Step 1: Understanding the Concept:
Prokaryotes (bacteria and archaea) are single-celled organisms that lack a membrane-bound nucleus and other complex internal organelles.
As a consequence of their simpler structural organization, prokaryotes are significantly smaller than eukaryotic cells.
Step 2: Detailed Explanation:
Let us analyze the standard scale of biological cells:
- Prokaryotic cells: Most bacteria have an average diameter or length ranging from $1$ to $10\,\mu\text{m}$ (micrometers). For example, *Escherichia coli* is typically about $1\text{--}2\,\mu\text{m}$ long.
- Eukaryotic cells: These are structurally larger and more complex, typically ranging from $10$ to $100\,\mu\text{m}$ in diameter.
- Nanometer scale ($1\text{--}100\,\text{nm}$): This scale is far too small for any living cell. It is the scale of individual biomolecules (like DNA and proteins) and viruses (which typically measure $20\text{--}400\,\text{nm}$).
Step 3: Final Answer:
Therefore, the average diameter of a prokaryotic cell lies in the range of $1\text{--}10\,\mu\text{m}$, which corresponds to option (A).