Understanding the Concept:
An $\text{S}_{\text{N}}1$ nucleophilic substitution mechanism proceeds via a two-step pathway where the rate-determining step involves the heterolytic cleavage of the carbon-leaving group bond to form a carbocation intermediate. The relative reactivity of alkyl halides under $\text{S}_{\text{N}}1$ conditions depends directly on the stability of the resulting carbocation intermediate.
Step 1: Evaluate the assertion by comparing the carbocation stability of the structures.
Let's look at the carbocations generated by each compound:
$\text{C}_6\text{H}_5\text{CH}_2\text{Br} \rightarrow \text{C}_6\text{H}_5\text{CH}_2^+$ (Benzyl carbocation, highly stabilized by resonance delocalization across the aromatic ring $\pi$-system).
$(\text{CH}_3)_2\text{CH-Br} \rightarrow (\text{CH}_3)_2\text{CH}^+$ (Isopropyl carbocation, a secondary carbocation stabilized by $+I$ inductive effects and 6 hyperconjugation structures).
$\text{CH}_3\text{CH}_2\text{Br} \rightarrow \text{CH}_3\text{CH}_2^+$ (Ethyl carbocation, a primary carbocation with minimal stabilization).
The stability order is: $\text{Benzyl}>\text{Isopropyl}>\text{Ethyl}$. This matches the stated reactivity trend, confirming the assertion is correct.
Step 2: Evaluate the reason and its logical link to the assertion.
The reason states that the benzyl carbocation is the most stable and the isopropyl carbocation is the least stable among the three compounds. This stability order explains why benzyl bromide undergoes substitution fastest and ethyl bromide slowest. Therefore, both statements are correct, and the reason provides the correct explanation for the assertion.