The correct answer is: C. sp and sp2
The central carbon in allene is bonded to two other carbons and two hydrogens. The terminal carbons are bonded to one other carbon and two hydrogens.
In order to minimize electron repulsion, the central carbon will hybridize its s and p orbitals to form three sp hybridized orbitals. These orbitals are arranged in a trigonal planar geometry with 120° angles between them. The two p orbitals that are not hybridized are perpendicular to the plane of the sp hybridized orbitals.
The terminal carbons will hybridize their s and p orbitals to form two sp2 hybridized orbitals. These orbitals are arranged in a trigonal planar geometry with 120° angles between them. The remaining p orbital is perpendicular to the plane of the sp2 hybridized orbitals.
The following diagram shows the hybridization of the carbon atoms in allene:
The sp hybridized orbitals on the central carbon are used to form sigma bonds with the two terminal carbons. The p orbitals on the central carbon are used to form pi bonds with the two terminal carbons. The sp2 hybridized orbitals on the terminal carbons are used to form sigma bonds with the central carbon and hydrogen atoms. The remaining p orbital on the terminal carbon is used to form a pi bond with the central carbon.
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