Walden inversion takes place in `SN^2` reaction.
Half-life period of `SN^2` reaction is inversely proportional to the concentration of the substrate or nucleophile or both.

Options

A. If both `(A)` and `(R )` are true, but `( R)` is the correct explanation of `(A)`
B. If both `(A)` and `( R)` are true, but `(R )` is not the correct explanation of `(A)`.
C. If `(A)` is true but `( R)` is false.
D. If `(A)` is false but `( R)` is true.

Explanation

To solve the question regarding Walden inversion and the half-life period of SN2 reactions, we can break it down into the following steps:

### Step 1: Understanding Walden Inversion
Walden inversion refers to the stereochemical change that occurs during an SN2 reaction. In an SN2 reaction, the nucleophile attacks the substrate from the opposite side of the leaving group, resulting in an inversion of configuration at the carbon center.

**Hint:** Recall that Walden inversion is a key feature of SN2 mechanisms due to the backside attack of the nucleophile.

### Step 2: Analyzing the Half-Life of SN2 Reactions
The half-life of an SN2 reaction is influenced by the concentrations of both the substrate and the nucleophile. The rate of an SN2 reaction is second-order, meaning it depends on the concentration of both reactants.

**Hint:** Remember that in a second-order reaction, the rate law is dependent on the concentration of both the substrate and the nucleophile.

### Step 3: Relationship of Half-Life with Concentration
For a second-order reaction, the half-life (T½) is inversely proportional to the concentration of the reactants. This means that as the concentration of either the substrate or the nucleophile increases, the half-life decreases.

**Hint:** Think about how increasing concentration affects the rate of reaction and subsequently the time it takes for half of the reactants to be consumed.

### Step 4: Conclusion
Both statements in the question are true:
1. Walden inversion occurs in SN2 reactions due to the backside attack of the nucleophile.
2. The half-life of an SN2 reaction is inversely proportional to the concentration of the substrate and/or the nucleophile.

**Hint:** When evaluating assertions and reasons, ensure to check if both are true and if the reason correctly explains the assertion.

### Final Answer
Both the assertion and reason are true, but the reason is not the correct explanation for the assertion.