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The structure of third member of the alkyne series is:
$A)\text{ H-C}\equiv \text{C-H}$
$\text{B) H-C}\equiv \text{C-C}{{\text{H}}_{\text{3}}}$
\[\text{C) H-C}\equiv \text{C-C}{{\text{H}}_{\text{2}}}\text{C}{{\text{H}}_{\text{3}}}\]
\[\text{D) H-C}\equiv \text{C-C}\equiv \text{C-H}\]
$\text{E) H-C}\equiv \text{C-CH=C}{{\text{H}}_{\text{2}}}$

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Hint: Alkynes are organic molecules having at least one carbon-carbon triple bond $(-C\equiv C-)$. They can be expressed with empirical formula ${{C}_{n}}{{H}_{2n-2}}$, where $''n''$ can be $2,3,4,5......$ and $n\ne 0,1$. First member of the alkyne family obtains by taking $n=2$.

Complete answer:
Alkyne is an unsaturated hydrocarbon with one C-C triple bond. Simplest alkyne is Acetylene $(HC\equiv CH)$having one triple bond. The term Hydrocarbon denotes that there is only Hydrogen and carbon and the term unsaturation denotes the presence of double or triple bonds.
General formula of alkyne family is ${{C}_{n}}{{H}_{2n-2}}$, where $n=2,3,4,5......$
For first member of alkyne family take $n=2,\text{ }{{\text{C}}_{\text{2}}}{{\text{H}}_{\text{2}}}\text{ }(H-C\equiv C-H)$
For second member of alkyne family take $n=3,\text{ }{{\text{C}}_{3}}{{\text{H}}_{4}}\text{ }(H-C\equiv C-C{{H}_{3}})$
For third member of alkyne family take \[n=4,\text{ }{{\text{C}}_{4}}{{\text{H}}_{6}}\text{ }(H-C\equiv C-C{{H}_{2}}C{{H}_{3}})\] i.e. but\[1\]yne

Hence the third member is but-\[1\]-yne, thus option C is correct.

Additional information:Lower members of the alkyne family (ethyne, propyne, and $1-$butyne etc) are gases and intermediate molecular mass alkynes are liquids and higher members are solid in at room temperature. Alkynes are generally hydrophobic in nature as general hydrocarbons. Alkynes are double unsaturated and two equivalents of ${{H}_{2}}$ gas can add to alkyne. The addition of ${{H}_{2}}$ gas is termed as hydrogenation or reduction of alkyne to alkane. Reduction of alkyne can stop at alkene by using Lindlar catalyst.
\[HC\equiv CH\text{ }\xrightarrow[1\text{ }atm]{Lindlar\text{ catalyst}}\text{ }{{\text{H}}_{\text{2}}}\text{C=C}{{\text{H}}_{2}}\]


Note: Carbon chain with any functional group other than one \[C-C\] triple bond is known as alkyne derivative and these are not pure members of the alkyne family. Acetylene is used as an efficient fuel and precursor of many important organic syntheses.