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I tried drawing the resonance structures but just cannot see how donating two electrons to a carbon that only needs one electron make it more stable?

I stumbled upon this question asked years ago where they say that hyperconjugation stabilizes the carbocation, but does not stabilize free radical that much.

I cannot seem to find a solid reasoning for it other than a Free Radical requires electron from an electron donating group. Note that I am just just highschooler knowing learning about intermediates for the first time. Any help would be much appreciated!

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Hyperconjugation means that the $\sigma$-bond orbital interacts with an adjacent empty anit-bonding orbital. This means that the interaction between a filled orbital and an empty orbital is the factor that stabilizes the carbocation in this case. However in the case of a carbon radical, there would be at least one electron in the anti-bonding (or non-bonding) orbital, which would be destabilizing the interaction. Just to clarify on the point why Hyperconjugation cannot stabilize a Carbon Free radical as much as a carbocation, the repulsion between the electrons would be larger in the case of a carbon free radical, than in the case of a carbocation.

I tried drawing the resonance structures but just cannot see how donating two electrons to a carbon that only needs one electron make it more stable?

enter image description here

As you said only 1 electron is needed,actually only 1 electron is donated as you can see in hyperconjugation structures above.

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