Step 1: Understanding the Question:
The question asks which alkyl halide undergoes racemization (formation of an optically inactive 50:50 mixture of enantiomers) when subjected to basic substitution conditions.
Step 2: Key Formula or Approach:
Racemization occurs primarily via an $\text{S}_\text{N}1$ mechanism. The substrate must fulfill two critical conditions:
1. It must contain a chiral (asymmetric) carbon center that holds the leaving group.
2. It should form a highly stable carbocation intermediate (such as a tertiary or resonance-stabilized benzylic carbocation) to favor the stepwise $\text{S}_\text{N}1$ pathway over the concerted $\text{S}_\text{N}2$ pathway.
Step 3: Detailed Explanation:
Let's evaluate the structural features of the key chiral options:
Option (C) represents sec-butyl chloride, $\text{CH}_3-\text{CH}^*(\text{Cl})-\text{CH}_2-\text{CH}_3$. It possesses a chiral center, but it forms a standard secondary carbocation which often undergoes significant competitive bi-molecular $\text{S}_\text{N}2$ substitution, leading to inversion rather than complete racemization.
Option (D) represents 1-chloro-1-phenylethane, $\text{C}_6\text{H}_5-\text{CH}^*(\text{Cl})-\text{CH}_3$. This molecule contains a chiral carbon. When the chloride leaving group departs, it generates a benzylic carbocation intermediate:
$$\text{C}_6\text{H}_5-\text{CH}^+-\text{CH}_3$$
This carbocation is exceptionally stable due to extensive $\pi$-resonance delocalization into the aromatic benzene ring. Because it is highly stable, the reaction proceeds cleanly via the $\text{S}_\text{N}1$ mechanism. The intermediate carbocation is completely planar, allowing the incoming hydroxide nucleophile ($\text{OH}^-$) to attack with equal probability from either the front or back face, producing a racemic mixture.
Step 4: Final Answer:
The compound most likely to undergo extensive racemization is $\text{C}_6\text{H}_5-\text{CH}(\text{Cl})-\text{CH}_3$, which matches option (D).