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The IUPAC name of the t-butyl group is:
A.2-methylpropyl
B.trimethyl methyl
C.1,1-dimethylethyl
D.2-methyl-2-propyl

Answer
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Hint: t-butyl group \[C{{H}_{3}}-C(C{{H}_{3}})-CH_{3}^{{}}\], or tertiary butyl group is a saturated hydrocarbon (alkane) arrangement in which one \[C\] atom is surrounded by 3 methyl groups \[C{{H}_{3}}\] and to the fourth bond any element or group \[A\] is attached.
It has the following structure:
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In IUPAC nomenclature, the first step is selecting the longest chain and numbering starts from the carbon atom to which a special element or group is attached gets the least number.
Complete answer:
The first step in naming a hydrocarbon is selection of the longest chain or parent chain that consists of carbon atoms. From the above figure, we can easily figure out that the longest chain will have 3 \[C\] atoms, thus the name of the alkyl group is propyl. This is the base name of the compound. It is called an alkyl because one of four bonds of \[C\] is free.
The second step is to number the carbon atoms in the parent chain such that substituent groups attached to the \[C\] atoms in it get assigned the least numerical value.
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The next step is to determine which elements are substituent groups attached to \[C\] atoms of the parent chain. Here \[C{{H}_{3}}\](methyl group) is attached to the 2nd carbon atom. Thus, the methyl prefix will be attached to the base name along with the position number to which carbon is the substituent group attached.
Hence, the name of the hydrocarbon is:
2-methylpropyl.
The correct option is (A) 2-methylpropyl

Note:A simple list of IUPAC nomenclature.
-Identify the longest carbon chain. This chain is called the parent chain.
-Identify all of the substituents (groups emanating from the parent chain).
-Number the carbons of the parent chain from the end that gives the substituents the lowest numbers. -When comparing a series of numbers, the series that is the "lowest" is the one which contains the lowest number at the occasion of the first difference. If two or more side chains are in equivalent positions, assign the lowest number to the one which will come first in the name.
-If the same substituent occurs more than once, the location of each point on which the substituent occurs is given. In addition, the number of times the substituent group occurs is indicated by a prefix (di, tri, tetra, etc.)