`BrCH_(2)-CH_(2)CH_(2)Br` reacts with `Na` in the presence of ether at `100^(@)C` to produce

Options

A. `BrCH_(2)-CH=CH_(2)`
B. `CH_(2)=C=CH_(2)`
C.
D. All of these

Explanation

To solve the problem, we need to analyze the reaction of the compound `BrCH2-CH2-CH2Br` (1,3-dibromopropane) with sodium (Na) in the presence of ether at a temperature of 100°C. This reaction is known as the Wurtz reaction, which is used to couple alkyl halides to form alkanes.

### Step-by-Step Solution:

1. **Identify the Reactants:**
The reactant is 1,3-dibromopropane, which has the structure:
\[ Br-CH_2-CH_2-CH_2-Br \]

2. **Understand the Reaction Conditions:**
The reaction is carried out with sodium (Na) in the presence of an ether solvent at 100°C.

3. **Reaction Mechanism:**
In the Wurtz reaction, sodium metal reacts with alkyl halides to form free radicals. Here, two bromine atoms will react with sodium:
\[ 2 \, Br-CH_2-CH_2-CH_2-Br + 2 \, Na \rightarrow 2 \, NaBr + \text{free radicals} \]

4. **Formation of Free Radicals:**
The reaction leads to the formation of two free radicals:
\[ CH_2^{\cdot} - CH_2 - CH_2^{\cdot} \]

5. **Coupling of Free Radicals:**
The free radicals will couple together to form a new carbon-carbon bond:
\[ CH_2^{\cdot} + CH_2^{\cdot} \rightarrow CH_2-CH_2-CH_2 \]

6. **Final Product:**
The final product of the reaction is propane (C3H8):
\[ CH_2-CH_2-CH_2 \]

### Conclusion:
The product formed from the reaction of `BrCH2-CH2-CH2Br` with `Na` in the presence of ether at `100°C` is propane (C3H8).