Step 1: Understanding the \(E_1\) Mechanism The \(E_1\) (unimolecular elimination) reaction proceeds via a carbocation intermediate. Carbocation stability directly correlates with reactivity; higher stability leads to a faster reaction rate. Step 2: Analyzing the Given Compounds The compounds feature halides (\(\text{Cl}\)) bonded to various carbon atoms. The reactivity sequence is determined by the stability of the carbocation formed upon halide dissociation. Step 3: Determining the Order of Reactivity (A) Primary Carbocation: Exhibits lowest stability, resulting in the slowest reaction. (B) Carbocation Undergoing Rearrangement: Rearrangement yields a more stable secondary or tertiary carbocation, thus increasing reactivity. (C) Five Hyperconjugating Structures: Contributes moderate carbocation stability. (D) Resonance-Stabilized Carbocation: Achieves maximum stability through electron delocalization, thereby enhancing reactivity. Step 4: Final Order of Reactivity The order of carbocation stability is:\[D>B>C>A\]Final Answer: The correct order is \( D>B>C>A \).