Which of the following statement regarding `S_(N)1` reaction shown by alkyl halide is incorrect?

Options

A. The added nucleophile plays no kinetic role in `S_(N^1)` reaction.
B. The `S_(N^1)` reaction involves the inversion of configuration of the optically active substrate.
C. The `S_(N^1)` reaction on the chiral starting material ends up with racemisation of the product.
D. The more stable the carbocation intermediate the faster the `S_(N^1)` reaction.

Explanation

To determine which statement regarding the \( S_N1 \) reaction shown by alkyl halides is incorrect, we need to analyze the characteristics of the \( S_N1 \) mechanism. Here’s a step-by-step breakdown:

### Step 1: Understand the \( S_N1 \) Reaction Mechanism
The \( S_N1 \) (unimolecular nucleophilic substitution) reaction is a two-step process:
1. **Formation of Carbocation**: The leaving group (halide ion) departs, resulting in the formation of a carbocation.
2. **Nucleophilic Attack**: A nucleophile attacks the carbocation, leading to the formation of the product.

### Step 2: Identify the Rate-Determining Step
In the \( S_N1 \) mechanism, the first step (formation of the carbocation) is the slow, rate-determining step (RDS). The rate of the reaction depends only on the concentration of the alkyl halide and not on the nucleophile.

### Step 3: Analyze the Configuration Change
The \( S_N1 \) reaction does not involve inversion of configuration. Instead, the nucleophile can attack from either side of the planar carbocation, which can lead to racemization if the starting material is chiral.

### Step 4: Consider the Stability of Carbocations
The stability of the carbocation intermediate is crucial. More stable carbocations (like tertiary carbocations) lead to faster \( S_N1 \) reactions.

### Step 5: Evaluate the Statements
Now, let's evaluate the statements provided:
1. The reaction is unimolecular and first-order.
2. The \( S_N1 \) reaction involves inversion of configuration.
3. The product can be a racemic mixture.
4. More stable carbocations lead to faster \( S_N1 \) reactions.

From the evaluation:
- Statement 1 is correct.
- Statement 2 is incorrect because \( S_N1 \) reactions do not involve inversion of configuration.
- Statement 3 is correct.
- Statement 4 is correct.

### Conclusion
The incorrect statement regarding \( S_N1 \) reactions is that they involve inversion of configuration.