Explain why `(CH_(3))_(3)overset(+)C`is more stable than `CH_(3)overset(+)CH_(2)` and `CH_(3)` is the least stable cation

Explanation

`(CH_(3))_(3)overset(+)(C)` has nine `alpha`-hydrogens and hence has nine hyperconjugation structures while `CH_(3)overset(+)(C)H_(2)` has only three `alpha`-hydrogens and hence has only three hyperconjugation structures. As a result, `(CH_(3))_(3)C^(+)` is more stable than `CH_(3)CH_(2)^(+)`. In contrast in `CH_(3)^(+)`, the vacant p-orbital is perpendicular to the plane in which the three C-H bonds lie and hence cannot overlap with it. Thus, `CH_(3)^(+)` is not stabilized by hyperconjugation and hence is the least stable of the three cations.