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Decay chain

In nuclear science a decay chain refers to the predictable series of radioactive disintegrations undergone by the nuclei of certain unstable chemical elements.

Radioactive isotopes do not usually decay directly to stable isotopes, but rather into another radioisotope. The isotope produced by this radioactive emission then decays into another, often radioactive isotope. This chain of decays always terminates in a stable isotope, whose nucleus no longer has the surplus of energy necessary to produce another emission of radiation. Such stable isotopes are then said to have nuclei that have reached their ground states.

The stages or steps in a decay chain are referred to by their relationship to previous or subsequent stages. Hence, a parent isotope is one that undergoes decay to form a daughter isotope. For example element 92, uranium, has an isotope with 143 neutrons (236U) and it decays into an isotope of element 90, thorium, with 142 neutrons (232Th). The daughter isotope may be stable or it may itself decay to form another daughter isotope. 232Th does this when it decays into radium-228. The daughter of a daughter isotope, such as 228Ra, is sometimes called a granddaughter isotope.

The time required for an atom of a parent isotope to decay into its daughter is fundamentally unpredictable and varies widely. For individual nuclei the process is not known to have determinable causes and the time at which it occurs is therefore completely random. The only prediction that can be made is statistical and expresses an average rate of decay. This rate can be represented by adjusting the curve of a decaying exponential distribution with a decay constant (λ) particular to the isotope. On this understanding the radioactive decay of an initial population of unstable atoms over time t follows the curve given by e−λt.

One of the most important properties of any radioactive material follows from this analysis, its half-life. This refers to the time required for half of a given number of radioactive atoms to decay and is inversely related to the isotope's decay constant, λ. Half-lives have been determined in laboratories for many radionuclides, and can range from nearly instantaneous—hydrogen-5 decays in less time than it takes for a photon to go from one end of its nucleus to the other—to fourteen orders of magnitude longer than the age of the universe: tellurium-128 has a half-life of 2.2×1024 years.

Quantity calculation with the Bateman-Function for 241Pu

The Bateman equation predicts the relative quantities of all the isotopes that compose a given decay chain once that decay chain has proceeded long enough for some of its daughter products to have reached the stable (i.e., nonradioactive) end of the chain. A decay chain that has reached this state, which may require billions of years, is said to be in equilibrium. A sample of radioactive material in equilibrium produces a steady and steadily decreasing quantity of radioactivity as the isotopes that compose it traverse the decay chain. On the other hand, if a sample of radioactive material has been isotopically enriched, meaning that a radioisotope is present in larger quantities than would exist if a decay chain were the only cause of its presence, that sample is said to be out of equilibrium. An unintuitive consequence of this disequilibrium is that a sample of enriched material may occasionally increase in radioactivity as daughter products that are more highly radioactive than their parents accumulate. Both enriched and depleted uranium provide examples of this phenomenon.

History

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The chemical elements came into being in two phases. The first commenced shortly after the Big Bang. From ten seconds to 20 minutes after the beginning of the universe the earliest condensation of light atoms was responsible for the manufacture of the four lightest elements. The vast majority of this primordial production consisted of the three lightest isotopes of hydrogen—protium, deuterium and tritium—and two of the nine known isotopes of helium—helium-3 and helium-4. Trace amounts of lithium-7 and beryllium-7 were likely also produced.

So far as is known, all heavier elements came into being starting around 100 million years later, in a second phase of nucleosynthesis that commenced with the birth of the first stars.[1] The nuclear furnaces that power stellar evolution were necessary to create large quantities of all elements heavier than helium, and the r- and s-processes of neutron capture that occur in stellar cores are thought to have created all such elements up to iron and nickel (atomic numbers 26 and 28). The extreme conditions that attend supernovae explosions are capable of creating the elements between oxygen and rubidium (i.e., atomic numbers 8 through 37). The creation of heavier elements, including those without stable isotopes—all elements with atomic numbers greater than lead's, 82—appears to rely on r-process nucleosynthesis operating amid the immense concentrations of free neutrons released during neutron star mergers.

Most of the isotopes of each chemical element present in the Earth today were formed by such processes no later than the time of our planet's condensation from the solar protoplanetary disc, around 4.5 billion years ago. The exceptions to these so-called primordial elements are those that have resulted from the radioactive disintegration of unstable parent nuclei as they progress down one of several decay chains, each of which terminates with the production of one of the 251 stable isotopes known to exist. Aside from cosmic or stellar nucleosynthesis, and decay chains the only other ways of producing a chemical element rely on atomic weapons, nuclear reactors (natural or manmade) or the laborious atom-by-atom assembly of nuclei with particle accelerators.

Unstable isotopes decay to their daughter products (which may sometimes be even more unstable) at a given rate; eventually, often after a series of decays, a stable isotope is reached: there are 251 stable isotopes in the universe. In stable isotopes, light elements typically have a lower ratio of neutrons to protons in their nucleus than heavier elements. Light elements such as helium-4 have close to a 1:1 neutron:proton ratio. The heaviest elements such as uranium have close to 1.5 neutrons per proton (e.g. 1.587 in uranium-238). No nuclide heavier than lead-208 is stable; these heavier elements have to shed mass to achieve stability, mostly by alpha decay. The other common way for isotopes with a high neutron to proton ratio (n/p) to decay is beta decay, in which the nuclide changes elemental identity while keeping the same mass number and lowering its n/p ratio. For some isotopes with a relatively low n/p ratio, there is an inverse beta decay, by which a proton is transformed into a neutron, thus moving towards a stable isotope; however, since fission almost always produces products which are neutron heavy, positron emission or electron capture are rare compared to electron emission. There are many relatively short beta decay chains, at least two (a heavy, beta decay and a light, positron decay) for every discrete weight up to around 207 and some beyond, but for the higher mass elements (isotopes heavier than lead) there are only four pathways which encompass all decay chains.[citation needed] This is because there are just two main decay methods: alpha radiation, which reduces the mass by 4 atomic mass units (amu), and beta, which does not change the mass number (just the atomic number and the p/n ratio). The four paths are termed 4n, 4n + 1, 4n + 2, and 4n + 3; the remainder from dividing the atomic mass by four gives the chain the isotope will use to decay. There are other decay modes, but they invariably occur at a lower probability than alpha or beta decay. (It should not be supposed that these chains have no branches: the diagram below shows a few branches of chains, and in reality there are many more, because there are many more isotopes possible than are shown in the diagram.) For example, the third atom of nihonium-278 synthesised underwent six alpha decays down to mendelevium-254,[2] followed by an electron capture (a form of beta decay) to fermium-254,[2] and then a seventh alpha to californium-250,[2] upon which it would have followed the 4n + 2 chain (radium series) as given in this article. However, the heaviest superheavy nuclides synthesised do not reach the four decay chains, because they reach a spontaneously fissioning nuclide after a few alpha decays that terminates the chain: this is what happened to the first two atoms of nihonium-278 synthesised,[3][4] as well as to all heavier nuclides produced.

Three of those chains have a long-lived isotope (or nuclide) near the top; this long-lived nuclide is a bottleneck in the process through which the chain flows very slowly, and keeps the chain below them "alive" with flow. The three long-lived nuclides are uranium-238 (half-life 4.5 billion years), uranium-235 (half-life 700 million years) and thorium-232 (half-life 14 billion years). The fourth chain has no such long-lasting bottleneck nuclide near the top, so almost all of the nuclides in that chain have long since decayed down to just before the end: bismuth-209. This nuclide was long thought to be stable, but in 2003 it was found to be unstable, with a very long half-life of 20.1 billion billion years;[5] it is the last step in the chain before stable thallium-205. Because this bottleneck is so long-lived, very small quantities of the final decay product have been produced, and for most practical purposes bismuth-209 is the final decay product.

In the distant past, during the first few million years of the history of the Solar System, there were more kinds of unstable high-mass nuclides in existence, and the four chains were longer, as they included nuclides that have since decayed away. Notably, 244Pu, 237Np, and 247Cm have half-lives over a million years and would have then been lesser bottlenecks high in the 4n, 4n+1, and 4n+3 chains respectively.[6] (There is no nuclide with a half-life over a million years above 238U in the 4n+2 chain.) Today some of these formerly extinct isotopes are again in existence as they have been manufactured. Thus they again take their places in the chain: plutonium-239, used in nuclear weapons, is the major example, decaying to uranium-235 via alpha emission with a half-life 24,500 years. There has also been large-scale production of neptunium-237, which has resurrected the hitherto extinct fourth chain.[7] The tables below hence start the four decay chains at isotopes of californium with mass numbers from 249 to 252.

Summary of the four decay chain pathways
Name of series Thorium Neptunium Uranium Actinium
Mass numbers 4n 4n+1 4n+2 4n+3
Long-lived nuclide 232Th
(244Pu)		 209Bi
(237Np)		 238U
 		 235U
(247Cm)
Half-life
(billions of years)		 14
(0.08)		 20100000000
(0.00214)		 4.5
 		 0.7
(0.0156)
End of chain 208Pb 205Tl 206Pb 207Pb

These four chains are summarised in the chart in the following section.

Types of decay

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This diagram illustrates the four decay chains discussed in the text: thorium (4n, in blue), neptunium (4n+1, in pink), radium (4n+2, in red) and actinium (4n+3, in green).

The four most common modes of radioactive decay are: alpha decay, beta decay, inverse beta decay (considered as both positron emission and electron capture), and isomeric transition. Of these decay processes, only alpha decay (fission of a helium-4 nucleus) changes the atomic mass number (A) of the nucleus, and always decreases it by four. Because of this, almost any decay will result in a nucleus whose atomic mass number has the same residue mod 4. This divides the list of nuclides into four classes. All the members of any possible decay chain must be drawn entirely from one of these classes.

Three main decay chains (or families) are observed in nature. These are commonly called the thorium series, the radium or uranium series, and the actinium series, representing three of these four classes, and ending in three different, stable isotopes of lead. The mass number of every isotope in these chains can be represented as A = 4n, A = 4n + 2, and A = 4n + 3, respectively. The long-lived starting isotopes of these three isotopes, respectively thorium-232, uranium-238, and uranium-235, have existed since the formation of the Earth, ignoring the artificial isotopes and their decays created since the 1940s.

Due to the relatively short half-life of its starting isotope neptunium-237 (2.14 million years), the fourth chain, the neptunium series with A = 4n + 1, is already extinct in nature, except for the final rate-limiting step, decay of bismuth-209. Traces of 237Np and its decay products do occur in nature, however, as a result of neutron capture in uranium ore.[8] The ending isotope of this chain is now known to be thallium-205. Some older sources give the final isotope as bismuth-209, but in 2003 it was discovered that it is very slightly radioactive, with a half-life of 2.01×1019 years.[9]

There are also non-transuranic decay chains of unstable isotopes of light elements, for example those of magnesium-28 and chlorine-39. On Earth, most of the starting isotopes of these chains before 1945 were generated by cosmic radiation. Since 1945, the testing and use of nuclear weapons has also released numerous radioactive fission products. Almost all such isotopes decay by either β− or β+ decay modes, changing from one element to another without changing atomic mass. These later daughter products, being closer to stability, generally have longer half-lives until they finally decay into stability.

Actinide alpha decay chains

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Actinides and fission products by half-life
Actinides[10] by decay chain Half-life
range (a) 		Fission products of 235U by yield[11]
4n 4n + 1 4n + 2 4n + 3 4.5–7% 0.04–1.25% <0.001%
228Ra№ 4–6 a 155Euþ
248Bk[12] > 9 a
244Cmƒ 241Puƒ 250Cf 227Ac№ 10–29 a 90Sr 85Kr 113mCdþ
232Uƒ 238Puƒ 243Cmƒ 29–97 a 137Cs 151Smþ 121mSn
249Cfƒ 242mAmƒ 141–351 a

No fission products have a half-life
in the range of 100 a–210 ka ...

241Amƒ 251Cfƒ[13] 430–900 a
226Ra№ 247Bk 1.3–1.6 ka
240Pu 229Th 246Cmƒ 243Amƒ 4.7–7.4 ka
245Cmƒ 250Cm 8.3–8.5 ka
239Puƒ 24.1 ka
230Th№ 231Pa№ 32–76 ka
236Npƒ 233Uƒ 234U№ 150–250 ka 99Tc₡ 126Sn
248Cm 242Pu 327–375 ka 79Se₡
1.33 Ma 135Cs₡
237Npƒ 1.61–6.5 Ma 93Zr 107Pd
236U 247Cmƒ 15–24 Ma 129I₡
244Pu 80 Ma

... nor beyond 15.7 Ma[14]

232Th№ 238U№ 235Uƒ№ 0.7–14.1 Ga

In the four tables below, the minor branches of decay (with the branching probability of less than 0.0001%) are omitted. The energy release includes the total kinetic energy of all the emitted particles (electrons, alpha particles, gamma quanta, neutrinos, Auger electrons and X-rays) and the recoil nucleus, assuming that the original nucleus was at rest. The letter 'a' represents a year (from the Latin annus).

In the tables below (except neptunium), the historic names of the naturally occurring nuclides are also given. These names were used at the time when the decay chains were first discovered and investigated. From these historical names one can locate the particular chain to which the nuclide belongs, and replace it with its modern name.

The three naturally-occurring actinide alpha decay chains given below—thorium, uranium/radium (from uranium-238), and actinium (from uranium-235)—each ends with its own specific lead isotope (lead-208, lead-206, and lead-207 respectively). All these isotopes are stable and are also present in nature as primordial nuclides, but their excess amounts in comparison with lead-204 (which has only a primordial origin) can be used in the technique of uranium–lead dating to date rocks.

Thorium series

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The 4n chain of thorium-232 is commonly called the "thorium series" or "thorium cascade". Beginning with naturally occurring thorium-232, this series includes the following elements: actinium, bismuth, lead, polonium, radium, radon and thallium. All are present, at least transiently, in any natural thorium-containing sample, whether metal, compound, or mineral. The series terminates with lead-208.

Plutonium-244 (which appears several steps above thorium-232 in this chain if one extends it to the transuranics) was present in the early Solar System,[6] and is just long-lived enough that it should still survive in trace quantities today,[15] though it is uncertain if it has been detected.[16]

The total energy released from thorium-232 to lead-208, including the energy lost to neutrinos, is 42.6 MeV.

Nuclide Historic names Decay mode Half-life
(a = years) 		Energy released
MeV 		Decay
product
Short Long
252Cf α 2.645 a 6.1181 248Cm
248Cm α 3.4×105 a 5.162 244Pu
244Pu α 8×107 a 4.589 240U
240U β− 14.1 h 0.39 240Np
240Np β− 1.032 h 2.2 240Pu
240Pu α 6561 a 5.1683 236U
236U Thoruranium[17] α 2.3×107 a 4.494 232Th
232Th Th Thorium α 1.405×1010 a 4.081 228Ra
228Ra MsTh1 Mesothorium 1 β− 5.75 a 0.046 228Ac
228Ac MsTh2 Mesothorium 2 β− 6.25 h 2.124 228Th
228Th RdTh Radiothorium α 1.9116 a 5.520 224Ra
224Ra ThX Thorium X α 3.6319 d 5.789 220Rn
220Rn Tn Thoron,
Thorium Emanation 		α 55.6 s 6.404 216Po
216Po ThA Thorium A α 0.145 s 6.906 212Pb
212Pb ThB Thorium B β− 10.64 h 0.570 212Bi
212Bi ThC Thorium C β− 64.06%
α 35.94% 		60.55 min 2.252
6.208 		212Po
208Tl
212Po ThC′ Thorium C′ α 294.4 ns[18] 8.954[19] 208Pb
208Tl ThC″ Thorium C″ β− 3.053 min 1.803[20] 208Pb
208Pb ThD Thorium D stable — — —

Neptunium series

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The 4n + 1 chain of neptunium-237 is commonly called the "neptunium series" or "neptunium cascade". In this series, only two of the isotopes involved are found naturally in significant quantities, namely the final two: bismuth-209 and thallium-205. Some of the other isotopes have been detected in nature, originating from trace quantities of 237Np produced by the (n,2n) knockout reaction in primordial 238U.[8] A smoke detector containing an americium-241 ionization chamber accumulates a significant amount of neptunium-237 as its americium decays. The following elements are also present in it, at least transiently, as decay products of the neptunium: actinium, astatine, bismuth, francium, lead, polonium, protactinium, radium, radon, thallium, thorium, and uranium. Since this series was only discovered and studied in 1947–1948,[21] its nuclides do not have historic names. One unique trait of this decay chain is that the noble gas radon is only produced in a rare branch (not shown in the illustration) but not the main decay sequence; thus, radon from this decay chain does not migrate through rock nearly as much as from the other three. Another unique trait of this decay sequence is that it ends in thallium (practically speaking, bismuth) rather than lead. This series terminates with the stable isotope thallium-205.

The total energy released from californium-249 to thallium-205, including the energy lost to neutrinos, is 66.8 MeV.

Nuclide Decay mode Half-life
(a = years) 		Energy released
MeV 		Decay product
249Cf α 351 a 5.813+.388 245Cm
245Cm α 8500 a 5.362+.175 241Pu
241Pu β− 14.4 a 0.021 241Am
241Am α 432.7 a 5.638 237Np
237Np α 2.14×106 a 4.959 233Pa
233Pa β− 27.0 d 0.571 233U
233U α 1.592×105 a 4.909 229Th
229Th α 7340 a 5.168 225Ra
225Ra β− 99.998%
α 0.002% 		14.9 d 0.36
5.097 		225Ac
221Rn
225Ac α 10.0 d 5.935 221Fr
221Rn β− 78%
α 22% 		25.7 min 1.194
6.163 		221Fr
217Po
221Fr α 99.9952%
β− 0.0048% 		4.8 min 6.458
0.314 		217At
221Ra
221Ra α 28 s 6.880 217Rn
217Po α 97.5%
β− 2.5% 		1.53 s 6.662
1.488 		213Pb
217At
217At α 99.992%
β− 0.008% 		32 ms 7.201
0.737 		213Bi
217Rn
217Rn α 540 μs 7.887 213Po
213Pb β− 10.2 min 2.028 213Bi
213Bi β− 97.80%
α 2.20% 		46.5 min 1.423
5.87 		213Po
209Tl
213Po α 3.72 μs 8.536 209Pb
209Tl β− 2.2 min 3.99 209Pb
209Pb β− 3.25 h 0.644 209Bi
209Bi α 2.01×1019 a 3.137 205Tl
205Tl . stable . .

Uranium series

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Uranium series 
(More comprehensive graphic)

The 4n+2 chain of uranium-238 is called the "uranium series" or "radium series". Beginning with naturally occurring uranium-238, this series includes the following elements: astatine, bismuth, lead, mercury, polonium, protactinium, radium, radon, thallium, and thorium. All are present, at least transiently, in any natural uranium-containing sample, whether metal, compound, or mineral. The series terminates with lead-206.

The total energy released from uranium-238 to lead-206, including the energy lost to neutrinos, is 51.7 MeV.

Parent
nuclide 		Historic name[22] Decay mode [RS 1] Half-life
(a= years) 		Energy released
MeV[RS 1] 		Decay
product[RS 1]
Short Long
250Cf α 13.08 a 6.12844 246Cm
246Cm α 4800 a 5.47513 242Pu
242Pu α 3.8×105 a 4.98453 238U
238U UI Uranium I α 4.468×109 a 4.26975 234Th
234Th UX1 Uranium X1 β− 24.10 d 0.273088 234mPa
234mPa UX2, Bv Uranium X2
Brevium 		IT, 0.16%
β−, 99.84% 		1.159 min 0.07392
2.268205 		234Pa
234U
234Pa UZ Uranium Z β− 6.70 h 2.194285 234U
234U UII Uranium II α 2.45×105 a 4.8698 230Th
230Th Io Ionium α 7.54×104 a 4.76975 226Ra
226Ra Ra Radium α 1600 a 4.87062 222Rn
222Rn Rn Radon,
Radium Emanation 		α 3.8235 d 5.59031 218Po
218Po RaA Radium A α, 99.980%
β−, 0.020% 		3.098 min 6.11468
0.259913 		214Pb
218At
218At α, 99.9%
β−, 0.1% 		1.5 s 6.874
2.881314 		214Bi
218Rn
218Rn α 35 ms 7.26254 214Po
214Pb RaB Radium B β− 26.8 min 1.019237 214Bi
214Bi RaC Radium C β−, 99.979%
α, 0.021% 		19.9 min 3.269857
5.62119 		214Po
210Tl
214Po RaC' Radium C' α 164.3 μs 7.83346 210Pb
210Tl RaC" Radium C" β− 1.3 min 5.48213 210Pb
210Pb RaD Radium D β−, 100%
α, 1.9×10−6% 		22.20 a 0.063487
3.7923 		210Bi
206Hg
210Bi RaE Radium E β−, 100%
α, 1.32×10−4% 		5.012 d 1.161234
5.03647 		210Po
206Tl
210Po RaF Radium F α 138.376 d 5.03647 206Pb
206Hg β− 8.32 min 1.307649 206Tl
206Tl β− 4.202 min 1.5322211 206Pb
206Pb RaG[23] Radium G stable - - -
  1. ^ a b c "Evaluated Nuclear Structure Data File". National Nuclear Data Center.

Actinium series

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The 4n+3 chain of uranium-235 is commonly called the "actinium series" or "actinium cascade". Beginning with the naturally-occurring isotope uranium-235, this decay series includes the following elements: actinium, astatine, bismuth, francium, lead, polonium, protactinium, radium, radon, thallium, and thorium. All are present, at least transiently, in any sample containing uranium-235, whether metal, compound, ore, or mineral. This series terminates with the stable isotope lead-207.

Actinium series 
(More detailed graphic)

In the early Solar System this chain went back to 247Cm. This manifests itself today as variations in 235U/238U ratios, since curium and uranium have noticeably different chemistries and would have separated differently.[6][24]

The total energy released from uranium-235 to lead-207, including the energy lost to neutrinos, is 46.4 MeV.

Nuclide Historic name Decay mode Half-life
(a = years) 		Energy released
MeV 		Decay
product
Short Long
251Cf α 900.6 a 6.176 247Cm
247Cm α 1.56×107 a 5.353 243Pu
243Pu β− 4.95556 h 0.579 243Am
243Am α 7388 a 5.439 239Np
239Np β− 2.3565 d 0.723 239Pu
239Pu α 2.41×104 a 5.244 235U
235U AcU Actin Uranium α 7.04×108 a 4.678 231Th
231Th UY Uranium Y β− 25.52 h 0.391 231Pa
231Pa Pa Protactinium α 32760 a 5.150 227Ac
227Ac Ac Actinium β− 98.62%
α 1.38% 		21.772 a 0.045
5.042 		227Th
223Fr
227Th RdAc Radioactinium α 18.68 d 6.147 223Ra
223Fr AcK Actinium K β− 99.994%
α 0.006% 		22.00 min 1.149
5.340 		223Ra
219At
223Ra AcX Actinium X α 11.43 d 5.979 219Rn
219At α 97.00%
β− 3.00% 		56 s 6.275
1.700 		215Bi
219Rn
219Rn An Actinon,
Actinium Emanation 		α 3.96 s 6.946 215Po
215Bi β− 7.6 min 2.250 215Po
215Po AcA Actinium A α 99.99977%
β− 0.00023% 		1.781 ms 7.527
0.715 		211Pb
215At
215At α 0.1 ms 8.178 211Bi
211Pb AcB Actinium B β− 36.1 min 1.367 211Bi
211Bi AcC Actinium C α 99.724%
β− 0.276% 		2.14 min 6.751
0.575 		207Tl
211Po
211Po AcC' Actinium C' α 516 ms 7.595 207Pb
207Tl AcC" Actinium C" β− 4.77 min 1.418 207Pb
207Pb AcD Actinium D . stable . .

See also

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Notes

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  1. ^ Bromm, Richard B. Larson, Volker. "The First Stars in the Universe". Scientific American. Retrieved 2024-09-29.{{cite web}}: CS1 maint: multiple names: authors list (link)
  2. ^ a b c K. Morita; Morimoto, Kouji; Kaji, Daiya; Haba, Hiromitsu; Ozeki, Kazutaka; Kudou, Yuki; Sumita, Takayuki; Wakabayashi, Yasuo; Yoneda, Akira; Tanaka, Kengo; et al. (2012). "New Results in the Production and Decay of an Isotope, 278113, of the 113th Element". Journal of the Physical Society of Japan. 81 (10): 103201. arXiv:1209.6431. Bibcode:2012JPSJ...81j3201M. doi:10.1143/JPSJ.81.103201. S2CID 119217928.
  3. ^ Morita, Kosuke; Morimoto, Kouji; Kaji, Daiya; Akiyama, Takahiro; Goto, Sin-Ichi; Haba, Hiromitsu; Ideguchi, Eiji; Kanungo, Rituparna; et al. (2004). "Experiment on the Synthesis of Element 113 in the Reaction 209Bi(70Zn, n)278113". Journal of the Physical Society of Japan. 73 (10): 2593–2596. Bibcode:2004JPSJ...73.2593M. doi:10.1143/JPSJ.73.2593.
  4. ^ Barber, Robert C.; Karol, Paul J; Nakahara, Hiromichi; Vardaci, Emanuele; Vogt, Erich W. (2011). "Discovery of the elements with atomic numbers greater than or equal to 113 (IUPAC Technical Report)". Pure and Applied Chemistry. 83 (7): 1485. doi:10.1351/PAC-REP-10-05-01.
  5. ^ J.W. Beeman; et al. (2012). "First Measurement of the Partial Widths of 209Bi Decay to the Ground and to the First Excited States". Physical Review Letters. 108 (6): 062501. arXiv:1110.3138. doi:10.1103/PhysRevLett.108.062501. PMID 22401058. S2CID 118686992.
  6. ^ a b c Davis, Andrew M. (2022). "Short-Lived Nuclides in the Early Solar System: Abundances, Origins, and Applications". Annual Review of Nuclear and Particle Science. 72: 339–363. doi:10.1146/annurev-nucl-010722-074615. Retrieved 23 November 2023.
  7. ^ Koch, Lothar (2000). Transuranium Elements, in Ullmann's Encyclopedia of Industrial Chemistry. Wiley. doi:10.1002/14356007.a27_167.
  8. ^ a b Peppard, D. F.; Mason, G. W.; Gray, P. R.; Mech, J. F. (1952). "Occurrence of the (4n + 1) series in nature" (PDF). Journal of the American Chemical Society. 74 (23): 6081–6084. doi:10.1021/ja01143a074.
  9. ^ Audi, G.; Kondev, F. G.; Wang, M.; Huang, W. J.; Naimi, S. (2017). "The NUBASE2016 evaluation of nuclear properties" (PDF). Chinese Physics C. 41 (3): 030001. Bibcode:2017ChPhC..41c0001A. doi:10.1088/1674-1137/41/3/030001.
  10. ^ Plus radium (element 88). While actually a sub-actinide, it immediately precedes actinium (89) and follows a three-element gap of instability after polonium (84) where no nuclides have half-lives of at least four years (the longest-lived nuclide in the gap is radon-222 with a half life of less than four days). Radium's longest lived isotope, at 1,600 years, thus merits the element's inclusion here.
  11. ^ Specifically from thermal neutron fission of uranium-235, e.g. in a typical nuclear reactor.
  12. ^ Milsted, J.; Friedman, A. M.; Stevens, C. M. (1965). "The alpha half-life of berkelium-247; a new long-lived isomer of berkelium-248". Nuclear Physics. 71 (2): 299. Bibcode:1965NucPh..71..299M. doi:10.1016/0029-5582(65)90719-4.
    "The isotopic analyses disclosed a species of mass 248 in constant abundance in three samples analysed over a period of about 10 months. This was ascribed to an isomer of Bk248 with a half-life greater than 9 [years]. No growth of Cf248 was detected, and a lower limit for the β− half-life can be set at about 104 [years]. No alpha activity attributable to the new isomer has been detected; the alpha half-life is probably greater than 300 [years]."
  13. ^ This is the heaviest nuclide with a half-life of at least four years before the "sea of instability".
  14. ^ Excluding those "classically stable" nuclides with half-lives significantly in excess of 232Th; e.g., while 113mCd has a half-life of only fourteen years, that of 113Cd is eight quadrillion years.
  15. ^ Hoffman, D. C.; Lawrence, F. O.; Mewherter, J. L.; Rourke, F. M. (1971). "Detection of Plutonium-244 in Nature". Nature. 234 (5325): 132–134. Bibcode:1971Natur.234..132H. doi:10.1038/234132a0. S2CID 4283169.
  16. ^ Lachner, J.; et al. (2012). "Attempt to detect primordial 244Pu on Earth". Physical Review C. 85 (1): 015801. Bibcode:2012PhRvC..85a5801L. doi:10.1103/PhysRevC.85.015801.
  17. ^ Trenn, Thaddeus J. (1978). "Thoruranium (U-236) as the extinct natural parent of thorium: The premature falsification of an essentially correct theory". Annals of Science. 35 (6): 581–97. doi:10.1080/00033797800200441.
  18. ^ Kondev, F. G.; Wang, M.; Huang, W. J.; Naimi, S.; Audi, G. (2021). "The NUBASE2020 evaluation of nuclear properties" (PDF). Chinese Physics C. 45 (3): 030001. doi:10.1088/1674-1137/abddae.
  19. ^ National Nuclear Data Center. "NuDat 3.0 database". Brookhaven National Laboratory. Retrieved 19 Feb 2022.
  20. ^ "Nuclear Data". nucleardata.nuclear.lu.se. Archived from the original on 2018-12-28. Retrieved 2023-03-21.
  21. ^ Thoennessen, M. (2016). The Discovery of Isotopes: A Complete Compilation. Springer. p. 20. doi:10.1007/978-3-319-31763-2. ISBN 978-3-319-31761-8. LCCN 2016935977.
  22. ^ Thoennessen, M. (2016). The Discovery of Isotopes: A Complete Compilation. Springer. p. 19. doi:10.1007/978-3-319-31763-2. ISBN 978-3-319-31761-8. LCCN 2016935977.
  23. ^ Kuhn, W. (1929). "LXVIII. Scattering of thorium C" γ-radiation by radium G and ordinary lead". The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. 8 (52): 628. doi:10.1080/14786441108564923. ISSN 1941-5982.
  24. ^ Tsaletka, R.; Lapitskii, A. V. (1960). "Occurrence of the Transuranium Elements in Nature". Russian Chemical Reviews. 29 (12): 684–689. Retrieved 20 January 2024.

References

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  • C.M. Lederer; J.M. Hollander; I. Perlman (1968). Table of Isotopes (6th ed.). New York: John Wiley & Sons.
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