[a confused chiral girl]

Hi,

I am wondering which orbitals interact to provide stability to the tert-butyl carbocation by hyperconjugation?

A. 3° carbon 2p orbital + methyl C 2s orbital
B. 3° carbon 2p orbital + methyl C-H σ orbital
C. 3° carbon sp2 orbital + methyl C-H σ orbital
D. 3° carbon 2p orbital + 3° carbon sp2 orbital

I have thought about this question for a long time, and I know that we can eliminate choice C) because sp2 and sigma orbital are both filled. thus, there would be no hyperconjugation.

Please help if you know which one is the answer. thank you!!

[Yggdrasil]

Think about the orientation of the carbocation's 2p orbital.  How would another orbital have to be positioned in order to stabilize the empty 2p orbital?

[PRIYA1022]

Hi,
  You are right in eliminating C.
 As hyperconjugation is a sigma-pi conjugation(electrons being provided by the overlap of a sigma bond and an empty p orbital of an electron deficient atom), the orbitals involved would be the empty 2p orbital from the 3⁰ carbon, and the sigma electrons from the C-H bond of the methyl group.
Does this give you a clue to pick the right answer?

[a confused chiral girl]

thanks for the replies first of all 

yes, Thank you priya. I would pick choice B) because that is where the carbon has empty p orbial and there is a sigma bond of the methyl group. This fits hyperconjugation because it is a sigma-pi conjugation, and choice A) and D) involve either sp2 orbital or s orbital of the methyl group, which are not sigma bond, thus incorrect! am I right?

I think I understand it now, thank you for the simple explanation and yet it makes a lot of sense and clear right away!! 
thanks again for all the replies~

[english]

The easiest way to find the answer, not that you shouldn't think about it more, is to realize that hyperconjugating orbitals in this case, coming from one of the neighboring C atoms, must be hybridized.

These are of course sigma bonds from C-C or C-H.

(you've already figure it out; just telling you how I approach it)