`[Co(NH_(3))_(4)(NO_(2))_(2)]CI` exhibits

Options

A. linkage isomerism, geometrical isomerism and optical isomerism
B. linkage isomerism, ionisation isomerism and optical isomerism
C. linkage isomerism, ionisation isomerism and geometrical isomerism
D. ionisation isomerism, geometrical isomerism and optical isomerism

Explanation

To solve the question regarding the complex `[Co(NH₃)₄(NO₂)₂]Cl` and determine the types of isomerism it exhibits, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Components of the Complex:**
- The complex is `[Co(NH₃)₄(NO₂)₂]Cl`.
- It contains cobalt (Co) as the central metal ion, four ammonia (NH₃) ligands, two nitrite (NO₂) ligands, and one chloride (Cl) ion.

2. **Determine the Type of Ligands:**
- Ammonia (NH₃) is a neutral ligand.
- Nitrite (NO₂) can act as a bidentate ligand, meaning it can bond through either nitrogen (N) or oxygen (O), leading to potential linkage isomerism.
- Chloride (Cl) is an anionic ligand.

3. **Linkage Isomerism:**
- Since the nitrite ion (NO₂) can coordinate through either the nitrogen atom or the oxygen atom, this complex can exhibit linkage isomerism.
- The two forms would be:
- One where NO₂ is bonded through nitrogen (N).
- Another where NO₂ is bonded through oxygen (O).

4. **Ionization Isomerism:**
- Ionization isomerism occurs when the anionic part of the complex can be exchanged with another ion in solution.
- In this case, the chloride ion (Cl⁻) can be exchanged with one of the nitrite ions (NO₂⁻), leading to different ionization forms:
- One form where Cl is outside the coordination sphere and NO₂ is inside.
- Another form where NO₂ is outside and Cl is inside.

5. **Geometrical Isomerism:**
- The complex can also exhibit geometrical isomerism due to the arrangement of the ligands around the cobalt ion.
- With two nitrite ligands, the complex can have:
- A **cis** isomer where the two NO₂ groups are adjacent to each other.
- A **trans** isomer where the two NO₂ groups are opposite each other.

6. **Optical Isomerism:**
- Optical isomerism is not applicable here because the complex does not have a chiral center. The presence of two identical ligands (NH₃) and the symmetrical arrangement does not allow for non-superimposable mirror images.

### Conclusion:
The complex `[Co(NH₃)₄(NO₂)₂]Cl` exhibits:
- Linkage isomerism (due to NO₂).
- Ionization isomerism (due to Cl⁻).
- Geometrical isomerism (cis and trans forms).

Thus, the answer is option C: linkage, ionization, and geometrical isomerism.