Final answer:
The correct structure of allene consists of the hydrogen atoms attached to the terminal carbon atoms lying in planes perpendicular to each other, due to the sp hybridization of the central carbon and sp2 hybridization of the terminal carbons.
Step-by-step explanation:
The molecule in question, allene (H2C=C=CH2), has a unique structure. The correct answer to the question is (c): the two H atoms on one C lie above and below the plane defined by the other CH2 group. The allene molecule features two consecutive double bonds, which give rise to different planes of hybrid orbitals due to the hybridization states of the carbon atoms.
The terminal carbon atoms of allene are hybridized as sp2, which would typically allow the formation of a planar structure. However, the central carbon atom is hybridized to sp, which results in perpendicular planes for the p-orbitals. The central carbon’s p-orbitals form π bonds with the p-orbitals of the terminal carbon atoms, and as a consequence, the hydrogen atoms attached to the terminal carbon atoms lie in planes that are perpendicular to each other. Thus, the molecule displays dibridged or cumulated diene geometry.