Geometric Isomers in Symmetric Polyene

Steps:

• Identify double bonds: terminal ones (1-2, 7-8) lack geometric isomerism due to identical substituents on one carbon.
• Confirm internal double bonds (3-4, 5-6) each allow cis (Z) or trans (E) configurations as each carbon has two different substituents.
• Calculate potential isomers: 2 bonds yield 2² = 4 configurations (EE, EZ, ZE, ZZ).
• Apply symmetry: the linear chain is symmetric, making EZ identical to ZE, resulting in 3 distinct isomers (EE, ZZ, EZ).

Why B is correct:

• Molecular symmetry reduces 4 configurations to 3 distinct geometric isomers, per isomerism rules for symmetric alkenes.

Why the others are wrong:

• A: Ignores the mixed cis-trans isomer.
• C: Counts 4 without accounting for symmetry equivalence.
• D: Overcounts by including terminal bond isomers or stereoisomers beyond geometric.

Final answer: B