Decay chain

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]

History

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 0.0000000000028% (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 AMUs, 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, Bi-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 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.

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 quite 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 beta− or beta+ decay modes, changing from one element to the 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[2] by decay chain				Half-life range (y)	Fission products of ^235U by yield[3]
4n	4n+1	4n+2	4n+3
						4.5–7%	0.04–1.25%	<0.001%
^228Ra^№				4–6	†		^155Eu^þ
^244Cm	^241Pu^ƒ	^250Cf	^227Ac^№	10–29		^90Sr	^85Kr	^113mCd^þ
^232U^ƒ		^238Pu^№	^243Cm^ƒ	29–97		^137Cs	^151Sm^þ	^121mSn
^248Bk[4]	^249Cf^ƒ	^242mAm^ƒ		141–351	No fission products have a half-life in the range of 100–210 k years ...
	^241Am^ƒ		^251Cf^ƒ[5]	430–900
		^226Ra^№	^247Bk	1.3 k – 1.6 k
^240Pu	^229Th^№	^246Cm	^243Am^ƒ	4.7 k – 7.4 k
	^245Cm^ƒ	^250Cm		8.3 k – 8.5 k
			^239Pu^ƒ№	24.1 k
		^230Th^№	^231Pa^№	32 k – 76 k
^236Np^ƒ	^233U^ƒ№	^234U^№		150 k – 250 k	‡	^99Tc^₡	^126Sn
^248Cm		^242Pu		327 k – 375 k			^79Se^₡
				1.53 M		^93Zr
	^237Np^№			2.1 M – 6.5 M		^135Cs^₡	^107Pd
^236U^№			^247Cm^ƒ	15 M – 24 M			^129I^₡
^244Pu^№				80 M	... nor beyond 15.7 M years[6]
^232Th^№		^238U^№	^235U^ƒ№	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 m  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

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	3.4×10^5 a	5.162	^244Pu
^244Pu			α	8×10^7 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			α	2.3×10^7 a	4.494	^232Th
^232Th	Th	Thorium	α	1.405×10^10 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	2.14·10^6 a	4.959	^233Pa
^233Pa	β^−	27.0 d	0.571	^233U
^233U	α	1.592·10^5 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	1.9·10^19 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 [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 % 9.654.468·10^9 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 Uranium X2, Brevium 234.043 IT 0.16 % -5.661.159 min 0.07392 ^234Pa 4.6168 ^234mPa UX2 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 % 5.392.455·10^5 a 4.8598 ^230Th 11.6708 ^230Th Io Ionium 230.033 α 100 % 4.887.54·10^4 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

"The Risk Assessment Information System: Radionuclide Decay Chain". The University of Tennessee. "Evaluated Nuclear Structure Data File". National Nuclear Data Center.

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
^239Pu			α	2.41·10^4 a	5.244	^235U
^235U	AcU	Actin Uranium	α	7.04·10^8 a	4.678	^231Th
^231Th	UY	Uranium Y	β^−	25.52 h	0.391	^231Pa
^231Pa		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	.	.

Beta decay chains in fission products

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

• Nuclear science
• Radioactive decay
• Decay product
• Radioisotopes (Radionuclide)

Notes

1. http://www.epa.gov/radon/
2. 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.
3. Specifically from thermal neutron fission of U-235, e.g. in a typical nuclear reactor.
4. 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."
5. This is the heaviest isotope with a half-life of at least four years before the "Sea of Instability".
6. 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.

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