The relationship between `[Co(NH_(2)-CH_(2)-underset(CH)underset(|)(CH)-CH_(2)-NH_(2))_(2)Cl_(2)]^(+)` and `[Co(NH_(2)-CH_(2)-CH_(2)-CH_(2)-NH_(2)]_(2)Cl_(2)]^(+)` is

Options

A. Linkage isomer
B. Ligand isomers
C. Coordination isomer
D. Solvate isomers

Answer

To determine the relationship between the two given cobalt complexes, we will analyze their structures and the types of isomerism they may exhibit. The complexes are:

1. \([Co(NH_2-CH_2-CH(CH_2)-NH_2)_2Cl_2]^+\)
2. \([Co(NH_2-CH_2-CH_2-CH_2-NH_2)_2Cl_2]^+\)

### Step 1: Identify the Coordination Complexes
Both complexes contain cobalt as the central metal ion, with ethylenediamine derivatives as ligands and chloride ions.

### Step 2: Analyze the Ligands
- In the first complex, the ligand is a derivative of ethylenediamine where one of the ethylene groups has a branching (CH).
- In the second complex, the ligand is a straight-chain ethylenediamine with no branching.

### Step 3: Determine the Type of Isomerism
Now, we need to analyze the types of isomerism that can occur between these two complexes:

1. **Linkage Isomers**: This type occurs when a ligand can coordinate to the metal in different ways (e.g., through different donor atoms). Since both complexes have the same ligands (only nitrogen is the donor), they cannot be linkage isomers.

2. **Ligand Isomers**: This type occurs when different ligands are present in the complexes. Since both complexes contain the same ligand type (ethylene diamine derivatives), they cannot be ligand isomers.

3. **Coordination Isomers**: This type occurs when there is an exchange of ligands between different coordination spheres (cationic and anionic parts). In this case, both complexes have the same ligands but differ in their structure, indicating they are coordination isomers.

4. **Solvate Isomers**: This type occurs when the complexes differ in the number of solvent molecules associated with them. Since there are no solvent molecules mentioned in the complexes, they cannot be solvate isomers.

### Conclusion
Based on the analysis, the two complexes are best classified as **coordination isomers** because they differ in the arrangement of the ligands around the cobalt ion while maintaining the same coordination number and type of ligands.

### Final Answer
The relationship between the two complexes is that they are **coordination isomers**.

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