(A): Reaction given below is possible
`2KCI + Br_2 to Cl_(2) + 2KBr`
(R): lighter halogen displaces larger halogen from its metal halides .

Options

A. Both A & R are true, R is the correct explanation of A
B. Both A & R are true, R is not correct explanation of A
C. A is true, R is false
D. A is false, R is true

Answer

To analyze the given question, we will break it down into two parts: (A) the reaction itself and (R) the statement regarding halogens.

### Step-by-Step Solution:

1. **Identify the Reaction**:
The reaction given is:
\[ 2KCl + Br_2 \rightarrow Cl_2 + 2KBr \]
Here, potassium chloride (KCl) reacts with bromine (Br2) to produce chlorine (Cl2) and potassium bromide (KBr).

**Hint**: Look at the reactants and products to identify which elements are involved in the reaction.

2. **Determine the Reactivity of Halogens**:
Halogens are arranged in the periodic table in order of increasing atomic number: Fluorine (F), Chlorine (Cl), Bromine (Br), Iodine (I), and Astatine (At). In this series, the reactivity decreases as you move down the group. Chlorine (Cl) is a lighter halogen compared to bromine (Br), which is a heavier halogen.

**Hint**: Remember that lighter halogens are generally more reactive than heavier ones.

3. **Evaluate the Reaction's Feasibility**:
According to the reactivity series of halogens, a lighter halogen can displace a heavier halogen from its compounds. In this case, chlorine (Cl) is displacing bromine (Br) from potassium bromide (KBr). Therefore, the reaction should be possible.

**Hint**: Use the concept of reactivity series to determine if one halogen can displace another.

4. **Assess Statement (R)**:
The statement (R) claims that "a lighter halogen displaces a larger halogen from its metal halides." This is true, as we have established that chlorine (the lighter halogen) can displace bromine (the larger halogen) from potassium bromide.

**Hint**: Think about the definitions of "lighter" and "larger" in the context of halogens and their reactivity.

5. **Conclusion**:
- (A) The reaction is **not possible** because the heavier halogen (bromine) cannot be displaced by the lighter halogen (chlorine) in this context.
- (R) The statement is **true** as lighter halogens can displace larger halogens from their metal halides.

Thus, the final assessment is:
- (A) is false.
- (R) is true.

### Final Answer:
- **A** is false, **R** is true. Therefore, the correct option is D.