The stability of the free radicals allyl, benzyl, 3°, 2°, 1° and \(CH_3\) is of the order

allyl=benzyl > 3° > 2° > 1° > \(CH_3\)

The correct answer is option 1. allyl=benzyl > 3° > 2° > 1° > \(CH_3\).

To understand the stability order of free radicals (allyl, benzyl, tertiary (3°), secondary (2°), primary (1°), and methyl (CH₃·)), we need to examine the factors that influence the stability of these radicals: resonance stabilization, hyperconjugation, and inductive effects.

Resonance Stabilization

Allyl Radical \((C_3\overset{•}{H_5})\):

The allyl radical is stabilized by resonance. The unpaired electron in the allyl radical can delocalize over the π-system of the adjacent double bond, which spreads out the electron density and increases stability.

Resonance structures of the allyl radical: 

Benzyl Radical:

The benzyl radical is highly stabilized due to resonance with the aromatic ring. The unpaired electron can delocalize over the entire aromatic system, significantly enhancing stability.

Resonance structures of the benzyl radical: 

Hyperconjugation and Inductive Effects

Tertiary Radical \((R_3\overset{•}{C})\):

A tertiary radical is stabilized by hyperconjugation and inductive effects from three alkyl groups. Hyperconjugation involves the donation of electron density from the C-H σ-bonds of the neighboring carbon atoms to the electron-deficient radical center, which helps stabilize the radical. Inductive effects from the alkyl groups also help stabilize the radical by donating electron density through σ-bonds.

Secondary Radical \((R_2\overset{•}{C}H)\):

A secondary radical is stabilized by hyperconjugation and inductive effects from two alkyl groups, but to a lesser extent than a tertiary radical due to fewer hyperconjugative interactions.

Primary Radical \((R\overset{•}{C}H_2)\):

A primary radical is stabilized by hyperconjugation and inductive effects from one alkyl group, making it less stable than secondary and tertiary radicals.

Methyl Radical \((\overset{•}{C}H_3)\): The methyl radical has no hyperconjugation and minimal inductive stabilization since there are no adjacent carbon atoms with C-H bonds to donate electron density. Hence, it is the least stable among these radicals.

Considering the above factors, the stability order of the radicals is:

1. Allyl Radical and Benzyl Radical: Both are highly stabilized by resonance. The resonance effect is a significant factor that provides more stabilization compared to hyperconjugation and inductive effects.

2. Tertiary Radical (3°): Stabilized by hyperconjugation and inductive effects from three alkyl groups.

3. Secondary Radical (2°): Stabilized by hyperconjugation and inductive effects from two alkyl groups.

4. Primary Radical (1°): Stabilized by hyperconjugation and inductive effects from one alkyl group.

5. Methyl Radical: Lacks significant hyperconjugation and inductive stabilization, making it the least stable.

Hence, the correct order of stability is: (1) allyl = benzyl > 3° > 2° > 1° > \(CH_3\)

This order correctly reflects the dominant role of resonance stabilization in allyl and benzyl radicals, followed by the stabilizing effects of hyperconjugation and inductive effects in alkyl-substituted radicals.