Concept:
An \(\text{S}_{\text{N}}1\) reaction proceeds through formation of a carbocation intermediate.
So the compound that forms the most stable carbocation will show the highest \(\text{S}_{\text{N}}1\) reactivity.
ip
Step 1: Recall carbocation stability order.
The stability order of carbocations is:
\[
3^\circ > 2^\circ > 1^\circ > \text{methyl}
\]
ip
Step 2: Classify the given alkyl iodides.
• n-Butyl iodide is primary
• sec-Butyl iodide is secondary
• Isobutyl iodide is primary
• tert-Butyl iodide is tertiary
e}
ip
Step 3: Identify the most reactive compound in \(\text{S}_{\text{N}}1\).
Since tert-butyl iodide forms the most stable tertiary carbocation, it reacts fastest by the \(\text{S}_{\text{N}}1\) mechanism.
ip
Hence, the correct answer is:
\[
\boxed{(D)\ \text{tert-Butyl iodide}}
\]