Isoomerisms exhibited by `[Cr(NH_(3))_(2)(H_(2)O)_(2)Cl_(2)]^(+)` are

Options

A. Isonisation, optical
B. Hydrate , optical
C. Geometrical , optical
D. Coordinate , geometrical

Answer

To determine the isomerisms exhibited by the complex ion \([Cr(NH_3)_2(H_2O)_2Cl_2]^+\), we can follow these steps:

### Step 1: Identify the Coordination Complex
The complex consists of chromium (Cr) as the central metal ion surrounded by two ammonia (NH₃) ligands, two water (H₂O) ligands, and two chloride (Cl) ligands.

### Step 2: Determine the Geometry of the Complex
The coordination number of chromium in this complex is 6 (since it is surrounded by six ligands). This typically leads to an octahedral geometry.

### Step 3: Analyze Possible Isomers
In an octahedral complex, we can have different arrangements of the ligands, leading to two main types of isomerism:

1. **Geometrical Isomerism**: This occurs due to different spatial arrangements of the ligands. In this case, we can have:
- **Cis Isomer**: where similar ligands are adjacent to each other.
- **Trans Isomer**: where similar ligands are opposite to each other.

2. **Optical Isomerism**: This occurs when a complex can exist in two non-superimposable mirror images (enantiomers). This typically happens in complexes that have no plane of symmetry.

### Step 4: Draw the Isomers
- **Cis Isomer**: In this arrangement, the two NH₃ ligands can be adjacent to each other, and the two H₂O ligands can also be adjacent.

- **Trans Isomer**: In this arrangement, the two NH₃ ligands are opposite each other, and the two H₂O ligands are also opposite each other.

### Step 5: Determine Optical Isomerism
- For the **cis isomer**, it can exhibit optical isomerism because it lacks a plane of symmetry.
- The **trans isomer** does not exhibit optical isomerism as it has a plane of symmetry.

### Conclusion
The complex \([Cr(NH_3)_2(H_2O)_2Cl_2]^+\) exhibits:
- **Geometrical Isomerism** (cis and trans)
- **Optical Isomerism** (only for the cis isomer)

Thus, the isomerisms exhibited by this complex are geometrical and optical.

### Final Answer
The correct answer is that the complex exhibits geometrical and optical isomerism.

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