See image — Isomerism and Stereochemistry Chemistry Question

💡 Solution & Explanation

Concept: A molecule is optically active if it is chiral, meaning it lacks an internal plane of symmetry (and cannot be superimposed on its mirror image). We must analyze each dimethylcyclobutane isomer for chirality. Step 1 - cis-1,2-dimethylcyclobutane: Both methyl groups are on the same side of the ring. This molecule has an internal plane of symmetry (a mirror plane bisecting the C1-C2 bond perpendicularly), making it a meso compound. It is optically INACTIVE. Step 2 - trans-1,2-dimethylcyclobutane: The two methyl groups are on opposite sides of the ring. C1 and C2 are both stereocenters. The trans isomer exists as a pair of non-superimposable mirror images (an enantiomeric pair). There is no internal plane of symmetry, so it is chiral and optically ACTIVE. Step 3 - cis-1,3-dimethylcyclobutane: The two methyl groups are on the same side. This molecule has a plane of symmetry (a mirror plane through C2 and C4, bisecting the ring), making it a meso compound. It is optically INACTIVE. Step 4 - trans-1,3-dimethylcyclobutane: The two methyl groups are on opposite sides. This molecule also has a plane of symmetry (through C1 and C3), making it achiral. It is optically INACTIVE. Why other options fail: - cis-1,2 is a meso compound (option b fails) - trans-1,3 has a plane of symmetry (option c fails) - cis-1,3 is a meso compound (option d fails) Only trans-1,2-dimethylcyclobutane lacks any internal plane of symmetry and exists as a chiral molecule, making it optically active. Therefore, the correct answer is A.