What is the hybridization of the central carbon of allene (1,2-propadiene) ?

An allene is when a carbon atom forms two separate double bonds, resulting in a linear structure.

H2C=C=CH2

The central carbon atom is forming two separate alkene bonds. Each carbon-carbon double bond is composed of a sigma bond and a pi bond. The central carbon atom forms two sigma bonds total and two pi bonds total. Since there are only two sigma bonds, only two hybrid orbitals are required. Therefore, only two atomic orbitals, an s + p orbital, are required to form the hybrid orbitals, which combine to form two sp orbitals. The central carbon atom is now sp hybridized.

This makes sense as the central carbon atom also forms two pi bonds and these are formed only from p-orbitals. Therefore, to form two pi bonds, that central carbon atom must have two p-orbitals available for bonding and this happens to be the case since only one s-orbital and one p-orbital were used in hybrid orbitals leaving two unhybridized p-orbitals.