Consider the following carbocations and the correct stability order for the above carbocations is
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When assessing carbocation stability, always look for extended resonance/conjugation first, as this is the dominant factor, then evaluate the number of alpha-hydrogens for hyperconjugation.
Step 1: Recall what stabilises a carbocation. A positive carbon is happier when nearby groups feed in electrons. The strength order is resonance > hyperconjugation > inductive effect. Step 2: Spot resonance first. Any carbocation next to a double bond or benzene ring (allylic or benzylic) is spread out by resonance and is the most stable. Step 3: Then look at branching. Without resonance, more alkyl groups touching the positive carbon help by hyperconjugation. So tertiary beats secondary beats primary. Step 4: Apply to the four ions. Rank each ion by how much resonance and then how many alkyl groups support the charge. Step 5: Build the order. Doing this for the given structures gives $(b)>(a)>(d)>(c)$, from most to least stable. Step 6: State the answer. \[ \boxed{(b)>(a)>(d)>(c)} \]
