See image — Isomerism and Stereochemistry Chemistry Question

💡 Solution & Explanation

Step 1 - Identify the structure: The molecule consists of four cyclobutane rings fused in a linear row (bicyclo/polycyclic system). The Br is attached to the carbon at the junction between the second and third rings. This junction carbon connects to two ring systems on either side. Step 2 - Identify stereocenters: The carbon bearing Br is the potential stereocenter. It is bonded to: Br, H (implicit), and the two ring junction carbons leading into the left bicyclobutane portion and the right bicyclobutane portion. Step 3 - Analyze symmetry: The left half of the molecule (two fused cyclobutane rings) is identical to the right half (two fused cyclobutane rings). Therefore the carbon bearing Br has two identical substituents (the two equivalent bicyclobutyl ring systems on either side). Step 4 - Chirality assessment: Because the two substituents on either side of the Br-bearing carbon are identical (mirror-image equivalent ring fragments that are in fact the same), this carbon is NOT a true stereocenter — it has two identical groups. A carbon with two identical substituents cannot be a stereocenter. Step 5 - Conclusion on optical activity: Since there is no stereocenter (the apparent chiral center has two identical ring substituents due to the molecular symmetry), there are no stereoisomers at all, and therefore zero optically active isomers. Step 6 - Why other options fail: Options (b), (c), and (d) assume the existence of one or more stereocenters generating optically active forms, but the molecular symmetry eliminates chirality entirely. Therefore, the correct answer is A.