Decay chain

In nuclear science, the decay chain refers to a series of radioactive decays of different radioactive decay products as a sequential series of transformations. It is also known as a "radioactive cascade". 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 between different parent-daughter pairs, but also randomly between identical pairings of parent and daughter isotopes. The decay of each single atom occurs spontaneously, and 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. 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, which is inversely related to λ. Half-lives have been determined in laboratories for many 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 (i.e. there is a one-to-one relationship between the numbers of decays in successive stages) but each stage releases a different quantity of energy. If and when equilibrium is achieved, each successive daughter 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 many individual transformations 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 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.

History

All the elements and isotopes found 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 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 about 200 stable isotopes in the universe. Stable isotopes have ratios of neutrons to protons in their nucleus which are typical about 1 for light elements (e.g. 1 in helium-4) and gradually increase to around 1.5 for the heaviest elements such as 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 decay method for isotopes with a 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. 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 is relatively 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 weight 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 weight by 4 atomic mass units (AMUs), and beta, which does not change the atomic 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 from dividing the atomic weight 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.)

Three of those chains have a long-lived isotope (or nuclide) near the top; this long-lived isotope 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 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 distant 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.

Types of decay

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 very slightly radioactive, with a half-life of 1.9×10¹⁹ years.

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

Actinides and fission products by half-life
Actinides by decay chain				Half-life range (a)	Fission products of 235U by yield
4n	4n + 1	4n + 2	4n + 3		4.5–7%	0.04–1.25%	<0.001%
228Ra№				4–6 a		155Euþ
248Bk				> 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	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
232Th№		238U№	235Uƒ№	0.7–14.1 Ga
₡,  has thermal neutron capture cross section in the range of 8–50 barns ƒ,  fissile №,  primarily a naturally occurring radioactive material (NORM) þ,  neutron poison (thermal neutron capture cross section greater than 3k barns)

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

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 (a=year)	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	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	299 ns	8.955	208Pb
208Tl	ThC″	Thorium C″	β−	3.053 min	4.999	208Pb
208Pb	ThD	Thorium D	stable	.	.	.

Neptunium series

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 (a=year)	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 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	1.9·1019 a	3.137	205Tl
205Tl	.	stable	.	.

Uranium series

(More comprehensive graphic)

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) Historic name (long) Atomic mass Decay mode Branch chance Half life Energy released, MeV Daughter nuclide Subtotal, MeV 238U UI Uranium I 238.051 α 100 % 4.468·109 a 4.26975 234Th 4.2698 234Th UX1 Uranium X1 234.044 β− 100 % 24.10 d 0.273088 234mPa 4.5428 234mPa UX2, Bv Uranium X2, Brevium 234.043 IT 0.16 % 1.159 min 0.07392 234Pa 4.6168 β− 99.84 % 1.159 min 2.268205 234U 6.8110 234Pa UZ Uranium Z 234.043 β− 100 % 6.70 h 2.194285 234U 6.8110 234U UII Uranium II 234.041 α 100 % 2.455·105 a 4.8598 230Th 11.6708 230Th Io Ionium 230.033 α 100 % 7.538·104 a 4.76975 226Ra 16.4406 226Ra Ra Radium 226.025 α 100 % 1600 a 4.87062 222Rn 21.3112 222Rn Rn Radon, Radium Emanation 222.018 α 100 % 3.8235 d 5.59031 218Po 26.9015 218Po RaA Radium A 218.009 β− 0.020 % 3.098 min 0.259913 218At 27.1614 α 99.980 % 3.098 min 6.11468 214Pb 33.0162 218At 218.009 β− 0.1 % 1.5 s 2.881314 218Rn 30.0428 α 99.9 % 1.5 s 6.874 214Bi 34.0354 218Rn 218.006 α 100 % 35 ms 7.26254 214Po 37.3053 214Pb RaB Radium B 214.000 β− 100 % 26.8 min 1.019237 214Bi 34.0354 214Bi RaC Radium C 213.999 β− 99.979 % 19.9 min 3.269857 214Po 37.3053 α 0.021 % 19.9 min 5.62119 210Tl 39.6566 214Po RaCI Radium CI 213.995 α 100 % 164.3 μs 7.83346 210Pb 45.1388 210Tl RaCII Radium CII 209.990 β− 100 % 1.30 min 5.48213 210Pb 45.1388 210Pb RaD Radium D 209.984 β− 100 % 22.20 a 0.063487 210Bi 45.2022 α 1.9·10−6 % 22.20 a 3.7923 206Hg 48.9311 210Bi RaE Radium E 209.984 β− 100 % 5.012 d 1.161234 210Po 46.3635 α 1.32·10−4 % 5.012 d 5.03647 206Tl 50.2387 210Po RaF Radium F 209.983 α 100 % 138.376 d 5.40745 206Pb 51.7709 206Hg 205.978 β− 100 % 8.32 min 1.307649 206Tl 50.2387 206Tl RaEII Radium EII 205.976 β− 100 % 4.202 min 1.532221 206Pb 51.7709 206Pb RaG Radium G 205.974 stable – – – – 51.7709

Actinium series

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.

(More detailed graphic)

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 (a=year)	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 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

• Nuclear physics
• Radioactive decay
• Valley of stability
• Decay product
• Radioisotopes (radionuclide)
• Radiometric dating

References

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

External links

• Nucleonica nuclear science portal
• Nucleonica's Decay Engine for professional online decay calculations
• Decay chains
• Government website listing isotopes and decay energies
• National Nuclear Data Center Freely available databases that can be used to check or construct decay chains. Fully referenced.
• The Live Chart of Nuclides - IAEA with decay chains
• Decay Chain Finder