[abcc]

i know the more alkyl gp substituted carbocation is more stable due to e- donating & hyperconjuncation, but how about the carbon radical why more alkyl substutients on the carbon radical is more stable? is it also due to the hyperconjuncation?? e.g. R3C. > R2HC. > RH2C.
thxthxthx

[Yggdrasil]

Yes.  Both carbocations and carbon radicals contain unhybridized p-orbitals which hyperconjugation will help to stabilize.

[movies]

Accordingly, radicals are also stabilized by adjacent electron donating groups like oxygen and nitrogen.

Think of it this way: radicals are atoms that are short an electron and therefore don't satisfy the octet rule.  If you have some sort of electron releasing group then you can increase the electron density on that atom so that it is closer to a full octet.

[abcc]

that means the structure is like this             
R3C. <----> R2C=C.H2
is it possible to have =C.H2???

[abcc]

that means the structure is like this             
R3C. <----> R2C=C.H2
is it possible to have =C.H2???

R3C. <----> R2C=C.H2
I HAVE this idea because of the hyperconjuncation of carbocation:
R3C+ <----> R2C=CH2

[movies]

To draw it that way you have to break a bond, which isn't really an accurate representation of hyperconjugation, but it predicts the right effect.  In your carbocation example, notice that you would also make a R+, which you left out, so in the same sense in the radical case you would make a R. and the double bond.

In the case of an electron donating group you get another (real) resonance structure where the radical is on the heteroatom, e.g. R2C(-)-O.