Final answer:
The p orbital on the carbon adjacent to a double bond in conjugated unsaturated systems is the unhybridized 2p orbital remaining after sp² hybridization, which forms the π bond in a double bond.
Step-by-step explanation:
The p orbital on the carbon adjacent to a double bond in conjugated unsaturated systems originates from the hybridization of the carbon atoms involved in the formation of the molecule. When carbon atoms hybridize, they combine their 2s and two of their 2p orbitals to form three sp² hybrid orbitals, which are used to form sigma (σ bonds) and to bond with hydrogen atoms. The remaining unhybridized 2p orbital, which is perpendicular to the plane of the sp² orbitals, is what forms the π bond in a double bond. This arrangement allows the unhybridized 2p orbitals on adjacent carbons to overlap side-by-side and form a conjugated system. In conjugation, these p orbitals can interact and delocalize electrons across the entire molecule, adding stability and unique properties to the molecule.