Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
Find the number of C-H bonds on the carbon atoms next to the positive carbon, in each of these carbocations. These are the bonds that can hyperconjugate.
Which ion is the most stable?
A covalent bond breaks by homolytic or by heterolytic fission. In homolytic fission each atom keeps one electron. This gives free radicals and is drawn with half-headed arrows. In heterolytic fission one atom takes both electrons. This gives a cation and an anion and is drawn with a full-headed arrow. A carbocation is flat and has six electrons. A carbanion is pyramidal with a lone pair. Alkyl groups and hyperconjugation make a carbocation or radical more stable: tertiary, secondary, primary, methyl. The order for a carbanion is the reverse.
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
(a) The positive carbon is joined to one carbon, , which holds hydrogen atoms. So there are bonds.
(b) The positive carbon is joined to a group () and a group (). Total: .
(c) The positive carbon is joined to three groups: .
Answer: , and . The tert-butyl cation has the most helpful bonds, so it is the most stable.
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