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. Most radioactive elements 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. 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 often emit more radioactivity than the original radioisotope. When equilibrium is achieved, a granddaughter isotope is present in proportion to its half-life; but since its activity is inversely proportional to its half-life, any nuclide in the decay chain finally contributes as much as the head of the chain. For example, natural uranium is not significantly radioactive, but pitchblende, a uranium ore, is 13 times more radioactive 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.

Types

This diagram illustrates the four decay chains discussed in the text: thorium (in blue), radium (in red), actinium (in green), and neptunium (in purple).

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 classes. 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 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. The plutonium isotopes plutonium-244 and plutonium-239 have also been found in trace amounts on earth.

Due to the quite short half-life of its starting isotope neptunium-237 (2.14e-06 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 many shorter chains, for example that of carbon-14. On Earth, most of the starting isotopes of these chains are generated by cosmic radiation.

Actinide alpha decay chains

Actinides				Half-life	Fission products
244Cm	241Puƒ	250Cf	227Ac№	10–22 y	medium		m is meta	85Kr	113mCd₡
232Uƒ		238Pu	243Cmƒ	29–90 y	137Cs	90Sr		151Sm₡	121mSn
ƒ for fissile	249Cfƒ	242mAmƒ	251Cfƒ	140 y – 1.6 ky	No fission products have a half-life in the range of 91 y – 210 ky
	241Am	226Ra№	247Bk
240Pu	229Th	246Cm	243Am	5–7 ky
4n	245Cmƒ	250Cm	239Puƒ	8–24 ky
236Npƒ	233Uƒ	230Th№	231Pa№	32–160 ky
248Cm	4n+1	234U№		211–348 ky	99Tc	₡ can capture		126Sn	79Se
236U	237Np	242Pu	247Cmƒ	0.37–23 My	135Cs₡	93Zr	107Pd	129I	long
244Pu	№ for NORM	4n+2	4n+3	80 My	6-7%	4-5%	1.25%	0.1-1%	<0.05%
232Th№		238U№	235Uƒ№	0.7–14 Gy	fission product yield

In the four tables below, the minor branches of decay (with the branching ratio 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.

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

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			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." In this series, only two of the isotopes involved are found naturally, namely those of bismuth and thallium. 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.

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	.	.

Radium series (also known as uranium series)

(More comprehensive graphic)

The 4n+2 chain of U-238 is commonly called the "radium series" (sometimes "uranium 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.

nuclide	historic name (short)	historic name (long)	decay mode	half-life (a=year)	energy released, MeV	product of decay
238U	UI	Uranium I	α	4.468·109 a	4.270	234Th
234Th	UX1	Uranium X1	β−	24.10 d	0.273	234mPa
234mPa	UX2	Uranium X2, Brevium	β− 99.84% IT 0.16%	1.16 min	2.271 0.074	234U 234Pa
234Pa	UZ	Uranium Z	β−	6.70 h	2.197	234U
234U	UII	Uranium II	α	245500 a	4.859	230Th
230Th	Io	Ionium	α	75380 a	4.770	226Ra
226Ra	Ra	Radium	α	1602 a	4.871	222Rn
222Rn	Rn	Radon, Radium Emanation	α	3.8235 d	5.590	218Po
218Po	RaA	Radium A	α 99.98% β− 0.02%	3.10 min	6.115 0.265	214Pb 218At
218At			α 99.90% β− 0.10%	1.5 s	6.874 2.883	214Bi 218Rn
218Rn			α	35 ms	7.263	214Po
214Pb	RaB	Radium B	β−	26.8 min	1.024	214Bi
214Bi	RaC	Radium C	β− 99.98% α 0.02%	19.9 min	3.272 5.617	214Po 210Tl
214Po	RaC'	Radium C'	α	0.1643 ms	7.883	210Pb
210Tl	RaC"	Radium C"	β−	1.30 min	5.484	210Pb
210Pb	RaD	Radium D	β−	22.3 a	0.064	210Bi
210Bi	RaE	Radium E	β− 99.99987% α 0.00013%	5.013 d	1.426 5.982	210Po 206Tl
210Po	RaF	Radium F	α	138.376 d	5.407	206Pb
206Tl	RaE"	Radium E"	β−	4.199 min	1.533	206Pb
206Pb	RaG	Radium G	-	stable	-	-

Actinium series

The 4n+3 chain of uranium-235 is commonly called the "actinium series". 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 detailed routes of uranium-235 decay.

nuclide	historic name (short)	historic name (long)	decay mode	half-life (a=year)	energy released, MeV	product of decay
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		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 uranium & plutonium 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)

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