Drawing of mechanisms for carbocation rearrangments involving hydride or alkyl shifts

Question

How can I draw plausbile mechanisms for carbocation rearrangements involving hydride or alkyl shifts (where the carbocations can undergo rearrangments to form more stable ions by the transfer of a hydride ion or alkyl group) for the following:

a) butane carbocation

b) 2-methylbutane carbocation

c) 1,1-dimethylcyclopentane carbocation

Answer 1

Here's an example of a carbocation rearrangement where a 1,2-hydride shift converts a 2° carbocation to a more stable 3° carbocation.

The standard way to show this is to use a curved arrow starting somewhere in the middle of the C–H bond of the hydrogen atom that is undergoing the 1,2-shift (along with the pair of electrons from its C–H bond). The head of the curved arrow points to the original carbocation center (where the C–H bond is moving to).

After the carbocation rearrangement has taken place the original carbocation center becomes a neutral carbon with 4 bonds, and the carbon that the hydrogen atom (plus electrons) shifted away from becomes the new carbocation center.