The increasing order of the reactivity of the following halides for the `S_(N)` 1 reaction is
`underset((I))underset(Cl)underset(|)(CH_(3))CHCH_(2)CH_(3) " " underset((II))(CH_(3)CH_(2)CH_(2)Cl) " " underset((III))(p-H_(3)CO-C_(6)H_(4)-CH_(2)Cl`

Options

A. `(III)lt(II)lt(I)`
B. `(II)lt(I)lt(III)`
C. `(I)lt(III)lt(II)`
D. `(II)lt(III)lt(I)`

Explanation

To determine the increasing order of reactivity of the given halides for the SN1 reaction, we need to analyze the stability of the carbocations that will be formed when the halide leaves. The more stable the carbocation, the more reactive the halide will be in an SN1 reaction.

### Step-by-Step Solution:

1. **Identify the Halides:**
We have three compounds:
- (I) (CH₃)CH(CH₂)CH₃Cl
- (II) CH₃CH₂CH₂Cl
- (III) p-H₃CO-C₆H₄-CH₂Cl

2. **Determine the Carbocation Formed:**
- For (I): When Cl leaves, we will get a secondary carbocation: (CH₃)C⁺H(CH₂)CH₃.
- For (II): When Cl leaves, we will get a primary carbocation: CH₃CH₂C⁺H₂.
- For (III): When Cl leaves, we will get a benzylic carbocation: p-H₃CO-C₆H₄-CH₂⁺.

3. **Evaluate Carbocation Stability:**
- **Primary Carbocation (II)**: Least stable due to only one alkyl group.
- **Secondary Carbocation (I)**: More stable than primary due to hyperconjugation from two alkyl groups.
- **Benzylic Carbocation (III)**: Most stable due to resonance stabilization from the aromatic ring.

4. **Order of Stability:**
Based on the stability of the carbocations:
- (II) Primary < (I) Secondary < (III) Benzylic

5. **Increasing Order of Reactivity:**
Since the reactivity in an SN1 reaction is directly related to the stability of the carbocation formed, the increasing order of reactivity for the halides is:
- (II) < (I) < (III)

### Final Answer:
The increasing order of reactivity of the given halides for the SN1 reaction is:
(II) < (I) < (III)