[[V]]

I would think this goes B,C,A

Obviously B is the most substituted, and stabilized via hyperconjucation.
The answer is actually B,A,C.

Heres my rational. Having an EN alpha to a carbocation is actually stabilizing. Having it beta is destabilizing. I view the radical as a delta + charge, so there is some slight stabilizing from the EN. Alternatively, the delta + can be so negligible, that Oxygen's electron withdrawing power just destabilizes it instead.

ALSO, why cant one of the lone pairs from oxygen participate in resonance with the radical on carbon in "C"? This is my biggest concern!

Thank you.

[g-bones]

The lone pair from oxygen CAN stabilize via resonance to create a charge separated species. To be honest, I am not sure between tertiary radical and a resonance stabilized secondary radical, but my instinct says resonance wins.

[[V]]

Thanks for the reply.
The conclusion I landed on is, the Oxygen's lone pair cant participate in resonance.
This is because in order for a lone pair or a radical to resonate, it needs an adjacent empty p-orbital. Oxygen is Sp3 hybridized, so it cant make that jump. So all it can do is partake in hyperconjucation.

HOWEVER!!!

When I draw the resonance structure with lone pairs, Oxygen has a formal charge of 0, but has 9 electrons in its valence. Since Oxygen cannot expand its octet, this does not happen.

So is my previous conclusion about Oxygen being Sp3 hybridized stil correct?

[g-bones]

remember you are not making another bond to oxygen with the radical species, you are simply jumping an electron from oxygen to the carbon to make the anionic carbon and cationic oxygen, this his how heteroatoms stabilize adjacent radicals via resonance.

[orgopete]

I don't mean to be contrarian, but how do we know the order is b)>a)>c)?

If someone were to ask me which would create a greater peroxide danger, isopentane or diethyl ether, I would have said diethyl ether. Why am I wrong?

[Honclbrif]

I'm with pete on this one. That was my reasoning too.