Final answer:
In cumulene, the types of orbitals that overlap to form its structure are s and p orbitals. This includes the end-to-end overlap to form sigma bonds, and the side-by-side overlap to form pi bonds. No d orbitals are involved in the bonding of cumulenes.
Step-by-step explanation:
In cumulene, the types of orbitals that overlap are primarily s and p orbitals. Cumulene molecules feature a carbon chain with alternating single and double bonds. To form these bonds, the carbon atoms undergo hybridization of their atomic orbitals. An s orbital can hybridize with one p orbital to form two sp hybrid orbitals or with two p orbitals to form three sp² hybrid orbitals or else with all three p orbitals to form four sp³ hybrid orbitals. These hybrid orbitals then overlap with adjacent similar hybrid orbitals or s orbitals of hydrogen to form bonds.
For the double bonds in cumulenes, one bond is always a sigma (σ) bond resulting from the end-to-end overlap of sp or sp² hybrid orbitals, while the additional bonds are pi (π) bonds formed from the side-by-side overlap of unhybridized p orbitals. In cumulene, because it lacks d orbitals in its bonding framework, there is no overlap involving d orbitals. Therefore, the correct answer to the question, which asks about the overlap in cumulene, is option 1: s and p orbitals.