A : Hybridization of carbon is `sp^(2)` in all its crystalline allotropes .
R : There are alternate double -single bonds in each allotrope of carbon .

Options

A. Both Assertion & Reason are true and the reason is the correct explanation of the assertion .
B. Both Assertion & Reason are true but the reason is not the correct explanation of the assertion .
C. Assertion is true statement but Reason is false .
D. Both Assertion and Reason are false statement .

Answer

To solve the question, we need to analyze both the assertion (A) and the reason (R) provided.

### Step 1: Analyze the Assertion (A)
The assertion states that "the hybridization of carbon is `sp^(2)` in all its crystalline allotropes."

- The crystalline allotropes of carbon include diamond and graphite.
- In diamond, each carbon atom is bonded to four other carbon atoms in a tetrahedral geometry, which corresponds to `sp^(3)` hybridization.
- In graphite, each carbon atom is bonded to three other carbon atoms, forming a planar structure with one unhybridized p-orbital, which corresponds to `sp^(2)` hybridization.

**Conclusion for Assertion (A)**: This statement is incorrect because carbon is `sp^(3)` hybridized in diamond, not `sp^(2)`.

### Step 2: Analyze the Reason (R)
The reason states that "there are alternate double-single bonds in each allotrope of carbon."

- In diamond, all the bonds are single (sigma) bonds, and there are no double bonds.
- In graphite, there are indeed alternate double and single bonds due to the presence of resonance structures.

**Conclusion for Reason (R)**: This statement is also incorrect because it implies that all allotropes of carbon have alternate double-single bonds, which is not true for diamond.

### Final Conclusion
Both the assertion and the reason are incorrect. Therefore, the correct answer is option four, which states that both A and R are false.