The question asks us to identify which compound is most reactive toward the $S_N 1$ reaction. The $S_N 1$ reaction is characterized by a two-step mechanism where the formation of a carbocation intermediate is crucial. Therefore, the stability of the carbocation formed plays a significant role in determining the reactivity of the compound toward $S_N 1$. More stable carbocations lead to faster reactions.
Let's evaluate the carbocation stability for each option:
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${C6H5CH2Br}: The carbocation $C6H5CH_2^+$ formed is benzyl, which is resonance-stabilized by the phenyl group. However, it is less stable compared to benzylic carbocations with additional stabilizing groups.
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${C6H5CH(C6H5)Br}: The carbocation $C6H5CH(C6H5)^+$ has two phenyl groups that can provide resonance stabilization, making it more stable than a simple benzyl carbocation.
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${C6H5CH(CH3)Br}: The carbocation $C6H5CH(CH3)^+$ would be a benzylic carbocation with one methyl group offering hyperconjugation, which is moderately stable.
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${C6H5C(CH3)(C6H5)Br}: The carbocation $C6H5C(CH3)(C6H5)^+$ formed here is a tertiary benzylic carbocation. It is highly stabilized due to multiple factors: resonance from both phenyl groups and hyperconjugation from the methyl group, making it the most stable and reactive towards the $S_N 1$ mechanism.
The compound ${C6H5C(CH3)(C6H5)Br} forms the most stable carbocation due to resonance and hyperconjugation, thus making it the most reactive in an $S_N 1$ reaction.
Therefore, the correct answer is: ${ C6H5C(CH3)(C6H5)Br}$.