Step 1: Understanding the Question:
We need to determine which of the given alkyl iodides lacks optical activity by checking for the absence of an asymmetric chiral carbon center.
Step 2: Detailed Explanation:
A molecule displays optical isomerism if it contains at least one chiral carbon atom—a tetrahedral carbon bonded to four entirely different atoms or groups. Let's inspect the structures:
2-Iodo-3-methylbutane: $\text{CH}_3\text{-C}^* \text{H(I)-CH(CH}_3)_2$. The $\text{C}_2$ carbon is chiral because it connects to -H, -I, $\text{-CH}_3$, and $\text{-CH(CH}_3)_2$.
3-Iodohexane: $\text{CH}_3\text{-CH}_2\text{-C}^* \text{H(I)-CH}_2\text{-CH}_2\text{-CH}_3$. The $\text{C}_3$ carbon is chiral as it binds to -H, -I, $\text{-C}_2\text{H}_5$, and $\text{-C}_3\text{H}_7$.
2-Iodopentane: $\text{CH}_3\text{-C}^* \text{H(I)-CH}_2\text{-CH}_2\text{-CH}_3$. The $\text{C}_2$ carbon is chiral since it binds to -H, -I, $\text{-CH}_3$, and $\text{-C}_3\text{H}_7$.
2-Iodo-2-methylbutane: $\text{CH}_3\text{-C(I)(CH}_3)\text{-CH}_2\text{-CH}_3$. The $\text{C}_2$ carbon is bonded to an iodine atom, an ethyl group, and
two identical methyl groups.
Because it has two identical methyl groups attached to the central carbon, 2-Iodo-2-methylbutane lacks a chiral center and cannot exhibit optical isomerism.
Step 3: Final Answer:
The compound that does not show optical activity is option (D).