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In nuclear science a decay chain refers to the predictable series of radioactive disintegrations undergone by the nuclei of certain unstable chemical elements.
Radionuclide 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 nuclide, whose nucleus no longer has the surplus of energy necessary to produce another emission of radiation. Such stable isotopes are then said to have reached their Ground state.
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 144 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. 228Ra in turn undergoes a further eight decays and transmutations until a stable isotope, 208Pb, is produced, terminating the decay chain of 236U.
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 .
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 uranium and Depleted uranium uranium provide examples of this phenomenon.
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 Primordial star. The nuclear furnaces that power stellar evolution were necessary to create large quantities of all elements heavier than helium, and the R-process and s-process
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 Nuclear weapon, nuclear reactors (natural or Nuclear reactor) 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. This is because there are just two main decay methods: alpha radiation, which reduces the mass number by 4, and beta, which leaves it unchanged. 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 follow in its 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, followed by an electron capture (a form of beta decay) to fermium-254, and then a seventh alpha to californium-250, 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, 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 4.463 billion years), uranium-235 (half-life 704 million years) and thorium-232 (half-life 14.1 billion years). The fourth chain has no such long-lasting bottleneck nuclide near the top, so that chain has long since decayed down to the last 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; 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 past, during the first few million years of the history of the Solar System, there were more 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 bottlenecks higher in the 4n, 4n+1, and 4n+3 chains respectively - 244Pu and 247Cm have been identified as having been present. (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, resurrecting the extinct fourth chain. 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 | Actinium |
| 4 n+3 | |
| 235U(247Cm) | |
| 0.704(0.0156) | |
| 207Pb |
These four chains are summarised in the chart in the following section.
Three of these are readily observed in nature, 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 the chain can be represented as A = 4 n, A = 4 n + 2, or A = 4 n + 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 (2.144 million years), the fourth chain, the neptunium series with A = 4 n + 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 reactions in uranium ore; neutron capture by natural thorium to give 233U is also possible. 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 .
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 at the same atomic mass. The later daughter products in such a chain, being closer to beta-stability, generally have the longer half-lives.
The energy release includes the total kinetic energy of all the emitted particles (, , Gamma rays, , and ) and the recoiling decay product nucleus; this corresponds to that calculated from atomic masses. The letter 'a' represents a year (from the Latin annus).
In the tables (except for the neptunium series), the historical names of the naturally occurring nuclides are also given. Such names were used at the time when the decay chains were first discovered and investigated; the system listed was only finalized in the 1920s but it would be too confusing to give earlier names also. From these historical names one can thus find the modern isotopic designation.
The three primordial 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 the lead isotopes are stable and are also present in nature as primordial nuclides, so their excess amounts in comparison with lead-204 (which has only a primordial origin) are required for accurate uranium–lead dating of rocks. Correlating more than one results in lead-lead dating, capable of even greater accuracy.
Plutonium-244 (which appears several steps above thorium-232) was present in the early Solar System, and is just long-lived enough that it should still survive in trace quantities today, though it probably has not been detected.
The total energy released from thorium-232 to lead-208, including the energy lost to neutrinos, is 42.65 MeV; from californium-252, 71.11 MeV. That last is the largest of the four chains, unsurprisingly for the shell-stability of the product.
Since this series was only discovered and studied in 1947–1948, its nuclides were never given historic names. Uniquely among the four, this decay chain has an isotope of radon only produced in a rare branch (not shown in the illustration) but not in the main decay sequence; thus, radon from this decay chain will hardly migrate through rock. Also uniquely, it ends in thallium (or, practically speaking, bismuth) rather than lead. This series terminates with the stable isotope thallium-205, 8 and 4 from neptunium.
The total energy released from neptunium-237 to thallium-205, including the energy lost to , is 49.29 MeV; from californium-249, 66.87 MeV. As the energy of the final step from bismuth to thallium, though known, will not be available until the inconceivable future, it may be better to quote the figures 46.16 MeV and 63.73 MeV to bismuth-209.
The total energy released from uranium-238 to lead-206, including the energy lost to neutrinos, is 51.69 MeV; from californium-250, 68.28 MeV.
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 therefore partitioned differently.
The total energy released from uranium-235 to lead-207, including the energy lost to neutrinos, is 46.40 MeV; from californium-251, 69.91 MeV.
Heavy nuclei (actinide) decay chains
In the four tables below, very minor branches of decay (branching probability less than one in a million) are omitted. Spontaneous fission is also omitted, though larger than this for the heaviest even nuclei and detectable down to thorium. All nuclear data is taken from unless otherwise noted. The historical names of isotopes are recorded in.
Thorium series
The 4n chain of thorium-232 is commonly called the "thorium series" or "thorium cascade". The series terminates with lead-208, 6 and 4 from thorium.
252Cf alpha decay 2.645 a 6.217 248Cm 248Cm α 3.48 a 5.162 244Pu 244Pu α 8.13 a 4.666 240U 240U beta decay 14.1 h 0.382 240mNpENSDF analysis available at 240mNp IT 0.12%
β− 99.88%7.22 min 0.018
2.209240Np
240Pu240Np β− 61.9 min 2.191 240Pu 240Pu α 6561 a 5.256 236U 236U Thoruranium α 2.342 a 4.573 232Th 232Th Th Thorium α 1.40 a 4.082 228Ra 228Ra MsTh1 Mesothorium 1 β− 5.75 a 0.046 228Ac 228Ac MsTh2 Mesothorium 2 β− 6.15 h 2.123 228Th 228Th RdTh Radiothorium α 1.9125 a 5.520 224Ra 224Ra ThX Thorium X α 3.632 d 5.789 220Rn 220Rn Tn Thoron,
Thorium Emanationα 55.6 s 6.405 216Po 216Po ThA Thorium A α 0.144 s 6.906 212Pb 212Pb ThB Thorium B β− 10.627 h 0.569 212Bi 212Bi ThC Thorium C β− 64.06%
α 35.94%60.55 min 2.252
6.207212Po
208Tl212Po ThC′ Thorium C′ α 294.4 ns 8.954 208Pb 208Tl ThC″ Thorium C″ β− 3.053 min 4.999 208Pb 208Pb ThD Thorium D stable
Neptunium series
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) spallation reaction in primordial 238U.
249Cf alpha decay 351 a 6.293 245Cm 245Cm α 8250 a 5.624 241Pu 241Pu beta decay 99.9975%
α 0.0025%14.33 a 0.021
5.140241Am
237U241Am α 432.6 a 5.638 237Np 237U β− 6.752 d 0.518 237Np 237Np α 2.144×106 a 4.957 233Pa 233Pa β− 26.98 d 0.570 233U 233U α 1.592×105 a 4.909 229Th 229Th α 7920 a 5.168 225Ra 225Ra β− 99.9974%
α 0.0026%14.8 d 0.356
5.097225Ac
221Rn225Ac α 9.919 d 5.935 221Fr 221Rn β− 78%
α 22%25.7 min 1.194
6.163221Fr
217Po221Fr α 99.9952%
β− 0.0048%4.801 min 6.457
0.313217At
221Ra221Ra α 25 s 6.880 217Rn 217Po α 97.5%
β− 2.5%1.53 s 6.662
1.488213Pb
217At217At α 99.992%
β− 0.008%32.6 ms 7.202
0.736213Bi
217Rn217Rn α 590 μs 7.888 213Po 213Pb β− 10.2 min 2.028 213Bi 213Bi β− 97.91%
α 2.09%45.6 min 1.422
5.988213Po
209Tl213Po α 3.705 μs 8.536 Lead 209Tl β− 2.162 min 3.970 209Pb 209Pb β− 3.235 h 0.644 209Bi 209Bi α 2.01×1019 a 3.137 205Tl 205Tl stable
Uranium series
The 4n+2 chain of uranium-238 is called the "uranium series" or "radium series", the latter from the first member known when it was named, radium-226. The series terminates with lead-206, 8 and 6 from uranium.
250Cf alpha decay 13.08 a 6.128 246Cm 246Cm α 4760 a 5.475 242Pu 242Pu α 3.75×105 a 4.984 238U 238U UI Uranium I α 4.463×109 a 4.270 234Th 234Th UX1 Uranium X1 beta decay 24.11 d 0.195 234mPa 234mPa UX2, Bv Uranium X2
BreviumIT 0.16%
β− 99.84%1.16 min 0.079
2.273234Pa
234U234Pa UZ Uranium Z β− 6.70 h 2.194 234U 234U UII Uranium II α 2.455×105 a 4.858 230Th 230Th Io Ionium α 7.54×104 a 4.770 226Ra 226Ra Ra Radium alpha decay 1600 a 4.871 222Rn 222Rn Rn Radon,
Radium Emanationα 3.8215 d 5.590 218Po 218Po RaA Radium A α 99.98%
β− 0.02%3.097 min 6.115
0.257214Pb
218At218At α 100%
β−1.28 s 6.876
2.883214Bi
218Rn218Rn α 33.75 ms 7.262 214Po 214Pb RaB Radium B β− 27.06 min 1.018 214Bi 214Bi RaC Radium C β− 99.979%
α 0.021%19.9 min 3.269
5.621214Po
210Tl214Po RaC' Radium C' α 163.5 μs 7.833 210Pb 210Tl RaC" Radium C" β−
β−n 0.009%1.30 min 5.481
0.296210Pb
209Pb (in neptunium series)210Pb RaD Radium D β−
α 1.9×10−6%22.2 a 0.0635
3.793210Bi
206Hg210Bi RaE Radium E β−
α 1.32×10−4%5.012 d 1.161
5.035210Po
206Tl210Po RaF Radium F α 138.376 d 5.407 206Pb 206Hg β− 8.32 min 1.307 206Tl 206Tl RaE" Radium E" β− 4.20 min 1.532 206Pb 206Pb RaG Radium G stable
Actinium series
The 4n+3 chain of uranium-235 is commonly called the "actinium series" or "actinium cascade", from the first member known when it was named, actinium-227. This series terminates with lead-207, 7 and 4 from uranium.
251Cf alpha decay 900 a 6.177 247Cm 247Cm α 1.56×107 a 5.353 243Pu 243Pu beta decay 4.955 h 0.578 243Am 243Am α 7350 a 5.439 239Np 239Np β- 2.356 d 0.723 239Pu 239Pu α 2.411×104 a 5.244 235U 235U AcU Actino-uranium α 7.04×108 a 4.678 231Th 231Th UY Uranium Y β− 25.52 h 0.391 231Pa 231Pa Pa Protoactinium α 3.27×104 a 5.150 227Ac 227Ac Ac Actinium β− 98.62%
α 1.38%21.772 a 0.045
5.042227Th
223Fr227Th RdAc Radioactinium α 18.693 d 6.147 223Ra 223Fr AcK Actinium K β− 99.994%
α 0.006%22.00 min 1.149
5.561223Ra
219At223Ra AcX Actinium X α 11.435 d 5.979 219Rn 219At α 93.6%
β− 6.4%56 s 6.342
1.567215Bi
219Rn219Rn An Actinon,
Actinium Emanationα 3.96 s 6.946 215Po 215Bi β− 7.6 min 2.171 215Po 215Po AcA Actinium A α
β− 2.3×10−4%1.781 ms 7.526
0.715211Pb
215At215At α 37 μs 8.177 211Bi 211Pb AcB Actinium B β− 36.16 min 1.366 211Bi 211Bi AcC Actinium C α 99.724%
β− 0.276%2.14 min 6.750
0.573207Tl
211Po211Po 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
Notes
External links
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