Decay chain

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In nuclear science, the decay chain refers to the radioactive decay of different discrete radioactive decay products as a chained series of transformations. They are also known as "radioactive cascades". Most radioisotopes do not decay directly to a stable state, but rather undergo a series of decays until eventually a stable isotope is reached.

Decay stages are referred to by their relationship to previous or subsequent stages. A parent isotope is one that undergoes decay to form a daughter isotope. One example of this is uranium (atomic number 92) decaying into thorium (atomic number 90). The daughter isotope may be stable or it may decay to form a daughter isotope of its own. The daughter of a daughter isotope is sometimes called a granddaughter isotope.

The time it takes for a single parent atom to decay to an atom of its daughter isotope can vary widely, not only for different parent-daughter chains, but also for identical pairings of parent and daughter isotopes. While the decay of a single atom occurs spontaneously, the decay of an initial population of identical atoms over time t, follows a decaying exponential distribution, e−λt, where λ is called a decay constant. Because of this exponential nature, one of the properties of an isotope is its half-life, the time by which half of an initial number of identical parent radioisotopes have decayed to their daughters. Half-lives have been determined in laboratories for thousands of radioisotopes (or, radionuclides). These can range from nearly instantaneous to as much as 1019 years or more.

The intermediate stages each emit the same amount of radioactivity as the original radioisotope (though not the same energy). When equilibrium is achieved, a granddaughter isotope is present in direct proportion to its half-life; but since its activity is inversely proportional to its half-life, each nuclide in the decay chain finally contributes as much radioactivity as the head of the chain, though not the same energy. For example, uranium-238 is weakly radioactive, but pitchblende, a uranium ore, is 13 times more radioactive than the pure uranium metal of the same amount because of the radium and other daughter isotopes it contains. Not only are unstable radium isotopes significant radioactivity emitters, but as the next stage in the decay chain they also generate radon, a heavy, inert, naturally occurring radioactive gas. Rock containing thorium and/or uranium (such as some granites) emits radon gas that can accumulate in enclosed places such as basements or underground mines. Radon exposure is considered the leading cause of lung cancer in non-smokers.[1]


All the elements and isotopes we encounter on Earth, with the exceptions of hydrogen, deuterium, helium, helium-3, and perhaps trace amounts of stable lithium and beryllium isotopes which were created in the Big Bang, were created by the s-process or the r-process in stars, and for those to be today a part of the Earth, must have been created not later than 4.5 billion years ago. All the elements created more than 4.5 billion years ago are termed primordial, meaning they were generated by the universe's stellar processes. At the time when they were created, those that were unstable began decaying immediately. All the isotopes which have half-lives less than 100 million years have been reduced to 2.8×10−12% or less of whatever original amounts were created and captured by Earth's accretion; they are of trace quantity today, or have decayed away altogether. There are only two other methods to create isotopes: artificially, inside a man-made (or perhaps a natural) reactor, or through decay of a parent isotopic species, the process known as the decay chain.

Unstable isotopes are in a continual struggle to become more stable; the ultimate goal is becoming one of the 200 or so stable isotopes in the universe. Stable isotopes have ratios of neutrons to protons in their nucleus that start out at 1 in stable helium-4 and smoothly rise to ~1.5 for lead (there is no complete stability for anything heavier than lead-208). The elements heavier than that have to shed weight to achieve stability, most usually as alpha decay. The other common method for isotopes of the proper weight but high neutron to proton ratio (n/p) is beta decay, in which the nuclide changes elemental identity while keeping the same weight and lowering its n/p ratio. Also there is an inverse beta decay, which assists isotopes too light in neutrons to approach the ideal; however, since fission almost always produces products which are neutron heavy, positron emission is relatively rare compared to beta 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 weight elements (often referred to as "transuranics", but actually used for all isotopes heavier than lead) there are only four pathways in which all are represented. This fact is made inevitable by the two decay methods possible: alpha radiation, which reduces the weight by 4 atomic mass units (AMU's), and beta, which does not change the weight at all (just the atomic number and the p/n ratio). The four paths are termed 4n, 4n + 1, 4n + 2, and 4n + 3; the remainder of the atomic weight divided 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.

Three of those chains have a long-lived isotope near the top; they are bottlenecks in the process through which the chain flows very slowly, and keep the chain below them "alive" with flow. The three materials 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 isotope, so almost all of the isotopes in that chain have long since decayed down to very near the stability at the bottom. Near the end of that chain is bismuth-209, which was long thought to be stable. Recently, however, bismuth-209 was found to be unstable with a half-life of 19 billion billion years; it is the last step before stable thallium-205. In the far past, around the time that the solar system formed, there were more kinds of unstable high-weight isotopes available, and the four chains were longer with isotopes that have since decayed away. Today we have manufactured extinct isotopes, which again take their former places: plutonium-239, the nuclear bomb fuel, as the major example has a half-life of "only" 24,500 years, and decays by alpha emission into uranium-235. In particular, we have through the large-scale production of neptunium-237 successfully resurrected the hitherto extinct fourth chain.[2]

Types of decay[edit]

This diagram illustrates the four decay chains discussed in the text: thorium (4n, in blue), neptunium (4n+1, in purple), 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 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, dividing all nuclides into four chains. The members of any possible decay chain must be drawn entirely from one of these classes. All four chains also produce helium-4 (alpha particles are helium-4 nuclei).

Three main decay chains (or families) are 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 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 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. The ending isotope of this chain is now known to be thallium-205. Some older sources give the final isotope as bismuth-209, but it was recently discovered that it is radioactive, with a half-life of 1.9×1019 years.

There are also non-transuranic decay chains, 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[edit]

Actinides and fission products by half-life
Actinides[3] by decay chain Half-life
range (y)
Fission products of 235U by yield[4]
4n 4n+1 4n+2 4n+3
4.5–7% 0.04–1.25% <0.001%
228Ra 4–6 155Euþ
244Cmƒ 241Puƒ 250Cf 227Ac 10–29 90Sr 85Kr 113mCdþ
232Uƒ 238Puƒ№ 243Cmƒ 29–97 137Cs 151Smþ 121mSn
248Bk[5] 249Cfƒ 242mAmƒ 141–351

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

241Amƒ 251Cfƒ[6] 430–900
226Ra 247Bk 1.3 k – 1.6 k
240Puƒ№ 229Th 246Cmƒ 243Amƒ 4.7 k – 7.4 k
245Cmƒ 250Cm 8.3 k – 8.5 k
239Puƒ№ 24.1 k
230Th 231Pa 32 k – 76 k
236Npƒ 233Uƒ№ 234U 150 k – 250 k 99Tc 126Sn
248Cm 242Puƒ 327 k – 375 k 79Se
1.53 M 93Zr
237Npƒ№ 2.1 M – 6.5 M 135Cs 107Pd
236U 247Cmƒ 15 M – 24 M 129I
244Pu 80 M

... nor beyond 15.7 M years[7]

232Th 238U 235Uƒ№ 0.7 G – 14.1 G

Legend for superscript symbols
₡  has thermal neutron capture cross section in the range of 8–50 barns
ƒ  fissile
metastable isomer
№  naturally occurring radioactive material (NORM)
þ  neutron poison (thermal neutron capture cross section greater than 3k barns)
†  range 4–97 y: Medium-lived fission product
‡  over 200,000 y: Long-lived fission product

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 U-238), and actinium (from U-235)—each ends with its own specific lead isotope (Pb-208, Pb-206, and Pb-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[edit]

Decay Chain Thorium.svg

The 4n chain of Th-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.

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

nuclide historic name (short) historic name (long) decay mode half-life
energy released, MeV product of decay
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 .39 240Np
240Np β 1.032 h 2.2 240Pu
240Pu α 6561 a 5.1683 236U
236U Thoruranium[8] 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
212Po ThC′ Thorium C′ α 299 ns 8.955 208Pb
208Tl ThC″ Thorium C″ β 3.053 min 4.999 208Pb
208Pb ThD Thorium D stable . . .

Neptunium series[edit]

Decay Chain(4n+1, Neptunium Series).svg

The 4n + 1 chain of Np-237 is commonly called the "neptunium series" or "neptunium cascade". In this series, only two of the isotopes involved are found naturally, namely the final two: bismuth-209 and thallium-205. 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, thallium, thorium, and uranium. Since this series was only studied more recently, its nuclides do not have historic names. One unique trait of this decay chain is that it does not include the noble-gas radon, and thus does not migrate through rock nearly as much as the other three decay chains.

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
energy released, MeV product of decay
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 14.9 d 0.36 225Ac
225Ac α 10.0 d 5.935 221Fr
221Fr α 4.8 min 6.3 217At
217At α 32 ms 7.0 213Bi
213Bi β 97.80%
α 2.20%
46.5 min 1.423
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 1.9·1019 a 3.137 205Tl
205Tl . stable . .

Uranium series[edit]

The 4n+2 chain of U-238 is called the "uranium series" or "radium series". Beginning with naturally occurring uranium-238, this series includes the following elements: astatine, bismuth, lead, 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 (short)
[citation needed]
historic name (long) atomic mass [RS 1] decay mode [RS 2] branch chance [RS 2] half life [RS 2] energy released, MeV [RS 2] daughter nuclide [RS 2] Subtotal MeV
238U UI Uranium I 238.051 α 100 % 9.654.468·109 a 4.26975 234Th 4.2698
234Th UX1 Uranium X1 234.044 β 100 % -1.1824.10 d 0.273088 234mPa 4.5428
234mPa UX2, Bv Uranium X2, Brevium 234.043 IT 0.16 % -5.661.159 min 0.07392 234Pa 4.6168
234mPa UX2, Bv Uranium X2, Brevium 234.043 β 99.84 % -5.661.159 min 2.268205 234U 6.8110
234Pa UZ Uranium Z 234.043 β 100 % -3.126.70 h 2.194285 234U 6.8110
234U UII Uranium II 234.041 α 100 % 5.392.455·105 a 4.8598 230Th 11.6708
230Th Io Ionium 230.033 α 100 % 4.887.54·104 a 4.76975 226Ra 16.4406
226Ra Ra Radium 226.025 α 100 % 3.201600 a 4.87062 222Rn 21.3112
222Rn Rn Radon, Radium Emanation 222.018 α 100 % -1.983.8235 d 5.59031 218Po 26.9015
218Po RaA Radium A 218.009 β 0.020 % -5.233.098 min 0.259913 218At 27.1614
218Po RaA Radium A 218.009 α 99.980 % -5.233.098 min 6.11468 214Pb 33.0162
218At 218.009 β 0.1 % -7.321.5 s 2.881314 218Rn 30.0428
218At 218.009 α 99.9 % -7.321.5 s 6.874 214Bi 34.0354
218Rn 218.006 α 100 % -8.9635 ms 7.26254 214Po 37.3053
214Pb RaB Radium B 214.000 β 100 % -4.2926.8 min 1.019237 214Bi 34.0354
214Bi RaC Radium C 213.999 β 99.979 % -4.4219.9 min 3.269857 214Po 37.3053
214Bi RaC Radium C 213.999 α 0.021 % -4.4219.9 min 5.62119 210Tl 39.6566
214Po RaC' Radium C' 213.995 α 100 % -11.28164.3 μs 7.83346 210Pb 45.1388
210Tl RaC" Radium C" 209.990 β 100 % -5.611.30 min 5.48213 210Pb 45.1388
210Pb RaD Radium D 209.984 β 100 % 1.3522.20 a 0.063487 210Bi 45.2022
210Pb RaD Radium D 209.984 α 0.0000019%1.9·10−6 % 1.3522.20 a 3.7923 206Hg 48.9311
210Bi RaE Radium E 209.984 β 100 % -1.865.012 d 1.161234 210Po 46.3635
210Bi RaE Radium E 209.984 α 0.000133%13.2·10−5 % -1.865.012 d 5.03647 206Tl 50.2387
210Po RaF Radium F 209.983 α 100 % -0.42138.376 d 5.40745 206Pb 51.7709
206Hg 205.978 β 100 % -4.808.32 min 1.307649 206Tl 50.2387
206Tl RaE" Radium E" 205.976 β 100 % -5.104.202 min 1.532221 206Pb 51.7709
206Pb RaG Radium G 205.974 stable - 999- - - 51.7709
  1. ^ "The Risk Assessment Information System: Radionuclide Decay Chain". The University of Tennessee. 
  2. ^ a b c d e "Evaluated Nuclear Structure Data File". National Nuclear Data Center. 

Actinium series[edit]

The 4n+3 chain of uranium-235 is commonly called the "actinium series" or "plutonium cascade". Beginning with the naturally-occurring isotope U-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.

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

nuclide historic name (short) historic name (long) decay mode half-life
energy released, MeV product of decay
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
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
223Ra AcX Actinium X α 11.43 d 5.979 219Rn
219At α 97.00%
β 3.00%
56 s 6.275
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
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
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 . .

Beta decay chains in fission products[edit]

Since the heavy original nuclei always have a greater proportion of neutrons, the fission product nuclei almost always start out with a neutron/proton ratio significantly greater than what is stable for their mass range. Therefore, they undergo multiple beta decays in succession, each converting a neutron to a proton. The first decays tend to have higher decay energy and shorter half-life. These last decays may have low decay energy and/or long half-life.

For example, uranium-235 has 92 protons and 143 neutrons. Fission takes one more neutron, then produces two or three more neutrons; assume that 92 protons and 142 neutrons are available for the two fission product nuclei. Suppose they have mass 99 with 39 protons and 60 neutrons (yttrium-99), and mass 135 with 53 protons and 82 neutrons (iodine-135), then the decay chains can be found in the tables below.

Nuclide Half-life
99Y 1.470(7) s
99Zr 2.1(1) s
99mNb 2.6(2) min
99Nb 15.0(2) s
99m2Mo 0.76(6) µs
99m1Mo 15.5(2) µs
99Mo 2.7489(6) d
99mTc 6.0058(12) h
99Tc 2.111(12)E+5 a
99Ru stable
Nuclide Half-life
135I 6.57(2) h
135Xe 9.14(2) h
135Cs 2.3(3)E+6 a
135Ba stable

See also[edit]


  1. ^
  2. ^ Koch, Lothar (2000). Transuranium Elements, in Ullmann's Encyclopedia of Industrial Chemistry. Wiley. doi:10.1002/14356007.a27_167. 
  3. ^ 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 isotopes have half-lives of at least four years (the longest-lived isotope 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.
  4. ^ Specifically from thermal neutron fission of U-235, e.g. in a typical nuclear reactor.
  5. ^ 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. 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 y. No growth of Cf248 was detected, and a lower limit for the β half-life can be set at about 104 y. No alpha activity attributable to the new isomer has been detected; the alpha half-life is probably greater than 300 y."
  6. ^ This is the heaviest isotope with a half-life of at least four years before the "Sea of Instability".
  7. ^ Excluding those "classically stable" isotopes with half-lives significantly in excess of 232Th; e.g., while 113mCd has a half-life of only fourteen years, that of 113Cd is nearly eight quadrillion years.
  8. ^ 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. 


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

External links[edit]