Explain hybridisation in acetylene?

Hint: Orbital hybridisation or hybridization is defined as the concept of mixing of the atomic orbitals to form new hybrid orbitals possessing different energies, shapes, etc., than the parent atomic orbitals suitable for the pairing of electrons to form chemical bonds in valence bond theory. Now, we know that carbon has four unpaired electrons so it can have four equal energy bonds. The hybridization of orbitals is also greatly favoured because the newly formed hybridized orbitals are lower in energy compared to their parent, unhybridized counterparts. This results in formation of more stable compounds when hybridization occurs.

Complete answer: If we consider the hybrid orbital picture of acetylene, then we see that both carbon atoms are sp-hybridized. In an sp-hybridized carbon atom, the 2s orbital combines with the 2\[{{p}_{x}}\] orbital to form two new sp hybrid orbitals that are equal in energy and are oriented at an angle of $180^o$ with respect to each other. \[{{C}_{2}}{{H}_{2}}\] has sp-hybridization and it is explained as the two carbon atoms undergo mixing of one s and one p-orbitals to form two sp-hybridized orbitals and these sp-hybridized orbital of the C-atoms make a C-C sigma bond while the other sp-hybrid orbital of each C-atom overlaps with the s-orbital of one of the H-atom to form a C-H sigma bond each.

Note: All the types of Alkanes have \[s{{p}^{3}}\] hybridization formed by one s-orbital and three p-orbitals which forms a single bond, all types of Alkene have \[s{{p}^{2}}\] hybridization formed by one s-orbital and two p-orbitals which forms a double bond and all types of Alkynes have sp hybridization formed by one s-orbital and three p-orbitals which forms a single bond. Hybridization can be calculate easily using the following shortcut:
Hybridisation = 0.5 (valence electron in central atom + number of atoms attached to central atom by single bond + negative charge - positive charge).