Which of the following isomerism is/are not shown by the complex `[Co(Cl_(2)(OH)_(2)(NH_(3))_(2)]Br?`

Options

A. Ionization
B. Linkage
C. Gemetrical
D. Optical

Explanation

To determine which type of isomerism is not shown by the complex \([Co(Cl_2(OH)_2(NH_3)_2)]Br\), we will analyze the possible types of isomerism: ionization isomerism, linkage isomerism, geometrical isomerism, and optical isomerism.

### Step-by-Step Solution:

1. **Identify the Coordination Complex**:
The given complex is \([Co(Cl_2(OH)_2(NH_3)_2)]Br\). It consists of a cobalt ion coordinated with two chloride ions, two hydroxide ions, and two ammonia molecules, with a bromide ion as a counter ion.

2. **Check for Ionization Isomerism**:
Ionization isomerism occurs when two compounds have the same formula but differ in the ions that are released in solution. In this case, if we exchange one chloride ion with the bromide ion, we can form a different ion in solution. Thus, this complex can show ionization isomerism.

**Conclusion**: The complex can show ionization isomerism.

3. **Check for Linkage Isomerism**:
Linkage isomerism occurs when a ligand can coordinate to the metal ion in more than one way (e.g., through different atoms). Common ligands that exhibit linkage isomerism include thiocyanate (SCN) and nitrite (NO2). In this complex, the ligands present (Cl, OH, NH3) do not have multiple donor atoms. Therefore, this complex cannot show linkage isomerism.

**Conclusion**: The complex cannot show linkage isomerism.

4. **Check for Geometrical Isomerism**:
Geometrical isomerism (cis-trans isomerism) occurs in octahedral complexes when there are different ligands. In this case, the arrangement of the two chloride ions and two hydroxide ions can lead to cis and trans forms. Therefore, this complex can show geometrical isomerism.

**Conclusion**: The complex can show geometrical isomerism.

5. **Check for Optical Isomerism**:
Optical isomerism occurs when a compound can exist in two non-superimposable mirror images (enantiomers). Since the cis form of this complex does not have a plane of symmetry, it can exhibit optical isomerism.

**Conclusion**: The complex can show optical isomerism.

### Final Answer:
The isomerism that is **not shown** by the complex \([Co(Cl_2(OH)_2(NH_3)_2)]Br\) is **linkage isomerism**.