Question

The cyclic cations having the same number of hyperconjugation are:

• A. A, C and D only
• B. A and B Only
• C. A and C Only
• D. B and C Only

Hint:

To determine hyperconjugation count: 1. Identify the carbocation center. 2. Look at the adjacent carbon atoms. 3. Count the number of hydrogens attached to those carbons (\(\beta\)-hydrogens). 4. Each \(\beta\)-hydrogen corresponds to one hyperconjugative structure.

Answer 1

The Correct Option is A

Concept:
Hyperconjugation is the delocalization of electrons from a C–H (or C–C) sigma bond adjacent to a carbocation center. The number of hyperconjugative structures depends directly on the number of beta-hydrogens available next to the positively charged carbon.

• Each beta-hydrogen contributes one hyperconjugative structure.
• In cyclic carbocations, the substituents attached to the carbocation determine how many beta-hydrogens are available.
• The stability of carbocations increases with the number of hyperconjugative structures.

Step 1: Analyze structure A.
The carbocation is adjacent to a CH3 group.
A methyl group has 3 hydrogens, all of which are beta-hydrogens.
Hence, A has 3 hyperconjugative structures.

Step 2: Analyze structure B.
The carbocation is adjacent to a CH2 group in the ring.
This group has only 2 hydrogens available for hyperconjugation.
Hence, B has 2 hyperconjugative structures.

Step 3: Analyze structure C.
The carbocation is adjacent to a CH3 group (similar to A).
Again, 3 beta-hydrogens are available.
Hence, C has 3 hyperconjugative structures.

Step 4: Analyze structure D.
The carbocation is adjacent to a CH3 group.
This provides 3 beta-hydrogens.
Hence, D has 3 hyperconjugative structures.

Step 5: Compare.
A, C, and D each have 3 hyperconjugative structures.
B has only 2 hyperconjugative structures.

Therefore, the cyclic cations having the same number of hyperconjugation are A, C, and D.