Islands across the sciences · nuclear physics · reference case

The chart of nuclides

The island this site is named after, drawn from the standard table of every known nucleus.

Sense of island: chart-island Data: NUBASE2020, published 2021 Tests no proposition

Every atom has a nucleus made of protons and neutrons, and each combination is called a nuclide. Of the 3,340 nuclides ever observed, 253 have never been seen to decay. The rest fall apart, some within a billionth of a trillionth of a second, others over billions of years. Drawn with neutrons across and protons up, the survivors make a thin band through a wide sea of decay, and past its far end physicists have predicted, since the 1960s, a second island that nobody has reached.

Which sense of island. This page uses the chart-island, Seaborg's sense: a region on a chart whose occupants outlast their neighbors. That is a convention about relative lifetime, not a claim about dynamics, and the theory page keeps it apart from the other two senses. The table near the end says, proposition by proposition, where the site's claims carry over to nuclei, where the resemblance is only one of form, and where it breaks.

The chart

Each square is one nuclide, placed by its number of neutrons (across) and protons (up). Hover over a square or tap it to read it. With a keyboard, focus the chart and use the arrow keys.

Known by 2020 Predicted, never observed

Loading the table.

Source: NUBASE2020 (Kondev, Wang, Huang, Naimi and Audi, 2021). Squares with the page's ink color have never been seen to decay. In the half-life view, paler squares decay faster (in dark mode, dimmer ones do), and faded squares have half-lives the evaluators estimated rather than measured. Thin lines mark the magic numbers of protons and neutrons (2, 8, 20, 28, 50, 82, 126), where nuclei hold together unusually well. The dashed outline is where theory puts the island of stability: 184 neutrons and, depending on the model, 114, 120 or 126 protons. Nuclides reported after the evaluation, such as rutherfordium-252 in 2025, are not on the chart.

What the chart shows

Every number in this section is counted from the table by a script and written into the page by another. None is typed by hand. The method is at the end of the page.

Rare

Of the 3,340 nuclides ever observed, 253 (7.6 percent) have never been seen to decay. The evaluators list 218 more that the trends of the chart say should exist, but nobody has made them. 288 have a measured abundance in nature: the 253 stable ones, 32 that decay so slowly that some survive from before the Earth formed, and three that are topped up by the decay of uranium. Others occur only in traces, made by cosmic rays or by the decay of uranium and thorium, and most of the chart exists only when made in a laboratory, a reactor or a star.

Bounded, and narrower as nuclei grow

No stable nucleus is heavier than lead-208 (82 protons, 126 neutrons). The share of observed nuclides that are stable falls as nuclei grow, from 14 percent among the lightest to about 8 percent among the heaviest that have any, and is zero above 208 nucleons.

Nucleons (mass number)	Observed	Stable	Share stable
1 to 40	283	40	14 percent
41 to 80	494	49	10 percent
81 to 120	595	54	9 percent
121 to 160	673	53	8 percent
161 to 208	696	57	8 percent
209 to 295	599	0	0 percent

The band also bends. Light stable nuclei carry about one neutron per proton (1.07 on average up to calcium), heavy ones about one and a half (1.47 on average from promethium to lead, and lead-208 carries 1.54). And it has holes: technetium (43) and promethium (61) have no stable isotope, and no stable nucleus has 5, 8, 147 or 151 nucleons. Tin, with the magic number of 50 protons, has the most stable isotopes: 10.

The reason is known. The strong force that binds a nucleus reaches only to its nearest neighbors, while the electric repulsion between protons reaches across the whole nucleus, so every proton pushes on every other. As a nucleus grows, the repulsion grows faster than the binding. Extra neutrons add binding without adding charge, which is why the band bends toward them, but past lead no arrangement is stable at all.

Persistence is not depth

In 246 of the 1,662 cases where both half-lives are measured (15 percent), a nucleus holding extra energy, in an excited state, outlives the same nucleus in its lowest-energy state. The extreme is tantalum-180. In its ground state it decays with a half-life of 8.2 hours. With 75.3 keV more energy it has never been seen to decay (half-life above 4.5 × 10¹⁶ years), and it is the only excited nuclear state found in nature.

Nuclide	Extra energy	Half-life, excited	Half-life, ground state
tantalum-180	75.3 keV	never seen to decay (> 4.5 × 10¹⁶ years)	8.2 hours
bismuth-210	271 keV	3 million years	5 days
polonium-212	2,923 keV	45 seconds	294 nanoseconds
silver-108	109 keV	439 years	2.4 minutes
silver-110	118 keV	250 days	25 seconds
holmium-166	5.97 keV	1,133 years	1.1 days
americium-242	48.6 keV	141 years	16 hours
indium-114	190 keV	50 days	1.2 minutes

What holds such states is a blocked exit, not a deeper well. To decay, the nucleus would have to change its spin by a large step, and transitions that need a large step are extremely slow. The newest superheavy nucleus shows the same thing: rutherfordium-252, reported in 2025 after this table was published, lives 60 nanoseconds in its ground state and about 13 microseconds in an excited one, some 200 times longer.

"Stable" means "not yet seen to decay"

For 55 of the 253 stable nuclides, experiments have looked for a decay and set only a lower limit on the half-life (calcium-40: more than 9.9 × 10²¹ years), and for 68 the table lists a decay that is allowed on energy grounds but has never been seen. Bismuth-209 was counted as stable until 2003, when its alpha decay was measured. Its half-life is 2.01 × 10¹⁹ years, about 1.5 billion times the age of the universe. On this chart, stable means not yet seen to decay.

The shore of the superheavy island

124 nuclides with 104 or more protons have been made, most of them a few atoms at a time. In all 13 of the elements with at least three measured half-lives, half-life rises with the number of neutrons: within an element, each added neutron multiplies it by about 2.1 on average. The most neutron-rich reached have 177 neutrons (nihonium-290, livermorium-293, tennessine-294 and oganesson-295), seven short of the 184 at which every model places the island. The longest-lived superheavy nucleus known is dubnium-268, at 1.2 days.

Measured half-lives of the elements with 104 to 118 protons, one line per element, against the number of neutrons, on a logarithmic scale. The dotted line at 162 neutrons marks a gap in the energy levels of deformed nuclei that lengthens the lives of its neighbors. The dashed line at 184 marks the island's predicted center, which no experiment has reached.

Charted from the inside out

The chart was filled in from the inside out. The stable nuclides were identified first (median year 1930), the radioactive ones up to bismuth later (median 1973), and the superheavy shore last (median 2004). The count of known nuclides passed 1,000 in 1954, 2,000 in 1977 and 3,000 in 2009. Press Play above the chart to watch it fill.

That order runs against a clause of proposition 2, that boundaries are observed before interiors, and the reason is instructive. Proposition 2 is about islands found by pushing a system until it fails to recover. The mainland of this chart was found by waiting: nature had already kept the stable nuclei for billions of years, and the unstable ones had to be made. For the superheavy island the clause does describe what happened: its shore is charted, and its interior is not.

Cost line and fragility line

The site admits an island claim only if it states what the island costs and where it breaks. For the nuclear island:

Cost line. Nothing is spent to keep a nucleus on the island: binding energy is released when a nucleus forms, not paid to hold it together. The cost on this chart is the cost of getting there. The heaviest elements have been made only a few atoms at a time, over months of continuous beam.

Fragility line. As nuclei grow, alpha decay and fission take over, which is where the band ends. Nuclei with 104 or more protons exist only because of the extra binding that closed shells give. Without it they would split apart almost at once. The predicted island is made entirely of that extra binding.

How the propositions meet the chart

The cross-domain rule lets a proposition move to a new domain only when its mathematical or causal structure transfers, not merely its vocabulary. Nuclear physics is a domain where the answers are known, which makes it a place to check the site's words rather than to test its claims.

Proposition	Stated in the sense of	On this chart	Status
P1 Sparsity	Basin-island, reduced to enclosure	The stable region is rare and bounded, and it narrows as nuclei grow. The cause has the same form as proposition 1's clause on coupling: a repulsion that couples every proton to every other grows faster with size than the binding, and past a size no arrangement holds. A shared form, not a test.	resemblance of form
P2 The evidence rule	Basin-island	On a chart-island, persistence is the definition of the island, so proposition 2 cannot be tested here. Two of its clauses still show. Excited states that outlive their ground state persist because the exit is blocked, not because the well is deeper. And every located island is a revisable estimate: bismuth-209 was stable until 2003, and the models still disagree on the proton number at the island's center.	illustration
P3 Exit statistics	Basin-island, stated for agent systems	Radioactive decay is the textbook memoryless exit: a nucleus that has lasted a billion years is exactly as likely to decay in the next second as one made a second ago. Proposition 3 borrows this structure (Kramers's 1940 escape rate is among its prior owners). Here it holds by physics, which makes decay the reference that a hazard estimate for agent systems should reproduce.	reference case
P4 Cost	All three	Does not carry over. A nucleus keeps its binding without spending anything: here depth is a stock, not a flow. That is proposition 4's own falsifier, depth persisting without expenditure, and it holds because a nucleus faces no drift: nothing wears it down while it waits. Charts like this one led version 0.2 of the theory to write that scope into the wording: proposition 4 is now stated for systems held by a throughput, which a nucleus is not.	does not transfer
P5, P6	Framing, stated for organizations	Not applied.	not applied

What this page is not

Nothing on this page tests a proposition. The physics is settled and the table was published in 2021, before this page existed, so there was nothing to pre-register. The page does three things. It shows the object the site is named after, measured rather than drawn. It checks the site's vocabulary against a system whose answers are known. And it marks where the resemblance ends. Instruments that can test propositions in other sciences will be listed under Islands across the sciences as they are built.

Source and method

Table: NUBASE2020, F.G. Kondev, M. Wang, W.J. Huang, S. Naimi and G. Audi, The NUBASE2020 evaluation of nuclear physics properties, Chinese Physics C 45, 030001 (2021), doi:10.1088/1674-1137/abddae. License: CC BY 3.0. File nubase_4.mas20.txt from the IAEA mirror of the Atomic Mass Data Center, retrieved 2026-09-29, 761,906 bytes, SHA-256 1585a5eea86c5e17e90307c7e6e786d060049c4039e392a261ff6db977df9859.

Errors in the table. A script checks the whole table for errors a reader can find without another source: impossible discovery years, stable nuclides listed with an observed decay, decay codes the format does not define, decay branches that add up to more than 100 percent, and natural abundances that do not add up to 100 percent. It found seven candidates. Five are errors. The published file is left as it is, and each correction is applied before anything is counted:

227Ac, discovery year: 1851 in the table, 1902 here. 1851 is before radioactivity was discovered in 1896. Fry and Thoennessen's survey of nuclide discoveries credits Giesel's 1902 paper. Source: C. Fry and M. Thoennessen, Discovery of the actinium, thorium, protactinium, and uranium isotopes, arXiv:1203.1194.
151Ho, beta-plus branch: B+=88 3 in the table, B+=78 3 here. The ground state's branches add up to 110 percent (beta-plus 88, alpha 22). The evaluated structure data give electron capture and beta-plus 78(3) percent, alpha 22(3). Source: IAEA LiveChart of Nuclides, ground state of holmium-151 (ENSDF evaluation by B. Singh), queried 2026-09-29.
126Pdp, decay-mode code: B=72 8 in the table, B-=72 8 here. The code 'B' has no sign. Palladium-126 has 80 neutrons, far more than any stable palladium isotope, so only beta-minus decay is possible. Source: the table's own format, and beta-plus is energetically impossible for this nucleus.
123Te, decay mode of a stable nuclide: EC=100 in the table, EC ? here. Tellurium-123 is listed as stable, with only a lower limit on its half-life, but its decay mode is written as an observed one. The table writes an allowed but unobserved decay with '?', as it does for every other stable nuclide. Source: the table's own format.
204Tl, decay-mode code: EC+B+=2.92 7 in the table, EC=2.92 7 here. 'EC+B+' is not a code the format defines. The decay energy of thallium-204 is too small for beta-plus emission, so the branch is electron capture, which the format writes EC. Source: the table's own format and the decay energy in the same evaluation.

The other two were checked and are right:

4He: Correct. Rutherford and Royds identified the alpha particle as helium-4 in 1908, before isotopes were named. The rule's 1913 threshold is for identifications by mass.
127Agn: Correct. This excited state of silver-127 was reported in Physics Letters B in 2021, and the evaluators included it.

Counting rules. A nuclide counts as observed when the table gives its year of discovery. The others are the evaluators' expectations from trends. Stable means listed as stable. A half-life counts as measured when it is not derived from trends, not a limit and not approximate. An excited state is compared with its ground state only when both half-lives are measured, or when the excited state is listed as stable. The predicted island's position is from the literature, not the table: Myers and Swiatecki (Nuclear Physics 81, 1966) and Sobiczewski, Gareev and Kalinkin (Physics Letters 22, 1966) put it at 114 protons and 184 neutrons. Self-consistent models put the proton number at 120 or 126 (Bender, Nazarewicz and Reinhard, Physics Letters B 515, 2001). Bismuth-209's decay: de Marcillac and colleagues, Nature 422, 2003. Rutherfordium-252: Khuyagbaatar and colleagues, arXiv:2501.08955, 2025.

Code. The code that reads the table refuses any file whose SHA-256 differs from the one above, and every number on this page is counted from the table, not typed by hand.