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What hybridization is involved in the carbon-carbon bonds?

Answer
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Hint: A sigma bond forms between one hybridised orbital from each of the carbon atoms in the carbon–carbon single bond. The orbitals in ethane are sp3-hybridized orbitals, but single bonds with various hybridizations do form between carbon atoms.

Complete answer:
A carbon atom can establish a covalent connection with another carbon atom in a variety of ways, the most common of which is a single bond (or a sigma bond).
The sigma bond is generated between one hybridised orbital from each of the two carbon atoms in this situation.
In alkanes like ethane, carbon's orbitals are $s{p^3}$ hybridized - this means that one s orbital and three p orbitals come together to form four $s{p^3}$ hybrid orbitals. Single bonds can form between carbon atoms with other hybridizations as well ( $s{p^2}$ with $s{p^2}$ , for example).Carbon atoms can create double bonds with a $s{p^2}$ hybridised orbital and an unhybridized p orbital in alkenes; these bonds, which consist of one sigma and one pi bond, are formed with a $s{p^2}$ hybridised orbital and an unhybridized p orbital.
The carbon atoms in alkynes can form triple bonds, which consist of one sigma and two pi bonds and are created by combining one $sp$ hybridised orbital with two unhybridized p
orbitals.

Note:
In an alkane, all of the carbon atoms are $s{p^3}$ hybridised with tetrahedral geometry. Alkenes and other atoms with a double bond commonly feature $s{p^2}$ hybridised carbons with trigonal planar shape. The triple bond, on the other hand, is only seen in alkynes with sp-hybridized carbon atoms.