The correct statement on the isomerism associated with the following complex ions.
`I [Ni(H_(2)O)_(5) NH_(3)]^(2+)`
`II . [Ni (H_(2) O)_(4) (NH_(3))_(2)]^(2+)`
`III. [Ni(H_(2)O)_(3)(NH_(3))_(3)]^(2+)`

Options

A. (a) and ( b) show only geometrical isomerism
B. (a) and ( b) show geometrical and optical isomerism
C. (b) and ( c ) show geomertical and optical isomerism
D. (b) and ( c ) show only geomertical isomerism

Answer

To solve the problem regarding the isomerism associated with the complex ions given, we will analyze each complex ion step by step.

### Step 1: Analyze Complex Ion I - [Ni(H₂O)₅(NH₃)]²⁺
1. **Identify the Coordination Number**: Nickel (Ni) in this complex has a coordination number of 6 (5 water molecules and 1 ammonia).
2. **Geometry**: The geometry of this complex is octahedral.
3. **Isomerism**:
- Since there are 5 identical ligands (water) and only 1 different ligand (ammonia), there are no possible geometrical isomers.
- There are also no optical isomers because there is no chiral center.

**Conclusion**: This complex does not exhibit any isomerism.

### Step 2: Analyze Complex Ion II - [Ni(H₂O)₄(NH₃)₂]²⁺
1. **Identify the Coordination Number**: Nickel has a coordination number of 6 (4 water molecules and 2 ammonia).
2. **Geometry**: The geometry is octahedral.
3. **Isomerism**:
- This complex can exhibit geometrical isomerism (cis and trans forms).
- **Cis Isomer**: Both ammonia ligands are adjacent to each other.
- **Trans Isomer**: The ammonia ligands are opposite each other.
- There are no optical isomers as both forms are not chiral.

**Conclusion**: This complex exhibits geometrical isomerism.

### Step 3: Analyze Complex Ion III - [Ni(H₂O)₃(NH₃)₃]²⁺
1. **Identify the Coordination Number**: Nickel has a coordination number of 6 (3 water molecules and 3 ammonia).
2. **Geometry**: The geometry is octahedral.
3. **Isomerism**:
- This complex can exhibit both facial (fac) and meridional (mer) isomerism.
- **Facial Isomer**: Three identical ligands (water or ammonia) occupy one face of the octahedron.
- **Meridional Isomer**: Three identical ligands lie in a plane that divides the octahedron into two equal halves.
- There are no optical isomers as both forms are not chiral.

**Conclusion**: This complex exhibits both facial and meridional geometrical isomerism.

### Final Summary of Isomerism:
- **Complex I**: No isomerism.
- **Complex II**: Geometrical isomerism (cis and trans).
- **Complex III**: Geometrical isomerism (fac and mer).

### Correct Statement:
The correct statement regarding the isomerism associated with the given complex ions is that Complex II and Complex III show geometrical isomerism, while Complex I does not show any isomerism.