What Makes an Element Radioactive

Bananas are radioactive. So is the concrete in most buildings, so is seawater, and so are you — a 70 kg human body runs at somewhere around 4,000 to 5,000 decays per second, mostly from potassium and carbon, neither of which appears on anybody's list of radioactive elements.

That is the first thing to get straight. Radioactivity is not a property of an element. It is a property of a nuclide — one specific combination of protons and neutrons. Potassium is not radioactive; potassium-40 is, and it makes up about one part in ten thousand of the potassium in your body, working through its 1.25-billion-year half-life the entire time you are carrying it. When a reference marks an element radioactive, what it almost always means is the much stronger statement that none of that element's isotopes are stable. On this site that is thirty-seven elements, and the reasoning behind the definition is set out on the methodology page.

The tug of war inside the nucleus

Two forces argue over every nucleus, and they have very different reach.

The strong nuclear force binds protons and neutrons to each other. It is enormously powerful and almost absurdly short-ranged — it acts over roughly the diameter of a couple of nucleons and then effectively stops. Each particle is glued to its immediate neighbours and to nothing else.

Electrostatic repulsion between protons is far weaker per pair, but it never stops. Every proton pushes on every other proton in the nucleus, however far apart they are.

That asymmetry decides everything. In a small nucleus, adding a proton adds binding from all its neighbours, so the strong force stays ahead. In a large nucleus, the surface-limited binding grows roughly with the number of nucleons while the repulsion grows with the square of the proton count, and eventually repulsion wins. It wins at exactly bismuth: every element above 83 has no stable isotope whatsoever.

Neutrons are the compromise. They feel the strong force and carry no charge, so they add binding without adding repulsion — which is why light nuclei sit happily with roughly equal protons and neutrons while heavy ones need about one and a half neutrons per proton. Plot every known nuclide by proton count against neutron count and the stable ones form a narrow curved band that bends away from the diagonal. Everything off that band is unstable, and the further off it lies, the faster it decays.

What a nucleus does about being in the wrong place

A nuclide with too many neutrons converts one into a proton, emitting an electron: beta-minus decay. A nuclide with too few does the reverse, either emitting a positron or capturing one of its own inner electrons. Both moves change the element while leaving the mass number alone, which is why decay tracks sideways across an isotope chart towards the band.

Heavy nuclei have a third option: eject a whole alpha particle — a helium-4 nucleus, which is exceptionally tightly bound and therefore energetically cheap to lose. That drops two protons and two neutrons at once, which is why the natural decay chains of uranium and thorium walk down the table in twos, with occasional beta steps sideways to correct the ratio. The heaviest nuclei can also simply split in two without being provoked, and spontaneous fission becomes the dominant fate for many of the superheavy elements.

Two elements that should be stable and are not

Technetium, element 43, sits in the middle of the table surrounded by perfectly ordinary metals, and every one of its isotopes is unstable. So does promethium at 61. Neither is heavy enough for the repulsion argument to apply, and for decades their absence was one of the loudest embarrassments in the search for the missing elements.

The explanation is Mattauch's isobar rule. Where two nuclides share a mass number and sit one proton apart, they are essentially never both stable: whichever has the higher energy decays into the other. Element 43 is boxed in by molybdenum on one side and ruthenium on the other, both of which have an unusually generous set of stable isotopes that occupy every mass number technetium might have used. Element 61 is squeezed identically between neodymium and samarium. They are not unstable because of anything about themselves; they are unstable because their neighbours got there first.

The consequence is that technetium is the lightest element with no stable isotope, and almost all of the technetium that has ever existed on Earth was made deliberately. Its metastable isotope technetium-99m is the workhorse of nuclear medicine, used in tens of millions of diagnostic scans a year — an element absent from nature doing more clinical work than most elements that are abundant in it.

Why some nuclei are absurdly reluctant

Nucleons occupy shells much as electrons do, and a filled nuclear shell confers extra binding. The counts that close a shell are 2, 8, 20, 28, 50, 82 and 126, and they are called magic numbers for the entirely unscientific reason that nobody could explain them when they were noticed.

The effects are visible in the data. Tin sits on the magic proton number 50, and no element in the table matches its tally of ten stable isotopes. Lead-208 has 82 protons and 126 neutrons, is doubly magic, and is the terminus of the uranium and thorium decay chains: three separate cascades of unstable nuclei all stop at the same address. Calcium manages the trick twice, with a doubly magic 40 and a second one at 48.

Shell effects also explain the strangest entries in the half-life record books. Bismuth-209 was believed stable for a century and a half; a French group observed its alpha decay in 2003, and the half-life — later confirmed at Gran Sasso — is around two times ten to the nineteenth years. Set against the roughly fourteen billion years the universe has existed, that is a factor of about a billion. It is listed here with a full natural abundance and is not flagged radioactive, because on any human or geological scale it is not doing anything. Tellurium-128 goes further still: its double beta decay has a half-life around ten to the twenty-fourth years, the longest ever measured for anything.

Which unstable elements survive, and why

If everything above bismuth decays, why is there any uranium left?

Because a few nuclides decay slowly enough to have outlasted the planet. Uranium-238's half-life is 4.47 billion years, essentially the age of the Earth, so about half the original stock is still here. Uranium-235's is 704 million years — six times shorter — which is why natural uranium is now only 0.72 per cent U-235 and was much richer in the deep past. That difference is not academic: at Oklo in Gabon, around 1.7 billion years ago, natural uranium was enriched enough that groundwater seeping through an ore body sustained fission reactions intermittently across a span measured in hundreds of millennia.

Elements with no long-lived isotope survive only as transients in those decay chains. Radium, polonium, francium and astatine exist in the crust in continuously replenished traces — francium's longest-lived isotope lasts 22 minutes, and the entire natural inventory of it on Earth at any instant is estimated at a few tens of grams.

Nuclides decay; elements are just where they are filed

Radioactivity is a statement about a specific nucleus, not about an element on a chart. A nucleus decays when its proton-to-neutron balance sits off the band of stability, or when it is simply too big for a short-range force to hold together against repulsion that is not short-range at all. That second limit lands at element 83, which is why everything past it is unstable.

Technetium and promethium are the two exceptions inside the stable region, excluded by an arithmetic accident about their neighbours. And the few unstable elements you can find in the ground are there either because their half-lives are comparable to the age of the Earth, or because something upstream in a decay chain is still making them.