Q.48 The stability of the following carbocation arises from hyperconjugation with _________
number of hydrogen atoms.

The given carbocation is stabilized by hyperconjugation with six hydrogen atoms.​​

Introduction

Hyperconjugation in isopropyl carbocation plays a crucial role in explaining its high stability compared with primary carbocations. In this article, the number of α‑hydrogen atoms participating in hyperconjugation is calculated step by step and linked to overall carbocation stability.​

Structure of the carbocation

• The drawn carbocation corresponds to the isopropyl carbocation, often written as (CH3)2CH+(CH3)2CH+.​

• The positively charged carbon is bonded to two methyl groups (Me) and one hydrogen, making it a secondary sp2sp2-hybridized center with an empty $p$ orbital.​

Counting α‑hydrogen atoms

• α‑Carbons are the carbons directly attached to the positively charged carbon; here, both methyl carbons are α‑carbons.​

• Each methyl group (Me = CH33) contributes three hydrogens, so the total α‑hydrogens available for hyperconjugation are $3+3=6$.​

Hyperconjugation and stability

• Hyperconjugation occurs when a C–H σ bond on an α‑carbon overlaps with the adjacent empty $p$ orbital of the carbocation, delocalizing the positive charge.​

• More α‑hydrogens mean more possible hyperconjugative (no‑bond resonance) structures, so an isopropyl carbocation with six α‑hydrogens is more stable than ethyl (3 α‑H) or methyl (0 α‑H) carbocations.​

Comparison with other carbocations

Thus, for the question “The stability of the following carbocation arises from hyperconjugation with ______ number of hydrogen atoms,” the correct filled blank is six (6) hydrogen atoms.