A: When butyne-2 is reacted with Na/liq. `NH_(3)` then trans-butene-2 is formed.
R : This reaction proceeds through free radical intermediate.

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion, then mark (1).
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion, then mark (2)
C. if Assertion is true statement but Reason is false, then mark (3)
D. If both Assertion and Reason are false statements, then mark (4)

Answer

To solve the question, we need to analyze the assertion and reasoning provided:

**Assertion (A):** When butyne-2 is reacted with Na/liquid NH₃, then trans-butene-2 is formed.
**Reason (R):** This reaction proceeds through a free radical intermediate.

### Step-by-Step Solution:

1. **Identify the Compound:**
- Butyne-2 (also known as 2-butyne) has the structure CH₃C≡CCH₃. It is an alkyne with a triple bond between the second and third carbon atoms.

2. **Understand the Reaction Conditions:**
- The reaction involves sodium (Na) in liquid ammonia (NH₃). This is a common method for the reduction of alkynes to alkenes.

3. **Reaction Mechanism:**
- The reaction of 2-butyne with Na/NH₃ leads to the formation of trans-butene-2. This is a reduction reaction where the triple bond is converted to a double bond.

4. **Formation of Trans-Butene-2:**
- During the reduction process, the alkyne is converted to an alkene. The product formed is trans-butene-2 (CH₃CH=CHCH₃), which is the trans isomer due to the anti-addition of hydrogen atoms across the double bond.

5. **Evaluate the Reasoning:**
- The reasoning states that the reaction proceeds through a free radical intermediate. However, the reduction of alkynes using sodium in liquid ammonia does not proceed through a free radical mechanism. Instead, it typically involves an electron transfer mechanism leading to the formation of a carbanion intermediate.

6. **Conclusion:**
- The assertion is true: 2-butyne does form trans-butene-2 when reacted with Na/NH₃. However, the reasoning is false because the reaction does not proceed through a free radical mechanism.

### Final Answer:
- Assertion (A) is true, and Reason (R) is false.