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

Hyperconjugation interaction in `(CH_3)_3 C^(oplus) (I)` is greater than that of `C` in `CH_3 overset (oplus) CH_2 (II)`, as `(I)` has nine `(C - H)` bonds and `(II)` has three `(C - H)` bonds.
In `overset (oplus) CH_3`, the vacant `p` orbital is perpendicular to the plane in which `(C- H)` bonds lies , hence cannot overlap with it.
Thus, `overset (oplus) CH_3` lacks hyperconjugative stability.