Step 1: Understanding the Concept:
Basicity in nitrogenous organic compounds is determined by the availability of the nitrogen's lone pair for protonation.
Delocalization of the lone pair via resonance or aromaticity significantly decreases basicity.
Conversely, systems that stabilize the positive charge of the conjugate acid (protonated form) via resonance are exceptionally basic.
Step 2: Detailed Explanation:
Let's analyze the three bicyclic structures:
- Compound I: This molecule has a nitrogen atom where the lone pair is part of an aromatic \(6\pi\) system (similar to pyrrole). Using this lone pair for protonation would break the aromaticity, which is highly unfavorable. Thus, I is the least basic.
- Compound III: Here, the nitrogen lone pair is in conjugation with one double bond (enamine-like). While it is delocalized, it is not part of an aromatic sextet. It is more available than the lone pair in I, but less so than a saturated amine.
- Compound II: This structure is unique. Upon protonation, the resulting cation is stabilized by extensive resonance through the conjugated diene system. In fact, this molecule can be viewed as an amidine-like or guanidine-like system where the positive charge in the conjugate acid is extremely stable. This makes II exceptionally basic.
Therefore, the correct increasing order of basicity is:
I < III < II.
Step 3: Final Answer:
The correct order is I < III < II, which corresponds to option (A).