`CD_(2)` = CH - `CH_(2) - `Br is subjected to `S_(N)1 and S_(N)`2 reactions separately, which of the following statement is correct ?

Options

A. both `S_(N)1 and S_(N)`2 give two products
B. Both `S_(N)1 and S_(N)2` give only product
C. `S_(N)1` gives two products but `S_(N)`2 gives only one product
D. `S_(N)1`gives one product but `S_(N)`2 gives two products

Answer

To solve the problem regarding the reactions of CD₂=CH-CH₂-Br with SN1 and SN2 mechanisms, let's break it down step by step.

### Step-by-Step Solution:

1. **Identify the Reaction Mechanisms**:
- **SN1 Mechanism**: This is a two-step process where the first step involves the formation of a carbocation after the leaving group (Br) departs. The second step involves the nucleophile attacking the carbocation.
- **SN2 Mechanism**: This is a one-step process where the nucleophile attacks the carbon atom simultaneously as the leaving group (Br) departs.

2. **Analyze the Structure**:
- The compound is CD₂=CH-CH₂-Br. The bromine (Br) is the leaving group.
- The carbon atom bonded to Br is a secondary carbon, which can stabilize a carbocation.

3. **SN2 Reaction**:
- In an SN2 reaction, the nucleophile will attack the carbon atom bonded to Br, leading to the simultaneous departure of Br.
- This results in the formation of one product: CD₂-CH(CH₂)-Br (where the nucleophile replaces Br).

4. **SN1 Reaction**:
- In an SN1 reaction, the first step is the departure of Br, forming a carbocation (CD₂=CH-CH₂⁺).
- The carbocation can be stabilized by resonance with the adjacent double bond.
- The nucleophile can attack the carbocation from either side, leading to two possible products:
- If the nucleophile attacks from the front, the product is CD₂-CH(CH₂)-Br.
- If the nucleophile attacks from the back, the product is CD₂Br-CH-CH₂.
- This results in a racemic mixture of products.

5. **Conclusion**:
- In the SN2 mechanism, only one product is formed.
- In the SN1 mechanism, two products are formed due to the possibility of attack from both sides of the planar carbocation.

### Final Answer:
- The correct statement is: In SN1, two products are formed, while in SN2, one product is formed.