of [Ar] 3d^5.
- Cyanide (CN^-) is a strong field ligand that causes pairing of electrons.
- Since there are 5 d-electrons in total and they remain unpaired, this complex is **paramagnetic**.

2. **Complex L: \( [Co(NH_3)_6]Cl_3 \)**
- Cobalt (Co) in this complex is in the +3 oxidation state (Co^3+), which has the electron configuration of [Ar] 3d^6.
- Ammonia (NH3) is also a strong field ligand, leading to pairing of electrons.
- All 6 d-electrons can pair up, making this complex **diamagnetic**.

3. **Complex M: \( Na_3[Co(oxalate)_3] \)**
- Cobalt (Co) is again in the +3 oxidation state (Co^3+), with a 3d^6 configuration.
- Oxalate (C2O4^2-) is a strong field ligand that also promotes electron pairing.
- Thus, this complex is **diamagnetic**.

4. **Complex N: \( [Ni(H_2O)_6]Cl_2 \)**
- Nickel (Ni) in this complex is in the +2 oxidation state (Ni^2+), which has the electron configuration of [Ar] 3d^8.
- Water (H2O) is a weak field ligand, which does not cause significant pairing of electrons.
- As a result, this complex has unpaired electrons and is **paramagnetic**.

5. **Complex O: \( K_2[Pt(CN)_4] \)**
- Platinum (Pt) in this complex is in the +2 oxidation state (Pt^2+), which has the electron configuration of [Xe] 4f^14 5d^8.
- Cyanide (CN^-) is a strong field ligand leading to paired electrons.
- Therefore, this complex is **diamagnetic**.

6. **Complex P: \( [Zn(H_2O)_6](NO_3)_2 \)**
- Zinc (Zn) is in the +2 oxidation state (Zn^2+), which has the electron configuration of [Ar] 3d^10.
- Since all 10 d-electrons are paired, this complex is also **diamagnetic**.

### Summary of Magnetic Properties:
- **Diamagnetic Complexes**: L, M, O, P
- **Paramagnetic Complexes**: K, N

### Final Answer:
The diamagnetic complexes among the given options are **L, M, O, and P**.