`[Co(NH_(3))_(4)Cl_(2)]^(+)` exhibits

Options

A. Geometrical isomerism
B. Optical isomerism
C. Linkage isomerism
D. Ionisation isomerism

Explanation

To solve the question regarding the isomerism exhibited by the complex `[Co(NH₃)₄Cl₂]⁺`, we will analyze the types of isomerism that can occur in coordination compounds.

### Step-by-Step Solution:

1. **Identify the Coordination Number and Geometry**:
- The complex `[Co(NH₃)₄Cl₂]⁺` has a cobalt (Co) central metal atom coordinated to four ammonia (NH₃) ligands and two chloride (Cl) ligands.
- The coordination number is 6 (4 from NH₃ and 2 from Cl), which typically leads to an octahedral geometry.

**Hint**: Remember that the coordination number helps determine the geometry of the complex.

2. **Determine Possible Isomerism**:
- In octahedral complexes, two main types of isomerism can occur: **geometrical isomerism** and **optical isomerism**.

**Hint**: Geometrical isomerism arises from different arrangements of ligands around the central atom.

3. **Geometrical Isomerism**:
- In this complex, we can have two types of geometrical isomers: **cis** and **trans**.
- **Cis Isomer**: The two chloride ligands are adjacent to each other.
- **Trans Isomer**: The two chloride ligands are opposite each other.

**Hint**: Visualize the arrangement of ligands in the octahedral structure to identify cis and trans configurations.

4. **Optical Isomerism**:
- Optical isomerism occurs when a molecule lacks a plane of symmetry and can exist as non-superimposable mirror images (enantiomers).
- In the case of `[Co(NH₃)₄Cl₂]⁺`, the presence of two identical ligands (NH₃) and two identical ligands (Cl) means that there is a plane of symmetry in both the cis and trans forms.
- Therefore, this complex does not exhibit optical isomerism.

**Hint**: Check for planes of symmetry to determine if optical isomerism is possible.

5. **Linkage Isomerism**:
- Linkage isomerism occurs when a ligand can bind to the metal in more than one way (e.g., nitrito can bind through nitrogen or oxygen).
- In this complex, both NH₃ and Cl are monodentate ligands, meaning they can only bind through one atom. Thus, linkage isomerism does not apply here.

**Hint**: Identify the nature of the ligands to determine if linkage isomerism is relevant.

6. **Ionization Isomerism**:
- Ionization isomerism occurs when the composition of the ions in solution differs.
- Since the complex `[Co(NH₃)₄Cl₂]⁺` does not dissociate into different ions in solution, this type of isomerism is not applicable.

**Hint**: Consider the dissociation of the complex in solution to evaluate ionization isomerism.

### Conclusion:
The complex `[Co(NH₃)₄Cl₂]⁺` exhibits **geometrical isomerism** (cis and trans forms) but does not exhibit optical isomerism, linkage isomerism, or ionization isomerism.