Assertion (A) . All the carbon atom in `H_(2)C = C = CH_(2)` are `sp^(2)`-hybridised.
Reason (R). In this molecule all the carbon atoms are attached to each other by double bonds

Options

A. Both A and R are correct and R is the correct explanation of A
B. Both A and R are correct but R is not the correct explanation of As
C. both A and R are not correct
D. A is not correct but R is correct

Explanation

To solve the assertion and reason question regarding the hybridization of carbon atoms in the compound \( H_2C = C = CH_2 \), we will follow these steps:

### Step 1: Identify the Structure
First, we need to draw the structure of the compound \( H_2C = C = CH_2 \). This compound consists of three carbon atoms connected by double bonds.

### Step 2: Determine the Hybridization of Each Carbon Atom
Next, we will determine the hybridization of each carbon atom based on the number of sigma bonds they form.

1. **First Carbon (C1)**:
- It is bonded to two hydrogen atoms and one carbon atom (C2) through a double bond.
- The bonds are:
- 2 C-H (sigma bonds)
- 1 C=C (the first bond is a sigma bond)
- Total sigma bonds = 2 (C-H) + 1 (C=C) = 3 sigma bonds.
- According to the hybridization rules, 3 sigma bonds correspond to \( sp^2 \) hybridization.

2. **Second Carbon (C2)**:
- It is bonded to one hydrogen atom and two carbon atoms (C1 and C3) through double bonds.
- The bonds are:
- 1 C-H (sigma bond)
- 2 C=C (the first bond of each double bond is a sigma bond)
- Total sigma bonds = 1 (C-H) + 1 (C1=C2) + 1 (C2=C3) = 3 sigma bonds.
- This carbon also has \( sp^2 \) hybridization.

3. **Third Carbon (C3)**:
- It is bonded to two hydrogen atoms and one carbon atom (C2) through a double bond.
- The bonds are:
- 2 C-H (sigma bonds)
- 1 C=C (the first bond is a sigma bond)
- Total sigma bonds = 2 (C-H) + 1 (C=C) = 3 sigma bonds.
- This carbon also has \( sp^2 \) hybridization.

### Step 3: Analyze the Assertion and Reason
- **Assertion (A)**: All the carbon atoms in \( H_2C = C = CH_2 \) are \( sp^2 \)-hybridized.
- This is **incorrect** because the middle carbon (C2) is actually \( sp \)-hybridized due to having only two sigma bonds.

- **Reason (R)**: In this molecule, all the carbon atoms are attached to each other by double bonds.
- This is **correct** because the structure clearly shows that the carbon atoms are connected by double bonds.

### Conclusion
- The assertion is incorrect, while the reason is correct. Therefore, the correct answer is that the assertion is false, but the reason is true.

### Final Answer
The assertion is incorrect, and the reason is correct.

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