Assertion `(A)` : All the `C` atoms of but-2-ene lie in one plane
Reason `(R )`: Double-bond `C` atoms are `sp^(2)`-hypbridised.

Options

A. If both `(A)` and `(R )` are correct and `(R )` is the correct explanation for `(A)`.
B. If both `(A)` and `(R )` are correct and `(R )` is not the correct explanation.
C. If `(A)` is correct and `(R )` is incorrect.
D. If both `(A)` and `(R )` are incorrect.

Explanation

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

**Assertion (A)**: All the carbon atoms of but-2-ene lie in one plane.
**Reason (R)**: Double-bonded carbon atoms are sp² hybridized.

### Step-by-Step Solution:

1. **Understanding But-2-ene Structure**:
- But-2-ene is an alkene with the molecular formula C₄H₈. It has the structure CH₃-CH=CH-CH₃.
- In this structure, there are four carbon atoms.

2. **Identifying Hybridization**:
- The carbon atoms involved in the double bond (the second and third carbon atoms) are sp² hybridized. This means they have a trigonal planar geometry with bond angles of approximately 120 degrees.
- The terminal carbon atoms (the first and fourth carbon atoms) are sp³ hybridized, which means they have a tetrahedral geometry with bond angles of approximately 109.5 degrees.

3. **Analyzing the Assertion**:
- The assertion states that all carbon atoms lie in one plane. Since the sp² hybridized carbon atoms are in a plane, they will lie in the same plane. However, the sp³ hybridized carbon atoms will not lie in the same plane due to their tetrahedral geometry.
- Therefore, the assertion that all carbon atoms of but-2-ene lie in one plane is **incorrect**.

4. **Analyzing the Reason**:
- The reason states that double-bonded carbon atoms are sp² hybridized, which is **correct**. This hybridization leads to a planar arrangement of the double-bonded carbon atoms.

5. **Conclusion**:
- Since the assertion is incorrect and the reason is correct, we conclude that the correct answer is that assertion A is incorrect, while reason R is correct.

### Final Answer:
- Both A and R are not correct, as A is incorrect and R is correct.