Illustrated Physics
physics, drawn
Concept

Beta decay — where it appears

A nuclear decay in which a neutron becomes a proton, or the reverse, emitting an electron and a neutrino. The electron's energy spectrum is a continuum rather than a line, and the shape of that continuum is a count of the ways three bodies can share a fixed energy — which is what the neutrino was proposed to supply.

Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.

A line is what two bodies give. The electron energy spectrum of tritium, against the vertical line a two-body decay would produce. A nucleus emitting one particle has no choice about how to share the energy: momentum conservation fixes it, and every electron comes out at the same energy. The observed spectrum is a continuum running from zero to the full available energy, with a mean at 0.31 of the endpoint. The shape is a count of the ways the energy can be divided between an electron and something else, and the something else was proposed for no other reason than that the shape requires one.

The energy that did not all arrive

A nucleus emitting one particle has no choice about the energy it comes out with — momentum conservation fixes it, and the spectrum is a line. Beta decay gives a continuum instead, from zero to the full available energy, and the shape of that continuum is a count of the ways the energy can be shared. Counting it required a third body nobody had seen, and the way the count approaches its endpoint is still the best place to weigh one.

quantum · Decay The half-life that depends on the electrons. Half-lives of 3 nuclides as neutral atoms and as bare nuclei, measured at a heavy-ion storage ring where fully stripped ions can be kept circulating for months. The changes are not corrections. ¹⁸⁷Re goes from 41.6 billion years to 32.9 — a factor of 1.26 billion — because a beta decay whose available energy is only 2.5 keV cannot put an electron into the continuum but can put one into an empty K orbital, and stripping the atom opens that channel. ¹⁶³Dy is stable as an atom and decays in 47 days as a bare nucleus, for the same reason. The rate is a property of the nucleus and of what surrounds it, not of the nucleus alone.

The half-life that chemistry can change

A nucleus has no clock, the usual account goes, and nothing outside it touches the rate. That is very nearly true and it is not exactly true. Electron capture takes an electron from the nucleus's own position, so its rate is proportional to how many electrons are there — which is chemistry, worth a per cent. And a nucleus stripped of every electron can gain a decay channel it did not have: rhenium-187 goes from forty-two billion years to thirty-three.

quantum · Decay The parabola a family of isobars lies on. The atomic masses of the nuclei with 91 nucleons, as energy above the lightest, against the number that are protons, from the semi-empirical mass formula: a parabola with zirconium-91 at the bottom, which is where the stable isobar is. Left of the floor the nuclei have too many neutrons and β-decay towards it, each step turning a neutron into a proton and releasing the mass difference — 8.2 MeV from Kr, 5.8 MeV from Rb, 3.4 MeV from Sr, 1.0 MeV from Y — the steps shrinking as the floor nears, because the slope of a parabola does. Right of it the nuclei have too many protons and decay the other way, by capturing an electron or, where the drop exceeds 1.022 MeV, by emitting a positron: 6.2 MeV from Tc, 3.8 MeV from Mo, 1.4 MeV from Nb. Every arrow points downhill in mass, and nothing else decides its direction.

The parabola that decides which way a nucleus decays

A weak decay turns a neutron into a proton or a proton into a neutron and leaves the number of nucleons alone, so it moves a nucleus sideways among its isobars. Whether it can happen, and in which direction, is settled by weighing: a decay goes wherever the atom ends up lighter, by any amount at all, except that emitting a positron needs two electron masses more. Laid out against proton number, the masses of a family of isobars fall on a parabola — or, for an even number of nucleons, on two — and the shape of that parabola is why potassium-40 decays both ways and germanium-76 can only take two steps at once.

relativity · Mass-energy

Named alongside it

The objects these essays reach for when they reach for this one.

DecayElectron capturePhase spaceProbability densityAtomic structureBinding energyConservation lawsDecay constantDouble beta decayEndpointEnergy conservationHalf-life

All concepts