The correct order of stability of given carbocations is :
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The general order of carbocation stability is: Resonance>Hyperconjugation>Inductive effect. Also, stability decreases as the s-character of the positively charged carbon increases: $sp^3>sp^2>sp$.
The stability of carbocations is determined by factors like resonance, hyperconjugation, and the electronegativity of the carbon atom holding the positive charge.
(A) Benzyl carbocation ($C_6H_5\overset{+}{C}H_2$): The positive charge is on an sp$^2$ hybridized carbon, and it is extensively stabilized by resonance, delocalizing the charge over the entire benzene ring. This makes it very stable.
(C) Ethyl carbocation ($CH_3-\overset{+}{C}H_2$): This is a primary (1$^\circ$) sp$^2$ hybridized carbocation. It is stabilized by the inductive effect (+I) and hyperconjugation from the three $\alpha$-hydrogens of the methyl group.
(B) Vinyl carbocation ($CH_2=\overset{+}{C}H$): The positive charge is on an sp hybridized carbon which is part of a double bond. An sp hybridized carbon is more electronegative than an sp$^2$ carbon, making it less capable of holding a positive charge. There is no resonance or hyperconjugation. This is very unstable.
(D) Ethynyl carbocation ($HC\equiv\overset{+}{C}$): The positive charge is on an sp hybridized carbon which is part of a triple bond. An sp carbon has 50% s-character and is highly electronegative, making it extremely unwilling to bear a positive charge. This is the least stable carbocation among the given options.
Comparing the stability effects: Resonance (A) is much stronger than hyperconjugation (C). The instability due to high s-character is most severe in (D) followed by (B).
Therefore, the correct order of stability is: Benzyl>Ethyl>Vinyl>Ethynyl.
A>C>B>D.
