Explain why `(CH_3)_3C^+` is more stable than `CH_3 CH_(2)^(+) and CH_(3)^(+)` is the least stable cation.

Explanation

Hyperconjugation interaction in carbocations depends upon the number of `alpha` -hydrogen atoms. It is greater in `(CH_3)_3 C^(+)` than in `(CH_3)_2 CH^(+)` because `(CH_3)_3 C^(+)` has nine `C - H` bonds while `(CH_3)_2 CH^(+)` has only six `C - H` bonds. Greater hyperconjugation means greater stability of the cation and hence `(CH_3)_3 C^(+)` is more than stable than `(CH_3)_2 CH^(+)`. In `CH_(3)^(+)`, the vacant p-orbital is perpendicular to the plane in which C-H bonds lie and hence there is no possibility of overlapping. Thus `CH_(3)^(+)` lacks hyperconjugation stability and is the least stable carbocation.