Step 1: Understanding the Structure:
The figure shows a five-carbon chain with a double bond and an \(-\text{NH}_2\) group. Written out: \(\text{CH}_3-\text{CH}=\text{CH}-\text{CH}(\text{CH}_3)-\text{NH}_2\), where the carbon bearing \(\text{NH}_2\) also carries a methyl that is part of the longest chain.
Step 2: Key Rule:
The longest chain containing the principal group (amine) and the double bond is chosen. The amine, being the principal group, gets the lowest locant, then the double bond.
Step 3: Detailed Explanation:
Chain: \(\text{CH}_3\) (C1) - \(\text{CH}(\text{NH}_2)\) (C2) - \(\text{CH}=\) (C3) \(=\text{CH}\) (C4) - \(\text{CH}_3\) (C5). Numbering from the end nearest the amine gives \(-\text{NH}_2\) at C2 and the double bond at C3. Name: pent-3-en-2-amine.
Step 4: Why the other options are wrong.
Pent-2-en-4-amine (A) numbers from the wrong end, giving the amine a higher locant (4) than necessary. Options (C) and (D) choose a four-carbon chain, but the longest chain has five carbons.
Final Answer:
The name is pent-3-en-2-amine, option (B).
\[ \boxed{\text{Pent-3-en-2-amine (B)}} \]
