Carbocations
The stability of carbocations can be explained by the Inductive Effect.
CH3++CH2(CH3) +CH(CH3)2+C(CH3)3 i.e. Methyl Primary (1°) Secondary (2°) Tertiary(3°)
We know that alkyl groups of organic chemistry are +I groups, that is, they release electrons through the sigma bonds.
Since the carbon is deficient of electrons, we can say that as the number of methyl group increases, the stability of the carbocation increases. Since the electropositive carbon is satiated by the electrons given by the methyl groups via +I effect.

Therefore, the stability order of carbocations in organic chemistry is of the order 3° > 2° > 1° > Methyl carbocation.
Hyperconjugation
When a C-H σ-bond is in conjugation with a carbocation, this effect is observed. A carbocation has a vacant p-orbital. The bonded σ-electron pair of the C-H bond is displaced toward the vacant p-atomic orbital. This increases the electron density in the empty p-AO.
It is, therefore, a resonance effect where a C-H bond breaks and the σ-electron pair is delocalized to the vacant p-AO of the carbonation. Since the bond between C and H is broken, it is also called ‘no bond resonance’. It is also referred to as the Baker-Nathan effect.

More the number of α-hydrogens in a carbocation, that many hyperconjugated structures would be possible. More the number of structures more is the stability of the species.
Stability of Carbanions
The stability of carbanions can be explained using the inductive effect.
CH3 — CH2(CH3) — CH(CH3)2 — C(CH3)3 i.e. Methyl Primary (1°) Secondary (2°) Tertiary (3°)
Since alkyl groups are electron releasing by nature through induction, we can say that more the number of methyl groups attached to the carbon having a negative charge, less would be its stability.

This is because, the carbon already has a negative charge, to which the methyl groups push electrons via induction. This results in inter-electronic repulsions and destabilizes the species.
Therefore the stability order for carbanions is as follows
3°< 2°< 1°< Methyl carbanion
Stability of Free Radicals
The stability of free radicals in organic chemistry follows the same trend as that of carbocations.
CH3–CH2(CH3)–CH(CH3)2–C(CH3)3 i.e. Methyl Primary (1°) — Secondary (2°) — Tertiary(3°)
Therefore, the stability order of free radicals is of order: 3° > 2° > 1° > Methyl carbocation
This can be explained with the help of Hyperconjugation that we saw, but here there would be an overlap between the σ-bond of C-H and the odd electron in the p-orbital of carbon.

Note: If there is a possibility of resonance, then that would make it more stable. This is because resonance affects the entire structure.
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