Step 1: Understanding the Concept:
Hückel's rule states that a planar, cyclic, conjugated system with (4n+2) \(\pi\)-electrons is aromatic.
Step 2: Detailed Explanation:
• (A) Cycloheptatrienyl cation (tropylium ion): C\(_7\)H\(_7^+\). It has 6 \(\pi\)-electrons (4n+2, n=1), is planar and cyclic, and is aromatic.
• (B) Cycloheptatriene: Non-aromatic (not fully conjugated, has a CH\(_2\) group).
• (C) Cyclooctatetraene: 8 \(\pi\)-electrons, tub-shaped (non-planar) to avoid antiaromaticity, so non-aromatic.
• (D) Cyclopentadienyl cation: C\(_5\)H\(_5^+\). It has 4 \(\pi\)-electrons (4n, n=1), would be antiaromatic if planar, so it is non-aromatic and unstable.
Step 3: Final Answer:
Cycloheptatrienyl cation is aromatic, which corresponds to option (A).