### Parent isotope

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.

## Types

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.[2]

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 short chains, for example those of magnesium-28 and chlorine-39. On Earth, most of the starting isotopes of these chains are generated by cosmic radiation.

## Actinide alpha decay chains

Actinides and fission products by half-life
Actinides[3] by decay chain Half-life
range (a)
Fission products by yield[4]
4n 4n+1 4n+2 4n+3
4.5–7% 0.04–1.25% <0.001%
228Ra 4–6 155Euþ
244Cm 241Puƒ 250Cf 227Ac 10–29 90Sr 85Kr 113mCdþ
232Uƒ 238Pu 243Cmƒ 29–97 137Cs 151Smþ 121mSn
249Cfƒ 242mAmƒ 141–351

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

241Am 251Cfƒ[5] 430–900
226Ra 247Bk 1.3k–1.6k
240Pu 229Th 246Cm 243Am 4.7k–7.4k
245Cmƒ 250Cm 8.3k–8.5k
239Puƒ 24.1k
230Th 231Pa 32k–76k
236Npƒ 233Uƒ 234U 150k–250k 99Tc 126Sn
248Cm 242Pu 327k–375k 79Se
1.53M 93Zr
237Np 2.1M–6.5M 135Cs 107Pd
236U 247Cmƒ 15M–24M 129I
244Pu 80M

...nor beyond 15.7M[6]

232Th 238U 235Uƒ№ 0.7G–14G

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 4a–97a: Medium-lived fission product
‡  over 200ka: Long-lived fission product

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 (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." 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.

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 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 bismuth-209 and the final isotope, 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.

The total energy released from californium-249 to bismuth-209, including the energy lost to neutrinos, is 63.7 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 . .

### Radium series (also known as uranium series)

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.

The total energy released from uranium-238 to lead-206, including the energy lost to neutrinos, is 51.7 MeV.

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
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
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 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 2.41·104 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