Show how a double and triple bond are formed between carbon atoms in
`C_(2)H_(4)` and

Explanation

`C_(2)H_(2)` (Acetylene) : In the formation of acetylene molecule, the two carbon atoms undergo sp hybridisation in their excited states `(1s^(2)2s^(1)2p_(x)^(1)2p_(y)^(1)2p_(z)^(1))`. As a result of which two sp hybrid orbitals form on each of them. All of them contain an electron, each. One sp hybrid orbital of each carbon atom overlaps Head - Head forming a sigma bond in-between them.

Now, the remaining two 'sp' hybrid orbitals overlap Head - Head with '1s' orbitals of two H - atoms forming two sigma bonds. Now, the unhybridised, pure `2p_(y)` and `2p_(z)` orbitals of each carbon atom overlap side - wise forming two pi bonds in-between them.
Thus, a triple bond is formed between the two carbon atoms. In total there are three sigma bonds and two pi bonds in acetylene molecule. The bond angle is `180^(@)`. The molecule is linear.