Atom Tunnelling in Real Systems: Hydrogen in Metals and the Ammonia Inversion

Whole atoms do tunnel, routinely, and it is measured rather than theoretical. The constraint is distance: atom tunnelling operates over sub-nanometre ranges, because transmission falls exponentially with barrier width times the square root of mass. ## Documented cases **The ammonia inversion.** In ammonia (NH₃) the nitrogen sits above the plane of three hydrogens and can flip to the mirror position. Classically it would have to pass through the plane, over an energy barrier. It tunnels instead, oscillating between the two configurations roughly 24 billion times per second. The resulting energy splitting produces a microwave transition near 24 GHz — the basis of the **ammonia maser**, built by Charles Townes and colleagues in 1954 and the direct ancestor of the laser. **Hydrogen in metals.** Hydrogen atoms move between interstitial sites in metals such as palladium and iron partly by tunnelling. The signature is that diffusion stops following the Arrhenius temperature law: classical hopping slows exponentially as temperature falls, while tunnelling does not, so the rate flattens out at low temperature instead of vanishing. In iron, tunnelling contributes to hydrogen diffusion well up towards room temperature and beyond, which matters for Hydrogen Embrittlement: The One-Way Trap for Hydrogen in Metals. **Surface diffusion at cryogenic temperature.** Single hydrogen atoms on clean copper surfaces switch from thermally activated hopping to essentially pure tunnelling below roughly 60 K, hopping between adsorption sites at a temperature-independent rate. **Heavy-atom tunnelling in chemistry.** Even carbon tunnels over sub-ångström distances in certain reactions — conformational flips and ring-opening reactions show rates far above what transition-state theory predicts at low temperature, and kinetic isotope effects far larger than mass alone explains. This is now a recognised factor in low-temperature and astrochemical reaction rates. **Enzyme catalysis.** Hydrogen and proton transfer in several enzymes shows tunnelling contributions, one reason enzymatic rates can exceed classical estimates. ## Why this doesn't add up to losing atoms Two features keep sub-nanometre tunnelling from producing net loss: **It is a random walk with no net direction.** An atom tunnelling between two equivalent sites is as likely to return as to advance. Net transport requires a *bias* — a gradient, or a trap the atom cannot leave. Where such an absorbing trap exists, net transfer does occur, which is exactly what hydrogen embrittlement is. **The atoms are chemically bound.** In tissue, hydrogen sits in C–H and O–H bonds of several eV. The bond, not the gap, sets the rate — so the gatekeeper is thermal bond-breaking, not tunnelling. See Can You Tunnel Through the Floor? The Compound Probability and the Barrier Maths.