Explanation:

In ethyne (also known as acetylene), the carbon-carbon bond is a triple bond consisting of one sigma bond and two pi bonds. The sigma bond is formed by the overlap of two atomic or hybrid orbitals on each carbon atom.

The atomic orbitals involved in the formation of the carbon-carbon sigma bond in ethyne are the sp orbitals on each carbon atom.

Formation of sp orbitals:
- Carbon has an atomic number of 6, which means it has six electrons. The electron configuration of carbon is 1s22s22p2.
- To form the sigma bond in ethyne, carbon undergoes hybridization, where one 2s orbital and two 2p orbitals combine to form three sp hybrid orbitals.
- The process of hybridization involves the mixing of atomic orbitals to form new hybrid orbitals with different shapes and energies.

Overlap of sp orbitals:
- In ethyne, each carbon atom forms two sigma bonds with its neighboring carbon atom.
- The two sp orbitals on each carbon atom overlap end-to-end to form two sigma bonds.
- This end-to-end overlap results in the formation of a strong and stable sigma bond.

Explanation of the given options:
a) sp3-sp3: This option is incorrect because ethyne does not involve sp3 hybridization. It involves sp hybridization.
b) s-s: This option is incorrect because ethyne involves the hybridization of carbon's s and p orbitals, not just the overlap of s orbitals.
c) sp-sp: This is the correct option. The carbon-carbon sigma bond in ethyne is formed by the overlap of two sp orbitals on each carbon atom.
d) sp-p: This option is incorrect because ethyne does not involve the overlap of sp and p orbitals. It involves the overlap of sp orbitals.

Therefore, the correct answer is option 'C' - sp-sp.