beta-hydrogen
/ BAY-tuh HY-droh-jen /
Every elimination needs a hydrogen in the right place to leave, and 'the right place' has a name. Label the carbon bearing the leaving group as the alpha carbon. The carbons directly bonded to it are the beta carbons, and any hydrogen on a beta carbon is a beta-hydrogen. It is the proton that an E1 or E2 removes, while the leaving group goes from the alpha carbon — the two departures, one carbon apart, that knit the double bond.
This little piece of bookkeeping carries real consequences. No beta-hydrogen, no elimination: a substrate whose alpha carbon has no neighbouring C-H simply cannot form an alkene this way, no matter how strong the base. When there are beta-hydrogens on two or more different beta carbons, the molecule can eliminate toward either, giving different alkenes — and that is exactly the situation Zaitsev's and Hofmann's rules adjudicate. Counting the distinct sets of beta-hydrogens is the first step in predicting the possible products of an elimination.
The Greek-letter scheme (alpha for the carbon with the functional group, beta for its neighbours, gamma beyond) is used all over organic chemistry, not just here — alpha-hydrogens next to a carbonyl, gamma-positions in conjugate addition, and so on. In elimination, though, beta is the star: the entire reaction is defined by removing a beta-hydrogen anti-periplanar (for E2) to the leaving group on the alpha carbon.
In 2-bromobutane, the alpha carbon (C2) bears Br; its beta carbons are C1 and C3. Removing a beta-H from C1 gives but-1-ene, while removing one from C3 gives but-2-ene — two possible elimination products from two sets of beta-hydrogens.
Beta-hydrogens sit on the carbons next to the leaving group; one of them leaves in elimination.
If the alpha carbon has no beta-hydrogen at all (for example neopentyl-type or bridgehead systems), elimination is blocked and the molecule can only substitute — a useful diagnostic.