Step 1: Understanding the Concept:
Naming organic compounds systematically requires following the official rules established by the International Union of Pure and Applied Chemistry (IUPAC). To name a branched alcohol correctly, you must first locate the longest continuous carbon chain containing the principal functional hydroxyl group ($-\text{OH}$) to establish the parent name, number the chain to give the functional group the lowest possible locator number, and then identify any remaining side branches.
Step 2: Detailed Explanation:
Let's analyze the given structural formula step-by-step:
1. Identify the Principal Functional Group: The molecule contains an $-\text{OH}$ group, which makes it an alcohol. The suffix for the parent name will end in "-ol".
2. Find the Longest Carbon Chain: Trace the longest continuous line of carbon atoms that links directly to the $-\text{OH}$ group. This straight path contains $3$ carbon atoms. A three-carbon alkane parent chain corresponds to propane.
3. Number the Chain: Number the chain starting from the right-hand side to give the carbon bonded to the hydroxyl group the lowest possible positional index ($1$):
- $\text{C}_1$ is bonded to $-\text{OH}$ ($\text{-CH}_2\text{-OH}$)
- $\text{C}_2$ is the middle carbon ($\text{-CH-}$)
- $\text{C}_3$ is the terminal methyl group ($\text{CH}_3\text{-}$)
This positioning means the parent name becomes propan-1-ol.
4. Identify Side Branches (Substituents): Look at the remaining group attached to the chain. There is a single $-\text{CH}_3$ (methyl) group branch branching off from the middle carbon ($\text{C}_2$). This side branch is designated as 2-methyl.
Combining the prefix and parent name yields the final systematic name: 2-Methylpropan-1-ol. This matches option (B).
Step 3: Final Answer:
The IUPAC name of the compound is 2-Methylpropan-1-ol, matching option (B).