See image — Isomerism and Stereochemistry Chemistry Question

💡 Solution & Explanation

Concept: Allene (H2C=C=CH2) is a cumulated diene. In allene, the two CH2 groups at either end are perpendicular to each other due to the geometry of the cumulated double bonds. The central carbon is sp-hybridized, and the two sets of pi bonds are orthogonal. Step 1: Understand the geometry of allene. The left CH2 plane and the right CH2 plane are perpendicular (90°) to each other. So if the left CH2 has its H atoms in the plane of the paper (one wedge, one dash means actually both in-plane for a CH2 group on sp2 carbon... let me reconsider). In allene, the left carbon's H-H axis is perpendicular to the right carbon's H-H axis. Step 2: Identify l1 and l2 from the diagram. l1 spans from the upper-left H to the upper-right H (a long diagonal distance across the entire molecule). l2 spans from the lower-left H to the lower-right H (another diagonal, but the two CH2 planes are perpendicular, so this is a shorter 3D distance). Step 3: In allene, the C=C=C backbone is linear. The two terminal carbons are separated by 2 × (C=C bond length) ≈ 2 × 1.31 Å = 2.62 Å. The left H atoms lie in one plane (say the xz-plane) and the right H atoms lie in the perpendicular plane (the yz-plane). l1 is drawn as spanning H(upper-left) to H(upper-right): since the planes are perpendicular, one H is in one plane and the other H is in the perpendicular plane. l2 spans H(lower-left) to H(lower-right) similarly. Step 4: More carefully, l1 as drawn in the image is the distance between one H on the left carbon and one H on the right carbon that are both projected upward — but because the planes are perpendicular, the actual 3D arrangement means l1 (top H to top H, in the plane of paper across the full molecule) is longer than l2 (bottom H to bottom H, which are displaced out of plane relative to each other). The arrow for l1 spans the full width of the molecule at the top, while l2 spans a shorter diagonal at the bottom. Step 5: l1 is the longer distance (across the full molecular width in-plane projection) and l2 is shorter (the H atoms on the bottom are on carbons whose H-H axes are perpendicular, making the bottom-to-bottom H distance shorter in 3D). Therefore l1 > l2. Why other options fail: (a) l1 = l2 would only be true if the geometry were symmetric in the same plane, which it is not due to perpendicular CH2 planes. (c) l1 < l2 is the reverse of the correct answer. (d) l2 = 2l1 is numerically incorrect. Therefore, the correct answer is B.