The give reaction
`H-underset(CH_3)underset(|)overset(CH_2-CH_3)overset(|)(C )-Br " "overset(Theta)overset(OH)(rarr)HO-underset(CH_3)underset(|)overset(CH_2-CH_3)overset(|)(C )-H`
Is an example of

Options

A. `S_E2`
B. `S_N1`
C. `S_N2`
D. `S_E1`

Answer

To determine the type of reaction represented by the given chemical equation, we can analyze the components and the process involved. The reaction involves an alkyl halide and a nucleophile (OH⁻) that leads to a product with an inversion of configuration. Here’s a step-by-step breakdown of the solution:

### Step-by-Step Solution:

1. **Identify the Reactants**:
- The reactant is an alkyl halide, specifically a bromide (C-Br), where C is a carbon atom bonded to alkyl groups (CH₃ and CH₂-CH₃).
- The nucleophile in this reaction is hydroxide ion (OH⁻).

2. **Understand the Reaction Type**:
- The reaction involves the substitution of the bromine atom (leaving group) by the hydroxide ion (nucleophile).
- This type of reaction is characterized by the nucleophile attacking the carbon atom bonded to the leaving group (bromine) from the opposite side, leading to an inversion of configuration.

3. **Mechanism of the Reaction**:
- The mechanism is bimolecular, meaning that both the substrate (alkyl halide) and the nucleophile (OH⁻) are involved in the rate-determining step.
- The nucleophile attacks the carbon from the back side, which is a hallmark of SN2 reactions.

4. **Transition State Formation**:
- During the reaction, a transition state is formed where the carbon atom temporarily has five bonds (three from alkyl groups, one from the incoming OH⁻, and one from the leaving Br⁻).
- This transition state leads to the simultaneous breaking of the C-Br bond and the formation of the C-OH bond.

5. **Product Formation**:
- The final product is an alcohol (C-OH) with the original alkyl groups remaining intact.
- The configuration at the carbon center has inverted due to the backside attack of the nucleophile.

6. **Conclusion**:
- Since the reaction exhibits characteristics of a bimolecular nucleophilic substitution (SN2), we conclude that the given reaction is an example of an SN2 reaction.

### Final Answer:
The given reaction is an example of an **SN2 reaction**.