2 phenylethylbromide when heated with NaOEt, elimination takes place. No deuterium exchange takes place when the reaction is
carried out in `C_(2)H_(5)OD` solvent. The mechanism will be

Options

A. E1 elimination
B. E2 elimination
C. E1cB elimination
D. E2 or E1cB

Explanation

To solve the problem, we need to analyze the reaction of 2-phenylethyl bromide when heated with sodium ethoxide (NaOEt) and determine the mechanism involved in the elimination process.

### Step-by-Step Solution:

1. **Identify the Reactants**:
The reactant in this case is 2-phenylethyl bromide, which can be represented as:
\[ \text{C}_6\text{H}_5\text{CH}_2\text{CH}_2\text{Br} \]
This compound has a bromine atom attached to a primary carbon adjacent to a phenyl group.

2. **Understand the Reaction Conditions**:
The reaction is carried out in the presence of sodium ethoxide (NaOEt), which is a strong base. The conditions suggest that elimination is favored.

3. **Consider the Mechanisms of Elimination**:
There are two primary mechanisms for elimination reactions:
- E1 (Unimolecular elimination)
- E2 (Bimolecular elimination)

4. **Analyze the Deuterium Exchange**:
The problem states that no deuterium exchange occurs when the reaction is conducted in a solvent of C2H5OD. This indicates that the hydrogen atom involved in the elimination is not being replaced or exchanged with deuterium from the solvent.

5. **Determine the Type of Elimination**:
The absence of deuterium exchange suggests that the hydrogen atom is not being removed to form a carbocation (which would be the case in an E1 mechanism). Instead, it indicates that the elimination occurs in a concerted manner, where the base abstracts a proton and the leaving group (bromine) departs simultaneously.

6. **Conclude the Mechanism**:
Since the reaction proceeds without the formation of a carbocation and involves a concerted mechanism, we conclude that the elimination occurs via the E2 mechanism.

The final product of the reaction will be an alkene, specifically styrene (C6H5CH=CH2), along with the by-products of ethanol and bromide ion.

### Final Answer:
The mechanism of the reaction is **E2 elimination**.