Which of the following cannot show linkage isomerism?

Options

A. `NO_(2)^(-)`
B. `SCN^(-)`
C. `CN^(-)`
D. `NH_(3)`

Answer

To determine which of the following cannot show linkage isomerism, we first need to understand what linkage isomerism is and the conditions under which it occurs.

### Step-by-Step Solution:

1. **Definition of Linkage Isomerism**:
Linkage isomerism occurs in coordination compounds when a ligand can bind to a metal atom in more than one way. This is typically seen with ambidentate ligands, which have two or more donor atoms capable of coordinating to the metal.

2. **Identify Ambidentate Ligands**:
Common examples of ambidentate ligands include thiocyanate (SCN⁻), which can bind through sulfur or nitrogen, and cyanide (CN⁻), which can bind through carbon or nitrogen.

3. **Analyze the Given Options**:
To answer the question, we need to analyze the ligands provided in the options (which were not explicitly listed in the question). We will consider common ligands that are known to show linkage isomerism and those that do not.

4. **Ligands That Cannot Show Linkage Isomerism**:
- **Monodentate Ligands**: Ligands that can only attach to the metal through one atom (like chloride, Cl⁻, or ammonia, NH₃) cannot show linkage isomerism because they do not have multiple donor atoms to form different structures.
- **Examples**: Ligands such as NH₃, Cl⁻, and H₂O are monodentate and cannot show linkage isomerism.

5. **Conclusion**:
Based on the analysis, if one of the options is a monodentate ligand (like NH₃ or Cl⁻), it cannot show linkage isomerism.

### Final Answer:
The ligand that cannot show linkage isomerism is the one that is a monodentate ligand.