Choose the correct order of stability of carbocation using concept of hyperconjugation
I `CH_(3)-overset(CH_(3))overset(|)underset(CH_(3))underset(|)(C^oplus)`
II. `CH_(3)-overset(CH_(3))overset(|)underset(H)underset(|)(C^(oplus))`
III. `CH_(3)overset(oplus)CH_(2)`
IV `overset(oplus)CH_(3)`

Options

A. `I lt II lt III lt IV`
B. `IV lt III lt II lt I`
C. `III lt IV lt II lt I`
D. All of the above

Answer

B

Explanation

The stability of carbocation on the basis of hyperconjugation can be explained as hyperconjugation stabilises the carbocation because electron density from the adjacent `pi` bond helps in dispersing the positive charge

In general greater the number of alkyl groups attached to a positively charged carbon atom the greater is the hyperconjugation interaction and stabilisation of the cation thus we have the following relative stability of carbocation
`CH_(3)-overset(CH_(3))overset(|)underset(CH_(3))underset(|)(C^oplus)gt(CH_(3))_(2)overset(+)CH gtCH_(3)oversetoplusCH_(2) gt oversetoplusCH_(3)`
Hence, stability of carbocation is directly proportional to number of alkyl group directly attached to carbocation carbon