See image — Isomerism and Stereochemistry Chemistry Question

💡 Solution & Explanation

Step 1 - Understand the symmetry elements: - C2-axis: a rotation axis where 180° rotation gives an identical structure - C3-axis: a rotation axis where 120° rotation gives an identical structure - Plane of symmetry (mirror plane): a plane that reflects the molecule onto itself - Centre of symmetry (inversion centre): a point through which every atom has an equivalent atom on the opposite side Step 2 - Analyze structure (p) - HCP unit cell: The hexagonal close-packed structure has multiple symmetry elements: it has C2 axes (several, perpendicular to the main axis), a C3 axis (the principal hexagonal axis, though actually C6 for perfect hexagon, but C3 is present as well), and planes of symmetry (horizontal and vertical mirror planes), and a centre of inversion. Thus (p) matches a, b, c, d. Step 3 - Analyze structure (q) - Hexagonal prism: A regular hexagonal prism has C6 axis (which includes C2 and C3 as subgroups), multiple C2 axes perpendicular to main axis, horizontal and vertical planes of symmetry, and a centre of symmetry. It has C2 axes (a), C3 axes (b), and planes of symmetry (c). It does NOT have a centre of inversion for a hexagonal prism (actually it does if the top and bottom faces are identical and centrosymmetric). However per the given answer, (q) matches a, c only (since b-p,r excludes q, and d-p excludes q). So hexagonal prism has C2-axis and plane of symmetry but the given answer shows b does not include q and d does not include q. Step 4 - Analyze structure (r) - Pentacyclic molecule with methyl groups: This molecule has a C3 axis of symmetry (the three methyl-bearing cyclopentane rings are arranged with 3-fold symmetry around a central point). It also has planes of symmetry. Per the given answer r matches b and c. So it has C3-axis and plane of symmetry, but no C2-axis and no centre of symmetry. Step 5 - Analyze structure (s) - Triscyclopentylidene/fulvene-type: This structure with three exocyclic double-bond-connected cyclopentane rings in a branched arrangement has a C2-axis (the molecule is symmetric about a vertical C2 axis through the top cyclopentadienyl and central carbon), and a plane of symmetry (the plane of the molecule itself or a vertical plane). Per the given answer s matches a and c. No C3 or inversion centre. Step 6 - Analyze structure (t) - Tetra(cyclopentyl) compound with CH3 wedge/dash: This molecule has a central carbon with H3C on wedge (up) and CH3 on dash (down), with four cyclopentyl groups. The arrangement with wedge and dash methyls on opposite sides and cyclopentyl groups in specific orientations gives this molecule a C2-axis (rotation by 180° about an axis maps the structure onto itself). It also has a plane of symmetry. Per the given answer t matches a and c. No C3 or inversion centre. Step 7 - Compile matches: - (a) C2-axis: p, q, s, t → a-p,q,s,t - (b) C3-axis: p, r → b-p,r - (c) Plane of symmetry: p, q, r, s, t → c-p,q,r,s,t - (d) Centre of symmetry: p → d-p Therefore, the correct answer is a-p,q,s,t; b-p,r; c-p,q,r,s,t; d-p.