Which types of orbital overlap are present in the bonding of a cumulene molecule?

• A. Sigma bonds formed by $\mathrm{sp}$ hybrid orbitals and one set of pi bonds formed by $p$ orbitals in the same plane
• B. Sigma bonds formed by $\mathrm{sp}$ hybrid orbitals and pi bonds formed by $\mathrm{sp}$ hybrid orbitals
• C. Sigma bonds formed by $\mathrm{sp}$ hybrid orbitals and two perpendicular sets of pi bonds formed by unhybridized $p$ orbitals
• D. Only sigma bonds formed by $\mathrm{sp}$ hybrid orbitals; no pi bonds are present

Answer: (C)

Verified step by step guidance

1. Identify the hybridization of the central carbon atoms in a cumulene molecule. Since cumulenes have consecutive double bonds, the carbons involved are typically sp hybridized.
2. Recall that sp hybridization involves mixing one s orbital and one p orbital, resulting in two sp hybrid orbitals oriented linearly (180° apart), which form sigma bonds.
3. Understand that the remaining two unhybridized p orbitals on each sp hybridized carbon are perpendicular to each other and to the axis of the sigma bonds.
4. Recognize that these two sets of unhybridized p orbitals form two perpendicular pi bonds, one set in one plane and the other set in a plane perpendicular to the first.
5. Conclude that the bonding in cumulenes consists of sigma bonds formed by sp hybrid orbitals and two perpendicular sets of pi bonds formed by unhybridized p orbitals.