Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
The 3-methylbutan-2-yl cation, , is a secondary carbocation. A hydrogen atom, together with its bonding pair of electrons, moves from the carbon next to the positive carbon to the positive carbon itself.
Draw the new ion and say whether it is primary, secondary or tertiary. Then count the C-H bonds on the carbon atoms next to the positive carbon, before and after the shift.
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.
Step 1. Before. The neighbours are with hydrogen atoms and with . Total: .
Step 2. The shift. The hydrogen moves to the positive carbon, which becomes . The carbon it left becomes the positive centre: .
Step 3. After. This ion is joined to two groups and one group: . It is a tertiary carbocation.
Answer: before and after. The shift gives a more stable ion, which is why carbocations often rearrange this way.
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