(N/A) The molecular formula of ethyne is $C_{2}H_{2}$. It is the first member of the alkyne series.
In ethyne,both carbon atoms undergo $sp$ hybridization. Each carbon atom possesses two non-hybridized $2p$ orbitals ($2p_{x}$ and $2p_{y}$).
The two $sp$ hybrid orbitals are linear,and they are perpendicular to the $2p_{x}$ and $2p_{y}$ orbitals.
Bond formation in ethyne:
$1$. Carbon-carbon sigma $(\sigma)$ bond: This is formed by the head-on overlapping of one $sp$ hybrid orbital from each of the two carbon atoms.
$2$. Carbon-hydrogen sigma $(\sigma)$ bond: The remaining $sp$ hybrid orbital of each carbon atom overlaps with the $1s$ orbital of a hydrogen atom along the internuclear axis,forming two $C-H$ sigma bonds.
$3$. Pi $(\pi)$ bonds: Each carbon atom has two unhybridized $p$-orbitals ($2p_{x}$ and $2p_{y}$) that are perpendicular to each other and to the molecular axis. These orbitals undergo lateral overlapping to form two $\pi$-bonds between the carbon atoms.
The $H-C-C$ bond angle is $180^{\circ}$,resulting in a linear geometry: $H-C\equiv C-H$.