Final answer:
A central carbon atom that is sp hybridized and has no lone pairs of electrons would have 2 pi bonds and 2 sigma bonds.
Step-by-step explanation:
A central carbon atom that is sp hybridized and has no lone pairs of electrons would have a linear geometry. In terms of bonding, this type of carbon atom would have 2 pi bonds and 2 sigma bonds.
The 2 pi bonds are formed by the overlap of unhybridized p orbitals, and the 2 sigma bonds result from the overlap of hybridized sp orbitals with other atoms.
Overall, the sp hybridized central carbon atom with no lone pairs of electrons would have 2 pi bonds and 2 sigma bonds.