Step 1: Understanding the Question:
The question asks to identify the hydrocarbon from the given options that does not belong to the same homologous series as the other three.
Step 2: Key Formula or Approach:
A homologous series is a group of organic compounds that share the same functional group and general molecular formula, with successive members differing by a structural unit of \(\text{--CH}_2\text{--}\).
Step 3: Detailed Explanation:
• Let us analyze each option:
- (A) \(\text{CH}_4\) (Methane): Saturated hydrocarbon with general formula \(\text{C}_n\text{H}_{2n+2}\) where \(n = 1\). This is an alkane.
- (B) \(\text{C}_2\text{H}_6\) (Ethane): Saturated hydrocarbon with general formula \(\text{C}_n\text{H}_{2n+2}\) where \(n = 2\). This is an alkane.
- (C) \(\text{C}_3\text{H}_8\) (Propane): Saturated hydrocarbon with general formula \(\text{C}_n\text{H}_{2n+2}\) where \(n = 3\). This is an alkane.
- (D) \(\text{C}_4\text{H}_8\) (Butene): Unsaturated hydrocarbon with general formula \(\text{C}_n\text{H}_{2n}\) where \(n = 4\). This is an alkene.
• Since \(\text{CH}_4\), \(\text{C}_2\text{H}_6\), and \(\text{C}_3\text{H}_8\) are all alkanes and belong to the alkane homologous series, \(\text{C}_4\text{H}_8\) stands out as an alkene.
Step 4: Final Answer:
The hydrocarbon \(\text{C}_4\text{H}_8\) does not belong to the same homologous series.