The correct increasing order of the reactivity of halides for `S_(N^(1))` reaction is:

Options

A. `CH_(3)-CH_(2)-Xlt(CH_(3))_(2)CH-XltCH_(2)=CH-CH_(2)-XltPhCH_(2)-X`
B. `(CH_(3))_(2)CH-XltCH_(3)-CH_(2)-XltCH_(2)=CH-CH_(2)-XltPhCH_(2)-X`
C. `PhCH_(2)-Xlt(CH_(3))_(2)CH-XltCH_(3)-CH_(2)-XltCH_(2)=CH-CH_(2)-X`
D. `CH_(2)=CH-CH_(2)-XltPh-CH_(2)-Xlt(CH_(3))_(2)CH-X
ltCH_(3)-CH_(2)-X`

Explanation

To determine the correct increasing order of the reactivity of halides for an SN1 reaction, we need to analyze the stability of the carbocations formed from these halides. The stability of the carbocation is crucial because the more stable the carbocation, the faster the reaction will proceed.

### Step-by-Step Solution:

1. **Identify the Halides**: Let's consider the halides we are comparing. For example, we can take:
- Halide 1: CH3CH2X (Primary halide)
- Halide 2: CH3CHXCH3 (Secondary halide)
- Halide 3: (CH3)2C=CHX (Tertiary halide with resonance)
- Halide 4: C6H5CH2X (Benzyl halide with resonance)

2. **Remove the Halide (X)**: In an SN1 reaction, the first step is the loss of the halide ion (X-) to form a carbocation. We will analyze the carbocations formed:
- Carbocation 1: CH3CH2+ (Primary carbocation)
- Carbocation 2: CH3C+HCH3 (Secondary carbocation)
- Carbocation 3: (CH3)2C=CH+ (Tertiary carbocation with resonance)
- Carbocation 4: C6H5CH2+ (Benzyl carbocation with resonance)

3. **Evaluate Carbocation Stability**: The stability of carbocations can be determined by the degree of substitution and the presence of resonance:
- Carbocation 1 (Primary) has no resonance and is the least stable.
- Carbocation 2 (Secondary) has more hyperconjugation and is more stable than Carbocation 1.
- Carbocation 3 (Tertiary) has resonance stabilization, making it more stable than both Carbocations 1 and 2.
- Carbocation 4 (Benzyl) also has resonance stabilization, which is very effective, making it the most stable.

4. **Rank the Carbocations**: Based on the stability of the carbocations formed:
- Carbocation 1 (Primary) < Carbocation 2 (Secondary) < Carbocation 3 (Tertiary) < Carbocation 4 (Benzyl)

5. **Determine the Reactivity Order**: Since the reactivity in an SN1 reaction is directly related to the stability of the carbocation, we can conclude the increasing order of reactivity:
- CH3CH2X (Primary) < CH3CHXCH3 (Secondary) < (CH3)2C=CHX (Tertiary) < C6H5CH2X (Benzyl)

### Final Answer:
The correct increasing order of the reactivity of halides for SN1 reaction is:
**CH3CH2X < CH3CHXCH3 < (CH3)2C=CHX < C6H5CH2X**