Step 1: \( S_\text{N}1 \) reaction mechanism.
In the \( S_\text{N}1 \) mechanism, the reactivity depends on the stability of the carbocation formed during the reaction. More stable carbocations lead to faster reactions. The order of stability for carbocations generally follows the trend:
\[
\text{Tertiary}>\text{Secondary}>\text{Primary}>\text{Methyl}
\]
Step 2: Analyze the compounds.
- Compound IV has a tertiary carbocation, which is the most stable and thus most reactive.
- Compound III has a secondary carbocation, making it next in reactivity.
- Compound I has a primary carbocation, so it is less reactive.
- Compound II has a methyl carbocation, the least stable and reactive.
Step 3: Conclusion.
The reactivity order is:
\[
\text{IV}>\text{III}>\text{I}>\text{II}
\]
Final Answer:
\[
\boxed{\text{IV}>\text{III}>\text{I}>\text{II}}
\]