See image — Isomerism and Stereochemistry Chemistry Question

💡 Solution & Explanation

# Optical Activity Analysis **Key Principle:** A molecule is optically active if it contains one or more **chiral centers** (asymmetric carbons bonded to four different groups) and lacks a plane of symmetry. ## Analysis of Each Option: **(A) $H_2C=C=CH_2$ (Allene)** - Central carbon is sp-hybridized (linear geometry) - No chiral centers → **Not optically active** **(B) Tetraphenylethene derivative** - Double bond between central carbons prevents free rotation - Molecule has a **plane of symmetry** (mirror plane through $C=C$ bond) - Achiral despite restricted rotation → **Not optically active** **(C) Bicyclic diamino compound** ✓ - Two bridged rings create a **bicyclic (bicyclo) system** - The bridgehead carbons are chiral centers (each bonded to 4 different groups): - Bridge atoms - Different ring portions - H atoms - **No plane of symmetry** exists - Contains stereogenic centers → **Optically active** **(D) Fluorinated benzoic acid** - Benzene ring carbons are sp² hybridized - No chiral centers - Despite asymmetric substituents, ring carbons cannot be chiral → **Not optically active** ## Answer: **(C)** is optically active because it possesses chiral bridgehead carbons with no compensating plane of symmetry.