Step 1: Understanding the Concept:
To find the IUPAC name, identify the longest carbon chain containing the principal functional group (here, the halogen atom).
Step 2: Key Formula or Approach:
The approach is to expand the condensed structural formula, number the longest parent chain starting from the end closer to the substituent, and name the substituents alphabetically.
Step 3: Detailed Explanation:
The given compound is \( \text{(CH}_3\text{)}_3\text{C}-\text{CH}_2\text{Br} \).
Expanding the structure, we see a central carbon attached to three methyl groups and one \( -\text{CH}_2\text{Br} \) group.
The longest continuous carbon chain that includes the carbon attached to the bromine atom is 3 carbons long (a propane chain).
We number the chain starting from the carbon directly attached to the bromine atom to give it the lowest locant.
Carbon-1 is the \( -\text{CH}_2\text{Br} \) carbon.
Carbon-2 is the central quaternary carbon, which has two remaining methyl groups attached as substituents.
Carbon-3 is one of the terminal methyl groups.
The substituents are one 'bromo' group at C-1 and two 'methyl' groups at C-2.
When writing the name, substituents are listed in alphabetical order.
Thus, 'bromo' comes before 'methyl'.
Combining these parts, the IUPAC name is 1-Bromo-2,2-dimethylpropane.
Step 4: Final Answer:
The IUPAC name is 1-Bromo-2,2-dimethylpropane.