alpha-carbon
/ AL-fuh CAR-bon /
Picture a carbonyl group — a carbon double-bonded to oxygen, the C=O at the heart of aldehydes, ketones, esters, and acids. The alpha-carbon is simply the carbon sitting right next to that carbonyl. Its hydrogens are the alpha-hydrogens. The Greek letters walk outward from the carbonyl: alpha is the first carbon over, beta is the next, gamma the one after that. So in acetone, CH3-CO-CH3, both methyl carbons are alpha-carbons.
Why single out this one carbon? Because it lives in the shadow of the carbonyl, and that changes everything about it. The neighbouring C=O is electron-hungry, and it makes the C-H bonds on the alpha-carbon unusually weak as acids. Pull one of those alpha-hydrogens off and the carbon left behind becomes a powerful nucleophile — a carbon that wants to attack and bond to other carbons. Ordinary carbons in an alkane cannot do this; the alpha-carbon can only because of who its neighbour is.
This single idea is the doorway to a whole chapter of organic chemistry. Almost every reaction that builds a new carbon-carbon bond from carbonyl compounds — the aldol, the Claisen, alkylation, the Michael addition — works by activating the alpha-carbon. If carbonyl addition (a nucleophile attacking the C=O carbon itself) is one face of carbonyl chemistry, alpha-carbon chemistry is the other face: the carbonyl turns its neighbour into a weapon.
In butan-2-one, CH3-CO-CH2-CH3, there are alpha-carbons on BOTH sides of the carbonyl: the CH3 group and the CH2 group are both alpha. The CH3 at the far right end is a beta-carbon and is not activated.
A carbonyl can have alpha-carbons on either side; both can be deprotonated.
A carbonyl with no alpha-hydrogens (like formaldehyde, HCHO, or benzaldehyde, PhCHO) simply cannot do alpha-carbon chemistry — there is nothing to remove. This is exactly why such compounds are useful as the unreactive partner in crossed aldol reactions.