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Isotopes of thorium

Thorium (90Th) has seven naturally occurring isotopes but none are stable. One isotope, 232Th, is relatively stable, with a half-life of 1.405×1010 years, considerably longer than the age of the Earth, and even slightly longer than the generally accepted age of the universe. This isotope makes up nearly all natural thorium, so thorium was considered to be mononuclidic. However, in 2013, IUPAC reclassified thorium as binuclidic, due to large amounts of 230Th in deep seawater. Thorium has a characteristic terrestrial isotopic composition and thus a standard atomic weight can be given.

Isotopes of thorium (90Th)
Main isotopes[1] Decay
abun­dance half-life (t1/2) mode pro­duct
227Th trace 18.68 d α 223Ra
228Th trace 1.9116 y α 224Ra
229Th trace 7917 y[2] α 225Ra
230Th 0.02% 75400 y α 226Ra
231Th trace 25.5 h β 231Pa
232Th 100.0% 1.405×1010 y α 228Ra
233Th trace 21.83 min β 233Pa
234Th trace 24.1 d β 234Pa
Standard atomic weight Ar°(Th)

Thirty-one radioisotopes have been characterized, with the most stable being 232Th, 230Th with a half-life of 75,380 years, 229Th with a half-life of 7,917 years,[2] and 228Th with a half-life of 1.92 years. All of the remaining radioactive isotopes have half-lives that are less than thirty days and the majority of these have half-lives that are less than ten minutes. One isotope, 229Th, has a nuclear isomer (or metastable state) with a remarkably low excitation energy,[5] recently measured to be 8.35574 eV[6] It has been proposed to perform laser spectroscopy of the 229Th nucleus and use the low-energy transition for the development of a nuclear clock of extremely high accuracy.[7][8][9]

The known isotopes of thorium range in mass number from 207[10] to 238.

List of isotopes edit

Nuclide
[n 1]
Historic
name
Z N Isotopic mass (Da)
[n 2][n 3]
Half-life
[n 4]
Decay
mode

[n 5]
Daughter
isotope

[n 6]
Spin and
parity
[n 7][n 8]
Natural abundance (mole fraction)
Excitation energy Normal proportion Range of variation
207Th[10] 90 117 9.7(+46.6−4.4) ms α 203Ra
208Th[11] 90 118 208.01791(4) 1.7(+1.7-0.6) ms α 204Ra 0+
209Th[12] 90 119 209.01772(11) 7(5) ms
[3.8(+69−15)]
α 205Ra 5/2−#
210Th 90 120 210.015075(27) 17(11) ms
[9(+17−4) ms]
α 206Ra 0+
β+ (rare) 210Ac
211Th 90 121 211.01493(8) 48(20) ms
[0.04(+3−1) s]
α 207Ra 5/2−#
β+ (rare) 211Ac
212Th 90 122 212.01298(2) 36(15) ms
[30(+20-10) ms]
α (99.7%) 208Ra 0+
β+ (.3%) 212Ac
213Th 90 123 213.01301(8) 140(25) ms α 209Ra 5/2−#
β+ (rare) 213Ac
214Th 90 124 214.011500(18) 100(25) ms α 210Ra 0+
215Th 90 125 215.011730(29) 1.2(2) s α 211Ra (1/2−)
216Th 90 126 216.011062(14) 26.8(3) ms α (99.99%) 212Ra 0+
β+ (.006%) 216Ac
216m1Th 2042(13) keV 137(4) μs (8+)
216m2Th 2637(20) keV 615(55) ns (11−)
217Th 90 127 217.013114(22) 240(5) μs α 213Ra (9/2+)
218Th 90 128 218.013284(14) 109(13) ns α 214Ra 0+
219Th 90 129 219.01554(5) 1.05(3) μs α[n 9] 215Ra 9/2+#
220Th 90 130 220.015748(24) 9.7(6) μs α[n 10] 216Ra 0+
221Th 90 131 221.018184(10) 1.73(3) ms α 217Ra (7/2+)
222Th 90 132 222.018468(13) 2.237(13) ms α[n 11] 218Ra 0+
223Th 90 133 223.020811(10) 0.60(2) s α 219Ra (5/2)+
224Th 90 134 224.021467(12) 1.05(2) s α 220Ra 0+
CD (rare) 208Pb
16O
225Th 90 135 225.023951(5) 8.72(4) min α (90%) 221Ra (3/2)+
EC (10%) 225Ac
226Th 90 136 226.024903(5) 30.57(10) min α 222Ra 0+
227Th Radioactinium 90 137 227.0277041(27) 18.68(9) d α 223Ra 1/2+ Trace[n 12]
228Th Radiothorium 90 138 228.0287411(24) 1.9116(16) y α 224Ra 0+ Trace[n 13]
CD (1.3×10−11%) 208Pb
20O
229Th 90 139 229.031762(3) 7.916(17)×103 y α 225Ra 5/2+ Trace[n 14]
229mTh 8.355733(10) eV[13] 7(1) μs[14] IT 229Th 3/2+
230Th[n 15] Ionium 90 140 230.0331338(19) 7.538(30)×104 y α 226Ra 0+ 0.0002(2)[n 16]
CD (5.6×10−11%) 206Hg
24Ne
SF (5×10−11%) (Various)
231Th Uranium Y 90 141 231.0363043(19) 25.52(1) h β 231Pa 5/2+ Trace[n 12]
α (10−8%) 227Ra
232Th[n 17] Thorium 90 142 232.0380553(21) 1.405(6)×1010 y α[n 18] 228Ra 0+ 0.9998(2)
SF (1.1×10−9%) (various)
CD (2.78×10−10%) 182Yb
26Ne
24Ne
233Th 90 143 233.0415818(21) 21.83(4) min β 233Pa 1/2+ Trace[n 19]
234Th Uranium X1 90 144 234.043601(4) 24.10(3) d β 234mPa 0+ Trace[n 16]
235Th 90 145 235.04751(5) 7.2(1) min β 235Pa (1/2+)#
236Th 90 146 236.04987(21)# 37.5(2) min β 236Pa 0+
237Th 90 147 237.05389(39)# 4.8(5) min β 237Pa 5/2+#
238Th 90 148 238.0565(3)# 9.4(20) min β 238Pa 0+
This table header & footer:
  1. ^ mTh – Excited nuclear isomer.
  2. ^ ( ) – Uncertainty (1σ) is given in concise form in parentheses after the corresponding last digits.
  3. ^ # – Atomic mass marked #: value and uncertainty derived not from purely experimental data, but at least partly from trends from the Mass Surface (TMS).
  4. ^ Bold half-life – nearly stable, half-life longer than age of universe.
  5. ^ Modes of decay:
  6. ^ Bold symbol as daughter – Daughter product is stable.
  7. ^ ( ) spin value – Indicates spin with weak assignment arguments.
  8. ^ # – Values marked # are not purely derived from experimental data, but at least partly from trends of neighboring nuclides (TNN).
  9. ^ Theoretically capable of β+ decay to 219Ac[1]
  10. ^ Theoretically capable of electron capture to 220Ac[1]
  11. ^ Theoretically capable of electron capture to 222Ac[1]
  12. ^ a b Intermediate decay product of 235U
  13. ^ Intermediate decay product of 232Th
  14. ^ Intermediate decay product of 237Np
  15. ^ Used in Uranium–thorium dating
  16. ^ a b Intermediate decay product of 238U
  17. ^ Primordial radionuclide
  18. ^ Theorized to also undergo ββ decay to 232U
  19. ^ Produced in neutron capture by 232Th

Uses edit

Thorium has been suggested for use in thorium-based nuclear power.

In many countries the use of thorium in consumer products is banned or discouraged because it is radioactive.

It is currently used in cathodes of vacuum tubes, for a combination of physical stability at high temperature and a low work energy required to remove an electron from its surface.

It has, for about a century, been used in mantles of gas and vapor lamps such as gas lights and camping lanterns.

Low dispersion lenses edit

Thorium was also used in certain glass elements of Aero-Ektar lenses made by Kodak during World War II. Thus they are mildly radioactive.[15] Two of the glass elements in the f/2.5 Aero-Ektar lenses are 11% and 13% thorium by weight. The thorium-containing glasses were used because they have a high refractive index with a low dispersion (variation of index with wavelength), a highly desirable property. Many surviving Aero-Ektar lenses have a tea colored tint, possibly due to radiation damage to the glass.

These lenses were used for aerial reconnaissance because the radiation level is not high enough to fog film over a short period. This would indicate the radiation level is reasonably safe. However, when not in use, it would be prudent to store these lenses as far as possible from normally inhabited areas; allowing the inverse square relationship to attenuate the radiation.[16]

Actinides vs. fission products edit

Actinides[17] by decay chain Half-life
range (a)
Fission products of 235U by yield[18]
4n 4n + 1 4n + 2 4n + 3 4.5–7% 0.04–1.25% <0.001%
228Ra 4–6 a 155Euþ
244Cmƒ 241Puƒ 250Cf 227Ac 10–29 a 90Sr 85Kr 113mCdþ
232Uƒ 238Puƒ 243Cmƒ 29–97 a 137Cs 151Smþ 121mSn
248Bk[19] 249Cfƒ 242mAmƒ 141–351 a

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

241Amƒ 251Cfƒ[20] 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
1.53 Ma 93Zr
237Npƒ 2.1–6.5 Ma 135Cs 107Pd
236U 247Cmƒ 15–24 Ma 129I
244Pu 80 Ma

... nor beyond 15.7 Ma[21]

232Th 238U 235Uƒ№ 0.7–14.1 Ga

Notable isotopes edit

Thorium-228 edit

228Th is an isotope of thorium with 138 neutrons. It was once named Radiothorium, due to its occurrence in the disintegration chain of thorium-232. It has a half-life of 1.9116 years. It undergoes alpha decay to 224Ra. Occasionally it decays by the unusual route of cluster decay, emitting a nucleus of 20O and producing stable 208Pb. It is a daughter isotope of 232U in the thorium decay series.

228Th has an atomic weight of 228.0287411 grams/mole.

Together with its decay product 224Ra it is used for alpha particle radiation therapy.[22]

Thorium-229 edit

229Th is a radioactive isotope of thorium that decays by alpha emission with a half-life of 7917 years.[2] 229Th is produced by the decay of uranium-233, and its principal use is for the production of the medical isotopes actinium-225 and bismuth-213.[23]

Thorium-229m edit

229Th has a nuclear isomer, 229m
Th
, with a remarkably low excitation energy of 8.355733(10) eV, corresponding to a photon frequency of 2020407±3 GHz (wavelength 148382.2±0.2 pm).[24][6][13] Although in the very high frequency vacuum ultraviolet frequency range, this is the only known opportunity for direct laser excitation of a nuclear state,[25] which could have applications like a nuclear clock of very high accuracy[8][9][26][27] or as a qubit for quantum computing.[28]

These applications were for a long time impeded by imprecise measurements of the isomeric energy, as laser excitation's exquisite precision makes it difficult to use to search a wide frequency range. There were many investigations, both theoretical and experimental, trying to determine the transition energy precisely and to specify other properties of the isomeric state of 229Th (such as the lifetime and the magnetic moment) before the frequency was accurately measured in 2024.[6][24][13]

History edit

Early measurements were done by producing the 29.5855 keV excited state of 229Th, and measuring the difference in emitted gamma ray energies as it decays to either the 229mTh (90%) or 229Th (10%) isomeric states.

In 1976, gamma ray spectroscopy first indicated that 229Th has a nuclear isomer, 229mTh, with a remarkably low excitation energy.[29] At that time the energy was inferred to be below 100 eV, purely based on the non-observation of the isomer's direct decay. However, in 1990, further measurements led to the conclusion that the energy is almost certainly below 10 eV,[30] making the isomer to be the one of lowest known excitation energy. In the following years, the energy was further constrained to 3.5±1.0 eV, which was for a long time the accepted energy value.[31]

Improved gamma ray spectroscopy measurements using an advanced high-resolution X-ray microcalorimeter were carried out in 2007, yielding a new value for the transition energy of 7.6±0.5 eV,[32] corrected to 7.8±0.5 eV in 2009.[33] This shift in isomeric energy from 3.5 eV to 7.8 eV possibly explains why several early attempts to directly observe the transition were unsuccessful. Still, most of the searches in the 2010s for light emitted by the isomeric decay failed to observe any signal,[34][35][36][37] pointing towards a potentially strong non-radiative decay channel. A direct detection of photons emitted in the isomeric decay was claimed in 2012[38] and again in 2018.[39] However, both reports were subject to controversial discussions within the community.[40][41]

A direct detection of electrons being emitted in the internal conversion decay channel of 229mTh was achieved in 2016.[42] However, at the time the isomer's transition energy could only be weakly constrained to between 6.3 and 18.3 eV. Finally, in 2019, non-optical electron spectroscopy of the internal conversion electrons emitted in the isomeric decay allowed for a determination of the isomer's excitation energy to 8.28±0.17 eV[43] However, this value appeared at odds with the 2018 preprint showing that a similar signal as an 8.4 eV xenon VUV photon can be shown, but with about 1.3+0.2
−0.1
 eV
less energy and an 1880 s lifetime.[39] In that paper, 229Th was embedded in SiO2, possibly resulting in an energy shift and altered lifetime, although the states involved are primarily nuclear, shielding them from electronic interactions.

As a peculiarity of its extremely low excitation energy, the lifetime of 229mTh very much depends on the electronic environment of the nucleus. In neutral 229Th, the isomer can decay by internal conversion within a few microseconds.[44][45][14] However, the isomeric energy is not enough to remove a second electron (thorium's second ionization energy is 11.5 eV), so internal conversion is impossible in Th+ ions. Radiative decay occurs with a half-life 8.4 orders of magnitude longer, predicted to be between 1000–10000 seconds.[45][46] Embedded in ionic crystals, ionization is not quite 100%, so a small amount of internal conversion occurs, leading to a recently measured lifetime of ≈600 s,[6][13] which can be extrapolated to a lifetime for isolated ions of 1740±50 s.[6]

In a 2018 experiment, it was possible to perform a first laser-spectroscopic characterization of the nuclear properties of 229mTh.[47] In this experiment, laser spectroscopy of the 229Th atomic shell was conducted using a 229Th2+ ion cloud with 2% of the ions in the nuclear excited state. This allowed probing for the hyperfine shift induced by the different nuclear spin states of the ground and the isomeric state. In this way, a first experimental value for the magnetic dipole and the electric quadrupole moment of 229mTh could be inferred.

In 2019, the isomer's excitation energy was constrained to 8.28±0.17 eV based on the direct detection of internal conversion electrons[43] and a secure population of 229mTh from the nuclear ground state was achieved by excitation of the 29 keV nuclear excited state via synchrotron radiation.[48] Additional measurements by a different group in 2020 produced a figure of 8.10±0.17 eV (153.1±3.2 nm wavelength).[49] Combining these measurements, the expected transition energy is 8.12±0.11 eV.[50]

In April 2024, two separate groups finally reported precision laser excitation Th4+ cations doped into ionic crystals (of CaF2 and LiSrAlF6 with additional interstitial F anions for charge compensation), giving a precise measurement of the transition energy.[24][7][6][13] This enables the construction of high-precision lasers which will measure the frequency up to the accuracy of the best atomic clocks.[9][27]

Thorium-230 edit

230Th is a radioactive isotope of thorium that can be used to date corals and determine ocean current flux. Ionium was a name given early in the study of radioactive elements to the 230Th isotope produced in the decay chain of 238U before it was realized that ionium and thorium are chemically identical. The symbol Io was used for this supposed element. (The name is still used in ionium–thorium dating.)

Thorium-231 edit

231Th has 141 neutrons. It is the decay product of uranium-235. It is found in very small amounts on the earth and has a half-life of 25.5 hours.[51] When it decays, it emits a beta ray and forms protactinium-231. It has a decay energy of 0.39 MeV. It has a mass of 231.0363043 grams/mole.

Thorium-232 edit

232Th is the only primordial nuclide of thorium and makes up effectively all of natural thorium, with other isotopes of thorium appearing only in trace amounts as relatively short-lived decay products of uranium and thorium.[52] The isotope decays by alpha decay with a half-life of 1.405×1010 years, over three times the age of the Earth and approximately the age of the universe. Its decay chain is the thorium series, eventually ending in lead-208. The remainder of the chain is quick; the longest half-lives in it are 5.75 years for radium-228 and 1.91 years for thorium-228, with all other half-lives totaling less than 15 days.[53]

232Th is a fertile material able to absorb a neutron and undergo transmutation into the fissile nuclide uranium-233, which is the basis of the thorium fuel cycle.[54] In the form of Thorotrast, a thorium dioxide suspension, it was used as a contrast medium in early X-ray diagnostics. Thorium-232 is now classified as carcinogenic.[55]

Thorium-233 edit

233Th is an isotope of thorium that decays into protactinium-233 through beta decay. It has a half-life of 21.83 minutes.[1] Traces occur in nature as the result of natural neutron activation of 232Th.[56]

Thorium-234 edit

234Th is an isotope of thorium whose nuclei contain 144 neutrons. 234Th has a half-life of 24.1 days, and when it decays, it emits a beta particle, and in doing so, it transmutes into protactinium-234. 234Th has a mass of 234.0436 atomic mass units (amu), and it has a decay energy of about 270 keV (kiloelectronvolts). Uranium-238 usually decays into this isotope of thorium (although in rare cases it can undergo spontaneous fission instead).

References edit

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  16. ^ Michael S. Briggs (January 16, 2002). . Archived from the original on August 12, 2015. Retrieved 2015-08-28.
  17. ^ 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 nuclides have half-lives of at least four years (the longest-lived nuclide 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.
  18. ^ Specifically from thermal neutron fission of uranium-235, e.g. in a typical nuclear reactor.
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    "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 [years]. No growth of Cf248 was detected, and a lower limit for the β half-life can be set at about 104 [years]. No alpha activity attributable to the new isomer has been detected; the alpha half-life is probably greater than 300 [years]."
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  21. ^ Excluding those "classically stable" nuclides with half-lives significantly in excess of 232Th; e.g., while 113mCd has a half-life of only fourteen years, that of 113Cd is eight quadrillion years.
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    • Wieser, Michael E. (2006). "Atomic weights of the elements 2005 (IUPAC Technical Report)". Pure and Applied Chemistry. 78 (11): 2051–2066. doi:10.1351/pac200678112051.
  • "News & Notices: Standard Atomic Weights Revised". International Union of Pure and Applied Chemistry. 19 October 2005.
  • Half-life, spin, and isomer data selected from the following sources.

isotopes, thorium, thorium, 90th, seven, naturally, occurring, isotopes, none, stable, isotope, 232th, relatively, stable, with, half, life, 1010, years, considerably, longer, than, earth, even, slightly, longer, than, generally, accepted, universe, this, isot. Thorium 90Th has seven naturally occurring isotopes but none are stable One isotope 232Th is relatively stable with a half life of 1 405 1010 years considerably longer than the age of the Earth and even slightly longer than the generally accepted age of the universe This isotope makes up nearly all natural thorium so thorium was considered to be mononuclidic However in 2013 IUPAC reclassified thorium as binuclidic due to large amounts of 230Th in deep seawater Thorium has a characteristic terrestrial isotopic composition and thus a standard atomic weight can be given Isotopes of thorium 90Th Main isotopes 1 Decay abun dance half life t1 2 mode pro duct 227Th trace 18 68 d a 223Ra 228Th trace 1 9116 y a 224Ra 229Th trace 7917 y 2 a 225Ra 230Th 0 02 75400 y a 226Ra 231Th trace 25 5 h b 231Pa 232Th 100 0 1 405 1010 y a 228Ra 233Th trace 21 83 min b 233Pa 234Th trace 24 1 d b 234PaStandard atomic weight Ar Th 232 0377 0 0004 3 232 04 0 01 abridged 4 viewtalkedit Thirty one radioisotopes have been characterized with the most stable being 232Th 230Th with a half life of 75 380 years 229Th with a half life of 7 917 years 2 and 228Th with a half life of 1 92 years All of the remaining radioactive isotopes have half lives that are less than thirty days and the majority of these have half lives that are less than ten minutes One isotope 229Th has a nuclear isomer or metastable state with a remarkably low excitation energy 5 recently measured to be 8 35574 eV 6 It has been proposed to perform laser spectroscopy of the 229Th nucleus and use the low energy transition for the development of a nuclear clock of extremely high accuracy 7 8 9 The known isotopes of thorium range in mass number from 207 10 to 238 Contents 1 List of isotopes 2 Uses 2 1 Low dispersion lenses 3 Actinides vs fission products 4 Notable isotopes 4 1 Thorium 228 4 2 Thorium 229 4 3 Thorium 229m 4 3 1 History 4 4 Thorium 230 4 5 Thorium 231 4 6 Thorium 232 4 7 Thorium 233 4 8 Thorium 234 5 ReferencesList of isotopes editNuclide n 1 Historicname Z N Isotopic mass Da n 2 n 3 Half life n 4 Decaymode n 5 Daughterisotope n 6 Spin andparity n 7 n 8 Natural abundance mole fraction Excitation energy Normal proportion Range of variation 207Th 10 90 117 9 7 46 6 4 4 ms a 203Ra 208Th 11 90 118 208 01791 4 1 7 1 7 0 6 ms a 204Ra 0 209Th 12 90 119 209 01772 11 7 5 ms 3 8 69 15 a 205Ra 5 2 210Th 90 120 210 015075 27 17 11 ms 9 17 4 ms a 206Ra 0 b rare 210Ac 211Th 90 121 211 01493 8 48 20 ms 0 04 3 1 s a 207Ra 5 2 b rare 211Ac 212Th 90 122 212 01298 2 36 15 ms 30 20 10 ms a 99 7 208Ra 0 b 3 212Ac 213Th 90 123 213 01301 8 140 25 ms a 209Ra 5 2 b rare 213Ac 214Th 90 124 214 011500 18 100 25 ms a 210Ra 0 215Th 90 125 215 011730 29 1 2 2 s a 211Ra 1 2 216Th 90 126 216 011062 14 26 8 3 ms a 99 99 212Ra 0 b 006 216Ac 216m1Th 2042 13 keV 137 4 ms 8 216m2Th 2637 20 keV 615 55 ns 11 217Th 90 127 217 013114 22 240 5 ms a 213Ra 9 2 218Th 90 128 218 013284 14 109 13 ns a 214Ra 0 219Th 90 129 219 01554 5 1 05 3 ms a n 9 215Ra 9 2 220Th 90 130 220 015748 24 9 7 6 ms a n 10 216Ra 0 221Th 90 131 221 018184 10 1 73 3 ms a 217Ra 7 2 222Th 90 132 222 018468 13 2 237 13 ms a n 11 218Ra 0 223Th 90 133 223 020811 10 0 60 2 s a 219Ra 5 2 224Th 90 134 224 021467 12 1 05 2 s a 220Ra 0 CD rare 208Pb16O 225Th 90 135 225 023951 5 8 72 4 min a 90 221Ra 3 2 EC 10 225Ac 226Th 90 136 226 024903 5 30 57 10 min a 222Ra 0 227Th Radioactinium 90 137 227 0277041 27 18 68 9 d a 223Ra 1 2 Trace n 12 228Th Radiothorium 90 138 228 0287411 24 1 9116 16 y a 224Ra 0 Trace n 13 CD 1 3 10 11 208Pb20O 229Th 90 139 229 031762 3 7 916 17 103 y a 225Ra 5 2 Trace n 14 229mTh 8 355733 10 eV 13 7 1 ms 14 IT 229Th 3 2 230Th n 15 Ionium 90 140 230 0331338 19 7 538 30 104 y a 226Ra 0 0 0002 2 n 16 CD 5 6 10 11 206Hg24Ne SF 5 10 11 Various 231Th Uranium Y 90 141 231 0363043 19 25 52 1 h b 231Pa 5 2 Trace n 12 a 10 8 227Ra 232Th n 17 Thorium 90 142 232 0380553 21 1 405 6 1010 y a n 18 228Ra 0 0 9998 2 SF 1 1 10 9 various CD 2 78 10 10 182Yb26Ne24Ne 233Th 90 143 233 0415818 21 21 83 4 min b 233Pa 1 2 Trace n 19 234Th Uranium X1 90 144 234 043601 4 24 10 3 d b 234mPa 0 Trace n 16 235Th 90 145 235 04751 5 7 2 1 min b 235Pa 1 2 236Th 90 146 236 04987 21 37 5 2 min b 236Pa 0 237Th 90 147 237 05389 39 4 8 5 min b 237Pa 5 2 238Th 90 148 238 0565 3 9 4 20 min b 238Pa 0 This table header amp footer view mTh Excited nuclear isomer Uncertainty 1s is given in concise form in parentheses after the corresponding last digits Atomic mass marked value and uncertainty derived not from purely experimental data but at least partly from trends from the Mass Surface TMS Bold half life nearly stable half life longer than age of universe Modes of decay CD Cluster decay EC Electron capture IT Isomeric transition Bold symbol as daughter Daughter product is stable spin value Indicates spin with weak assignment arguments Values marked are not purely derived from experimental data but at least partly from trends of neighboring nuclides TNN Theoretically capable of b decay to 219Ac 1 Theoretically capable of electron capture to 220Ac 1 Theoretically capable of electron capture to 222Ac 1 a b Intermediate decay product of 235U Intermediate decay product of 232Th Intermediate decay product of 237Np Used in Uranium thorium dating a b Intermediate decay product of 238U Primordial radionuclide Theorized to also undergo b b decay to 232U Produced in neutron capture by 232ThUses editThorium has been suggested for use in thorium based nuclear power In many countries the use of thorium in consumer products is banned or discouraged because it is radioactive It is currently used in cathodes of vacuum tubes for a combination of physical stability at high temperature and a low work energy required to remove an electron from its surface It has for about a century been used in mantles of gas and vapor lamps such as gas lights and camping lanterns Low dispersion lenses edit Thorium was also used in certain glass elements of Aero Ektar lenses made by Kodak during World War II Thus they are mildly radioactive 15 Two of the glass elements in the f 2 5 Aero Ektar lenses are 11 and 13 thorium by weight The thorium containing glasses were used because they have a high refractive index with a low dispersion variation of index with wavelength a highly desirable property Many surviving Aero Ektar lenses have a tea colored tint possibly due to radiation damage to the glass These lenses were used for aerial reconnaissance because the radiation level is not high enough to fog film over a short period This would indicate the radiation level is reasonably safe However when not in use it would be prudent to store these lenses as far as possible from normally inhabited areas allowing the inverse square relationship to attenuate the radiation 16 Actinides vs fission products editActinides and fission products by half life vte Actinides 17 by decay chain Half life range a Fission products of 235U by yield 18 4n 4n 1 4n 2 4n 3 4 5 7 0 04 1 25 lt 0 001 228Ra 4 6 a 155Euth 244Cmƒ 241Puƒ 250Cf 227Ac 10 29 a 90Sr 85Kr 113mCdth 232Uƒ 238Puƒ 243Cmƒ 29 97 a 137Cs 151Smth 121mSn 248Bk 19 249Cfƒ 242mAmƒ 141 351 a No fission products have a half life in the range of 100 a 210 ka 241Amƒ 251Cfƒ 20 430 900 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 53 Ma 93Zr 237Npƒ 2 1 6 5 Ma 135Cs 107Pd 236U 247Cmƒ 15 24 Ma 129I 244Pu 80 Ma nor beyond 15 7 Ma 21 232Th 238U 235Uƒ 0 7 14 1 Ga has thermal neutron capture cross section in the range of 8 50 barnsƒ fissile primarily a naturally occurring radioactive material NORM th neutron poison thermal neutron capture cross section greater than 3k barns Notable isotopes editThorium 228 edit 228Th is an isotope of thorium with 138 neutrons It was once named Radiothorium due to its occurrence in the disintegration chain of thorium 232 It has a half life of 1 9116 years It undergoes alpha decay to 224Ra Occasionally it decays by the unusual route of cluster decay emitting a nucleus of 20O and producing stable 208Pb It is a daughter isotope of 232U in the thorium decay series 228Th has an atomic weight of 228 0287411 grams mole Together with its decay product 224Ra it is used for alpha particle radiation therapy 22 Thorium 229 edit 229Th is a radioactive isotope of thorium that decays by alpha emission with a half life of 7917 years 2 229Th is produced by the decay of uranium 233 and its principal use is for the production of the medical isotopes actinium 225 and bismuth 213 23 Thorium 229m edit 229Th has a nuclear isomer 229m Th with a remarkably low excitation energy of 8 355733 10 eV corresponding to a photon frequency of 2020 407 3 GHz wavelength 148382 2 0 2 pm 24 6 13 Although in the very high frequency vacuum ultraviolet frequency range this is the only known opportunity for direct laser excitation of a nuclear state 25 which could have applications like a nuclear clock of very high accuracy 8 9 26 27 or as a qubit for quantum computing 28 These applications were for a long time impeded by imprecise measurements of the isomeric energy as laser excitation s exquisite precision makes it difficult to use to search a wide frequency range There were many investigations both theoretical and experimental trying to determine the transition energy precisely and to specify other properties of the isomeric state of 229Th such as the lifetime and the magnetic moment before the frequency was accurately measured in 2024 6 24 13 History edit Early measurements were done by producing the 29 5855 keV excited state of 229Th and measuring the difference in emitted gamma ray energies as it decays to either the 229mTh 90 or 229Th 10 isomeric states In 1976 gamma ray spectroscopy first indicated that 229Th has a nuclear isomer 229mTh with a remarkably low excitation energy 29 At that time the energy was inferred to be below 100 eV purely based on the non observation of the isomer s direct decay However in 1990 further measurements led to the conclusion that the energy is almost certainly below 10 eV 30 making the isomer to be the one of lowest known excitation energy In the following years the energy was further constrained to 3 5 1 0 eV which was for a long time the accepted energy value 31 Improved gamma ray spectroscopy measurements using an advanced high resolution X ray microcalorimeter were carried out in 2007 yielding a new value for the transition energy of 7 6 0 5 eV 32 corrected to 7 8 0 5 eV in 2009 33 This shift in isomeric energy from 3 5 eV to 7 8 eV possibly explains why several early attempts to directly observe the transition were unsuccessful Still most of the searches in the 2010s for light emitted by the isomeric decay failed to observe any signal 34 35 36 37 pointing towards a potentially strong non radiative decay channel A direct detection of photons emitted in the isomeric decay was claimed in 2012 38 and again in 2018 39 However both reports were subject to controversial discussions within the community 40 41 A direct detection of electrons being emitted in the internal conversion decay channel of 229mTh was achieved in 2016 42 However at the time the isomer s transition energy could only be weakly constrained to between 6 3 and 18 3 eV Finally in 2019 non optical electron spectroscopy of the internal conversion electrons emitted in the isomeric decay allowed for a determination of the isomer s excitation energy to 8 28 0 17 eV 43 However this value appeared at odds with the 2018 preprint showing that a similar signal as an 8 4 eV xenon VUV photon can be shown but with about 1 3 0 2 0 1 eV less energy and an 1880 s lifetime 39 In that paper 229Th was embedded in SiO2 possibly resulting in an energy shift and altered lifetime although the states involved are primarily nuclear shielding them from electronic interactions As a peculiarity of its extremely low excitation energy the lifetime of 229mTh very much depends on the electronic environment of the nucleus In neutral 229Th the isomer can decay by internal conversion within a few microseconds 44 45 14 However the isomeric energy is not enough to remove a second electron thorium s second ionization energy is 11 5 eV so internal conversion is impossible in Th ions Radiative decay occurs with a half life 8 4 orders of magnitude longer predicted to be between 1000 10000 seconds 45 46 Embedded in ionic crystals ionization is not quite 100 so a small amount of internal conversion occurs leading to a recently measured lifetime of 600 s 6 13 which can be extrapolated to a lifetime for isolated ions of 1740 50 s 6 In a 2018 experiment it was possible to perform a first laser spectroscopic characterization of the nuclear properties of 229mTh 47 In this experiment laser spectroscopy of the 229Th atomic shell was conducted using a 229Th2 ion cloud with 2 of the ions in the nuclear excited state This allowed probing for the hyperfine shift induced by the different nuclear spin states of the ground and the isomeric state In this way a first experimental value for the magnetic dipole and the electric quadrupole moment of 229mTh could be inferred In 2019 the isomer s excitation energy was constrained to 8 28 0 17 eV based on the direct detection of internal conversion electrons 43 and a secure population of 229mTh from the nuclear ground state was achieved by excitation of the 29 keV nuclear excited state via synchrotron radiation 48 Additional measurements by a different group in 2020 produced a figure of 8 10 0 17 eV 153 1 3 2 nm wavelength 49 Combining these measurements the expected transition energy is 8 12 0 11 eV 50 In April 2024 two separate groups finally reported precision laser excitation Th4 cations doped into ionic crystals of CaF2 and LiSrAlF6 with additional interstitial F anions for charge compensation giving a precise measurement of the transition energy 24 7 6 13 This enables the construction of high precision lasers which will measure the frequency up to the accuracy of the best atomic clocks 9 27 Thorium 230 edit 230Th is a radioactive isotope of thorium that can be used to date corals and determine ocean current flux Ionium was a name given early in the study of radioactive elements to the 230Th isotope produced in the decay chain of 238U before it was realized that ionium and thorium are chemically identical The symbol Io was used for this supposed element The name is still used in ionium thorium dating Thorium 231 edit 231Th has 141 neutrons It is the decay product of uranium 235 It is found in very small amounts on the earth and has a half life of 25 5 hours 51 When it decays it emits a beta ray and forms protactinium 231 It has a decay energy of 0 39 MeV It has a mass of 231 0363043 grams mole Thorium 232 edit Main article Thorium 232 232Th is the only primordial nuclide of thorium and makes up effectively all of natural thorium with other isotopes of thorium appearing only in trace amounts as relatively short lived decay products of uranium and thorium 52 The isotope decays by alpha decay with a half life of 1 405 1010 years over three times the age of the Earth and approximately the age of the universe Its decay chain is the thorium series eventually ending in lead 208 The remainder of the chain is quick the longest half lives in it are 5 75 years for radium 228 and 1 91 years for thorium 228 with all other half lives totaling less than 15 days 53 232Th is a fertile material able to absorb a neutron and undergo transmutation into the fissile nuclide uranium 233 which is the basis of the thorium fuel cycle 54 In the form of Thorotrast a thorium dioxide suspension it was used as a contrast medium in early X ray diagnostics Thorium 232 is now classified as carcinogenic 55 Thorium 233 edit 233Th is an isotope of thorium that decays into protactinium 233 through beta decay It has a half life of 21 83 minutes 1 Traces occur in nature as the result of natural neutron activation of 232Th 56 Thorium 234 edit 234Th is an isotope of thorium whose nuclei contain 144 neutrons 234Th has a half life of 24 1 days and when it decays it emits a beta particle and in doing so it transmutes into protactinium 234 234Th has a mass of 234 0436 atomic mass units amu and it has a decay energy of about 270 keV kiloelectronvolts Uranium 238 usually decays into this isotope of thorium although in rare cases it can undergo spontaneous fission instead References edit a b c d e Kondev F G Wang M Huang W J Naimi S Audi G 2021 The NUBASE2020 evaluation of nuclear properties PDF Chinese Physics C 45 3 030001 doi 10 1088 1674 1137 abddae a b c Varga Z Nicholl A Mayer K 2014 Determination of the 229Th half life Physical Review C 89 6 064310 doi 10 1103 PhysRevC 89 064310 Standard Atomic Weights Thorium CIAAW 2013 Prohaska Thomas Irrgeher Johanna Benefield Jacqueline Bohlke John K Chesson Lesley A Coplen Tyler B Ding Tiping Dunn Philip J H Groning Manfred Holden Norman E Meijer Harro A J 2022 05 04 Standard atomic weights of the elements 2021 IUPAC Technical Report Pure and Applied Chemistry doi 10 1515 pac 2019 0603 ISSN 1365 3075 E Ruchowska 2006 Nuclear structure of 229Th PDF Physical Review C 73 4 044326 Bibcode 2006PhRvC 73d4326R doi 10 1103 PhysRevC 73 044326 hdl 10261 12130 a b c d e f Tiedau J Okhapkin M V Zhang K Thielking J Zitzer G Peik E et al 29 April 2024 Laser Excitation of the Th 229 Nucleus PDF Physical Review Letters 132 182501 doi 10 1103 PhysRevLett 132 182501 The nuclear resonance for the Th4 ions in Th CaF2 is measured at the wavelength 148 3821 5 nm frequency 2020 409 7 THz and the fluorescence lifetime in the crystal is 630 15 s corresponding to an isomer half life of 1740 50 s for a nucleus isolated in vacuum a b Atomic Nucleus Excited with Laser A Breakthrough after Decades Press release TU Wien 29 April 2024 Retrieved 29 April 2024 a b Peik E Tamm Chr 2003 01 15 Nuclear laser spectroscopy of the 3 5 eV transition in 229Th PDF Europhysics Letters 61 2 181 186 Bibcode 2003EL 61 181P doi 10 1209 epl i2003 00210 x S2CID 250818523 Archived PDF from the original on 2024 04 14 Retrieved 2024 04 30 a b c Campbell C J Radnaev A G Kuzmich A Dzuba V A Flambaum V V Derevianko A 2012 A single ion nuclear clock for metrology at the 19th decimal place PDF Physical Review Letters 108 12 120802 arXiv 1110 2490 Bibcode 2012PhRvL 108l0802C doi 10 1103 PhysRevLett 108 120802 PMID 22540568 S2CID 40863227 Retrieved 2024 04 30 a b Yang H B et al 2022 New isotope 207Th and odd even staggering in a decay energies for nuclei with Z gt 82 and N lt 126 Physical Review C 105 L051302 Bibcode 2022PhRvC 105e1302Y doi 10 1103 PhysRevC 105 L051302 S2CID 248935764 Cardona J A H 2012 Production and decay properties of neutron deficient isotopes with N lt 126 and 74 Z 92 at SHIP Goethe Universitat Frankfury Allemagne H Ikezoe et al 1996 alpha decay of a new isotope of 209Th Physical Review C 54 4 2043 2046 Bibcode 1996PhRvC 54 2043I doi 10 1103 PhysRevC 54 2043 PMID 9971554 a b c d e Elwell R Schneider Christian Jeet Justin Terhune J E S Morgan H W T Alexandrova A N Tran Tan Hoang Bao Derevianko Andrei Hudson Eric R 18 April 2024 Laser excitation of the 229Th nuclear isomeric transition in a solid state host arXiv 2404 12311 physics atom ph a narrow laser linewidth limited spectral feature at 148 38219 4 stat 20 sys nm 2020 407 3 5 stat 30 sys GHz that decays with a lifetime of 568 13 stat 20 sys s This feature is assigned to the excitation of the 229Th nuclear isomeric state whose energy is found to be 8 355733 2 stat 10 lt sys gt eV in 229Th LiSrAlF6 a b Seiferle B von der Wense L Thirolf P G 2017 Lifetime measurement of the 229Th nuclear isomer Physical Review Letters 118 4 042501 arXiv 1801 05205 Bibcode 2017PhRvL 118d2501S doi 10 1103 PhysRevLett 118 042501 PMID 28186791 S2CID 37518294 A half life of 7 1 ms has been measured f2 5 Aero Ektar Lenses permanent dead link Some images Michael S Briggs January 16 2002 Aero Ektar Lenses Archived from the original on August 12 2015 Retrieved 2015 08 28 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 nuclides have half lives of at least four years the longest lived nuclide 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 Specifically from thermal neutron fission of uranium 235 e g in a typical nuclear reactor 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 Bibcode 1965NucPh 71 299M 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 years No growth of Cf248 was detected and a lower limit for the b half life can be set at about 104 years No alpha activity attributable to the new isomer has been detected the alpha half life is probably greater than 300 years This is the heaviest nuclide with a half life of at least four years before the sea of instability Excluding those classically stable nuclides with half lives significantly in excess of 232Th e g while 113mCd has a half life of only fourteen years that of 113Cd is eight quadrillion years Thor Medical production of alpha emitters for cancer treatment May 2023 Report to Congress on the extraction of medical isotopes from U 233 Archived 2011 09 27 at the Wayback Machine U S Department of Energy March 2001 a b c Thirolf Peter April 29 2024 Shedding Light on the Thorium 229 Nuclear Clock Isomer Physics Vol 17 doi 10 1103 Physics 17 71 Tkalya E V Varlamov V O Lomonosov V V Nikulin S A 1996 Processes of the nuclear isomer 229mTh 3 2 3 5 1 0 eV Resonant excitation by optical photons Physica Scripta 53 3 296 299 Bibcode 1996PhyS 53 296T doi 10 1088 0031 8949 53 3 003 S2CID 250744766 von der Wense Lars Seiferle Benedict Thirolf Peter G March 2018 Towards a 229Th based nuclear clock Measurement Techniques 60 12 1178 1192 arXiv 1811 03889 Bibcode 2018arXiv181103889V doi 10 1007 s11018 018 1337 1 S2CID 119359298 a b Thirolf Peter G et al March 2020 Phase Transition in the Thorium Isomer Story XXXVI Mazurian Lakes Conference on Physics 1 7 November 2019 PDF Acta Physica Polonica B Vol 51 no 3 Piaski Pisz County Poland pp 561 570 arXiv 2108 13388 doi 10 5506 APhysPolB 51 561 Originally presented as Characterization of the elusive 229mTh isomer milestones towards a nuclear clock Raeder S Sonnenschein V Gottwald T Moore I D Reponen M Rothe S Trautmann N Wendt K 2011 Resonance ionization spectroscopy of thorium isotopes towards a laser spectroscopic identification of the low lying 7 6 eV isomer of 229Th J Phys B At Mol Opt Phys 44 16 165005 arXiv 1105 4646 Bibcode 2011JPhB 44p5005R doi 10 1088 0953 4075 44 16 165005 S2CID 118379032 Kroger L A Reich C W 1976 Features of the low energy level scheme of 229Th as observed in the a decay of 233U Nuclear Physics A 259 1 29 60 Bibcode 1976NuPhA 259 29K doi 10 1016 0375 9474 76 90494 2 Reich C W Helmer R G Jan 1990 Energy separation of the doublet of intrinsic states at the ground state of 229Th Physical Review Letters 64 3 American Physical Society 271 273 Bibcode 1990PhRvL 64 271R doi 10 1103 PhysRevLett 64 271 PMID 10041937 Helmer R G Reich C W April 1994 An Excited State of 229Th at 3 5 eV Physical Review C 49 4 1845 1858 Bibcode 1994PhRvC 49 1845H doi 10 1103 PhysRevC 49 1845 PMID 9969412 B R Beck et al 2007 04 06 Energy splitting in the ground state doublet in the nucleus 229Th Physical Review Letters 98 14 142501 Bibcode 2007PhRvL 98n2501B doi 10 1103 PhysRevLett 98 142501 PMID 17501268 S2CID 12092700 Beck BR Wu CY Beiersdorfer P Brown GV Becker JA Moody KJ Wilhelmy JB Porter FS Kilbourne CA Kelley RL 2009 07 30 Improved value for the energy splitting of the ground state doublet in the nucleus 229Th PDF 12th Int Conf on Nuclear Reaction Mechanisms Varenna Italy LLNL PROC 415170 Archived from the original PDF on 2017 01 27 Retrieved 2014 05 14 Jeet Justin Schneider Christian Sullivan Scott T Rellergert Wade G Mirzadeh Saed Cassanho A et al 23 June 2015 Results of a Direct Search Using Synchrotron Radiation for the Low Energy Physical Review Letters 114 25 253001 arXiv 1502 02189 Bibcode 2015PhRvL 114y3001J doi 10 1103 physrevlett 114 253001 PMID 26197124 S2CID 1322253 Yamaguchi A Kolbe M Kaser H Reichel T Gottwald A Peik E May 2015 Experimental search for the low energy nuclear transition in 229Th with undulator radiation New Journal of Physics 17 5 053053 Bibcode 2015NJPh 17e3053Y doi 10 1088 1367 2630 17 5 053053 von der Wense Lars 2016 On the direct detection of 229mTh PDF PhD thesis Ludwig Maximilian University of Munich ISBN 978 3 319 70461 6 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Peter G Seiferle Benedict von der Wense Lars 2019 10 28 The 229 thorium isomer doorway to the road from the atomic clock to the nuclear clock Journal of Physics B Atomic Molecular and Optical Physics 52 20 203001 Bibcode 2019JPhB 52t3001T doi 10 1088 1361 6455 ab29b8 von der Wense Lars Seiferle Benedict Laatiaoui Mustapha Neumayr Jurgen B Maier Hans Jorg Wirth Hans Friedrich et al 5 May 2016 Direct detection of the 229Th nuclear clock transition Nature 533 7601 47 51 arXiv 1710 11398 Bibcode 2016Natur 533 47V doi 10 1038 nature17669 PMID 27147026 S2CID 205248786 a b Seiferle B von der Wense L Bilous P V Amersdorffer I Lemell C Libisch F Stellmer S Schumm T Dullmann C E Palffy A Thirolf P G 12 September 2019 Energy of the 229Th nuclear clock transition Nature 573 7773 243 246 arXiv 1905 06308 Bibcode 2019Natur 573 243S doi 10 1038 s41586 019 1533 4 PMID 31511684 S2CID 155090121 Karpeshin F F Trzhaskovskaya M B 2007 Impact of the electron environment on the lifetime of the 229Thm low 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Retrieved 2010 01 25 World Nuclear Association Thorium Archived from the original on 2013 02 16 Retrieved 2010 01 25 Krasinskas Alyssa M Minda Justina Saul Scott H Shaked Abraham Furth Emma E 2004 Redistribution of thorotrast into a liver allograft several years following transplantation a case report Mod Pathol 17 1 117 120 doi 10 1038 modpathol 3800008 PMID 14631374 Peppard D F Mason G W Gray P R Mech J F 1952 Occurrence of the 4n 1 series in nature PDF Journal of the American Chemical Society 74 23 6081 6084 doi 10 1021 ja01143a074 Archived PDF from the original on 2019 04 29 Isotope masses from Audi Georges Bersillon Olivier Blachot Jean Wapstra Aaldert Hendrik 2003 The NUBASE evaluation of nuclear and decay properties Nuclear Physics A 729 3 128 Bibcode 2003NuPhA 729 3A doi 10 1016 j nuclphysa 2003 11 001 Isotopic compositions and standard atomic masses from de Laeter John Robert Bohlke John Karl De Bievre Paul Hidaka Hiroshi Peiser H Steffen Rosman Kevin J R Taylor Philip D P 2003 Atomic weights of the elements Review 2000 IUPAC Technical Report Pure and Applied Chemistry 75 6 683 800 doi 10 1351 pac200375060683 Wieser Michael E 2006 Atomic weights of the elements 2005 IUPAC Technical Report Pure and Applied Chemistry 78 11 2051 2066 doi 10 1351 pac200678112051 News amp Notices Standard Atomic Weights Revised International Union of Pure and Applied Chemistry 19 October 2005 Half life spin and isomer data selected from the following sources G Audi A H Wapstra C Thibault J Blachot O Bersillon 2003 The NUBASE evaluation of nuclear and decay properties PDF Nuclear Physics A 729 1 3 128 Bibcode 2003NuPhA 729 3A doi 10 1016 j nuclphysa 2003 11 001 Archived from the original PDF on 2011 07 20 National Nuclear Data Center NuDat 2 x database Brookhaven National Laboratory Holden Norman E 2004 11 Table of the Isotopes In Lide David R ed CRC Handbook of Chemistry and Physics 85th ed Boca Raton Florida CRC Press ISBN 978 0 8493 0485 9 Retrieved from https en wikipedia org w index php title Isotopes of thorium amp oldid 1222030512 Thorium 230, wikipedia, wiki, book, books, library,

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