Isotopes of uranium
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Standard atomic weight Ar°(U) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
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Uranium (92U) is a naturally occurring radioactive element that has no stable isotope. It has two primordial isotopes, uranium-238 and uranium-235, that have long half-lives and are found in appreciable quantity in the Earth's crust. The decay product uranium-234 is also found. Other isotopes such as uranium-233 have been produced in breeder reactors. In addition to isotopes found in nature or nuclear reactors, many isotopes with far shorter half-lives have been produced, ranging from 214U to 242U (with the exception of 220U). The standard atomic weight of natural uranium is 238.02891(3).
Natural uranium consists of three main isotopes, 238U (99.2739–99.2752% natural abundance), 235U (0.7198–0.7202%), and 234U (0.0050–0.0059%).[5] All three isotopes are radioactive (i.e., they are radioisotopes), and the most abundant and stable is uranium-238, with a half-life of 4.4683×109 years (about the age of the Earth).
Uranium-238 is an alpha emitter, decaying through the 18-member uranium series into lead-206. The decay series of uranium-235 (historically called actino-uranium) has 15 members and ends in lead-207. The constant rates of decay in these series makes comparison of the ratios of parent-to-daughter elements useful in radiometric dating. Uranium-233 is made from thorium-232 by neutron bombardment.
Uranium-235 is important for both nuclear reactors (energy production) and nuclear weapons because it is the only isotope existing in nature to any appreciable extent that is fissile in response to thermal neutrons, i.e., thermal neutron capture has a high probability of inducing fission. A chain reaction can be sustained with a sufficiently large (critical) mass of uranium-235. Uranium-238 is also important because it is fertile: it absorbs neutrons to produce a radioactive isotope that subsequently decays to the isotope plutonium-239, which also is fissile.
List of isotopes
Nuclide [n 1] |
Historic name |
Z | N | Isotopic mass (Da)[6] [n 2][n 3] |
Half-life[1] |
Decay mode[1] [n 4] |
Daughter isotope [n 5][n 6] |
Spin and parity[1] [n 7][n 8] |
Natural abundance (mole fraction) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Excitation energy[n 8] | Normal proportion[1] | Range of variation | |||||||||||||||||
214U[7] | 92 | 122 | 0.52+0.95 −0.21 ms |
α | 210Th | 0+ | |||||||||||||
215U | 92 | 123 | 215.026720(11) | 1.4(0.9) ms | α | 211Th | 5/2−# | ||||||||||||
β+? | 215Pa | ||||||||||||||||||
216U[8] | 92 | 124 | 216.024760(30) | 2.25+0.63 −0.40 ms |
α | 212Th | 0+ | ||||||||||||
216mU | 2206 keV | 0.89+0.24 −0.16 ms |
α | 212Th | 8+ | ||||||||||||||
217U[9] | 92 | 125 | 217.024660(86)# | 19.3+13.3 −5.6 ms |
α | 213Th | (1/2−) | ||||||||||||
β+? | 217Pa | ||||||||||||||||||
218U[8] | 92 | 126 | 218.023505(15) | 650+80 −70 μs |
α | 214Th | 0+ | ||||||||||||
218mU | 2117 keV | 390+60 −50 μs |
α | 214Th | 8+ | ||||||||||||||
IT? | 218U | ||||||||||||||||||
219U | 92 | 127 | 219.025009(14) | 60(7) μs | α | 215Th | (9/2+) | ||||||||||||
β+? | 219Pa | ||||||||||||||||||
221U | 92 | 129 | 221.026323(77) | 0.66(14) μs | α | 217Th | (9/2+) | ||||||||||||
β+? | 221Pa | ||||||||||||||||||
222U | 92 | 130 | 222.026058(56) | 4.7(0.7) μs | α | 218Th | 0+ | ||||||||||||
β+? | 222Pa | ||||||||||||||||||
223U | 92 | 131 | 223.027961(63) | 65(12) μs | α | 219Th | 7/2+# | ||||||||||||
β+? | 223Pa | ||||||||||||||||||
224U | 92 | 132 | 224.027636(16) | 396(17) μs | α | 220Th | 0+ | ||||||||||||
β+? | 224Pa | ||||||||||||||||||
225U | 92 | 133 | 225.029385(11) | 62(4) ms | α | 221Th | 5/2+# | ||||||||||||
226U | 92 | 134 | 226.029339(12) | 269(6) ms | α | 222Th | 0+ | ||||||||||||
227U | 92 | 135 | 227.0311811(91) | 1.1(0.1) min | α | 223Th | (3/2+) | ||||||||||||
β+? | 227Pa | ||||||||||||||||||
228U | 92 | 136 | 228.031369(14) | 9.1(0.2) min | α (97.5%) | 224Th | 0+ | ||||||||||||
EC (2.5%) | 228Pa | ||||||||||||||||||
229U | 92 | 137 | 229.0335060(64) | 57.8(0.5) min | β+ (80%) | 229Pa | (3/2+) | ||||||||||||
α (20%) | 225Th | ||||||||||||||||||
230U | 92 | 138 | 230.0339401(48) | 20.23(0.02) d | α | 226Th | 0+ | ||||||||||||
SF ? | (various) | ||||||||||||||||||
CD (4.8×10−12%) | 208Pb 22Ne | ||||||||||||||||||
231U | 92 | 139 | 231.0362922(29) | 4.2(0.1) d | EC | 231Pa | 5/2+# | ||||||||||||
α (.004%) | 227Th | ||||||||||||||||||
232U | 92 | 140 | 232.0371548(19) | 68.9(0.4) y | α | 228Th | 0+ | ||||||||||||
CD (8.9×10−10%) | 208Pb 24Ne | ||||||||||||||||||
SF (10−12%) | (various) | ||||||||||||||||||
CD? | 204Hg 28Mg | ||||||||||||||||||
233U | 92 | 141 | 233.0396343(24) | 1.592(2)×105 y | α | 229Th | 5/2+ | Trace[n 9] | |||||||||||
CD (≤7.2×10−11%) | 209Pb 24Ne | ||||||||||||||||||
SF ? | (various) | ||||||||||||||||||
CD ? | 205Hg 28Mg | ||||||||||||||||||
234U[n 10][n 11] | Uranium II | 92 | 142 | 234.0409503(12) | 2.455(6)×105 y | α | 230Th | 0+ | [0.000054(5)][n 12] | 0.000050– 0.000059 | |||||||||
SF (1.64×10−9%) | (various) | ||||||||||||||||||
CD (1.4×10−11%) | 206Hg 28Mg | ||||||||||||||||||
CD (≤9×10−12%) | 208Pb 26Ne | ||||||||||||||||||
CD (≤9×10−12%) | 210Pb 24Ne | ||||||||||||||||||
234mU | 1421.257(17) keV | 33.5(2.0) ms | IT | 234U | 6− | ||||||||||||||
235U[n 13][n 14][n 15] | Actin Uranium Actino-Uranium |
92 | 143 | 235.0439281(12) | 7.038(1)×108 y | α | 231Th | 7/2− | [0.007204(6)] | 0.007198– 0.007207 | |||||||||
SF (7×10−9%) | (various) | ||||||||||||||||||
CD (8×10−10%) | 215Pb 20Ne | ||||||||||||||||||
CD (8×10−10%) | 210Pb 25Ne | ||||||||||||||||||
CD (8×10−10%) | 207Hg 28Mg | ||||||||||||||||||
235m1U | 0.076737(18) keV | 25.7(1) min | IT | 235U | 1/2+ | ||||||||||||||
235m2U | 2500(300) keV | 3.6(18) ms | SF | (various) | |||||||||||||||
236U | Thoruranium[10] | 92 | 144 | 236.0455661(12) | 2.342(3)×107 y | α | 232Th | 0+ | Trace[n 16] | ||||||||||
SF (9.6×10−8%) | (various) | ||||||||||||||||||
CD (≤2.0×10−11%)[11] | 208Hg 28Mg | ||||||||||||||||||
CD (≤2.0×10−11%)[11] | 206Hg 30Mg | ||||||||||||||||||
236m1U | 1052.5(6) keV | 100(4) ns | IT | 236U | 4− | ||||||||||||||
236m2U | 2750(3) keV | 120(2) ns | IT (87%) | 236U | (0+) | ||||||||||||||
SF (13%) | (various) | ||||||||||||||||||
237U | 92 | 145 | 237.0487283(13) | 6.752(2) d | β− | 237Np | 1/2+ | Trace[n 17] | |||||||||||
237mU | 274.0(10) keV | 155(6) ns | IT | 237U | 7/2− | ||||||||||||||
238U[n 11][n 13][n 14] | Uranium I | 92 | 146 | 238.050787618(15)[12] | 4.468(3)×109 y | α | 234Th | 0+ | [0.992742(10)] | 0.992739– 0.992752 | |||||||||
SF (5.44×10−5%) | (various) | ||||||||||||||||||
β−β− (2.2×10−10%) | 238Pu | ||||||||||||||||||
238mU | 2557.9(5) keV | 280(6) ns | IT (97.4%) | 238U | 0+ | ||||||||||||||
SF (2.6%) | (various) | ||||||||||||||||||
239U | 92 | 147 | 239.0542920(16) | 23.45(0.02) min | β− | 239Np | 5/2+ | Trace[n 18] | |||||||||||
239m1U | 133.7991(10) keV | 780(40) ns | IT | 239U | 1/2+ | ||||||||||||||
239m2U | 2500(900)# keV | >250 ns | SF? | (various) | 0+ | ||||||||||||||
IT? | 239U | ||||||||||||||||||
240U | 92 | 148 | 240.0565924(27) | 14.1(0.1) h | β− | 240Np | 0+ | Trace[n 19] | |||||||||||
α? | 236Th | ||||||||||||||||||
241U[13] | 92 | 149 | 241.06031(5) | ~40 min[14][15] | β− | 241Np | 7/2+# | ||||||||||||
242U | 92 | 150 | 242.06296(10)[14] | 16.8(0.5) min | β− | 242Np | 0+ | ||||||||||||
This table header & footer: |
- ^ mU – Excited nuclear isomer.
- ^ ( ) – Uncertainty (1σ) 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).
- ^
Modes of decay:
CD: Cluster decay EC: Electron capture SF: Spontaneous fission - ^ Bold italics symbol as daughter – Daughter product is nearly stable.
- ^ Bold symbol as daughter – Daughter product is stable.
- ^ ( ) spin value – Indicates spin with weak assignment arguments.
- ^ a b # – Values marked # are not purely derived from experimental data, but at least partly from trends of neighboring nuclides (TNN).
- ^ Intermediate decay product of 237Np
- ^ Used in uranium–thorium dating
- ^ a b Used in uranium–uranium dating
- ^ Intermediate decay product of 238U
- ^ a b Primordial radionuclide
- ^ a b Used in Uranium–lead dating
- ^ Important in nuclear reactors
- ^ Intermediate decay product of 244Pu, also produced by neutron capture of 235U
- ^ Neutron capture product, parent of trace quantities of 237Np
- ^ Neutron capture product; parent of trace quantities of 239Pu
- ^ Intermediate decay product of 244Pu
Actinides vs fission products
Actinides[16] by decay chain | Half-life range (a) |
Fission products of 235U by yield[17] | ||||||
---|---|---|---|---|---|---|---|---|
4n | 4n + 1 | 4n + 2 | 4n + 3 | 4.5–7% | 0.04–1.25% | <0.001% | ||
228Ra№ | 4–6 a | 155Euþ | ||||||
248Bk[18] | > 9 a | |||||||
244Cmƒ | 241Puƒ | 250Cf | 227Ac№ | 10–29 a | 90Sr | 85Kr | 113mCdþ | |
232Uƒ | 238Puƒ | 243Cmƒ | 29–97 a | 137Cs | 151Smþ | 121mSn | ||
249Cfƒ | 242mAmƒ | 141–351 a |
No fission products have a half-life | |||||
241Amƒ | 251Cfƒ[19] | 430–900 a | ||||||
226Ra№ | 247Bk | 1.3–1.6 ka | ||||||
240Pu | 229Th | 246Cmƒ | 243Amƒ | 4.7–7.4 ka | ||||
245Cmƒ | 250Cm | 8.3–8.5 ka | ||||||
239Puƒ | 24.1 ka | |||||||
230Th№ | 231Pa№ | 32–76 ka | ||||||
236Npƒ | 233Uƒ | 234U№ | 150–250 ka | 99Tc₡ | 126Sn | |||
248Cm | 242Pu | 327–375 ka | 79Se₡ | |||||
1.33 Ma | 135Cs₡ | |||||||
237Npƒ | 1.61–6.5 Ma | 93Zr | 107Pd | |||||
236U | 247Cmƒ | 15–24 Ma | 129I₡ | |||||
244Pu | 80 Ma |
... nor beyond 15.7 Ma[20] | ||||||
232Th№ | 238U№ | 235Uƒ№ | 0.7–14.1 Ga | |||||
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Uranium-214
Uranium-214 is the lightest known isotope of uranium. It was discovered at the Spectrometer for Heavy Atoms and Nuclear Structure (SHANS) at the Heavy Ion Research Facility in Lanzhou, China in 2021, produced by firing argon-36 at tungsten-182. It undergoes alpha decay with a half-life of 0.5 ms.[21][22][23][24]
Uranium-232
Uranium-232 has a half-life of 68.9 years and is a side product in the thorium cycle. It has been cited as an obstacle to nuclear proliferation using 233U, because the intense gamma radiation from 208Tl (a daughter of 232U, produced relatively quickly) makes 233U contaminated with it more difficult to handle. Uranium-232 is a rare example of an even-even isotope that is fissile with both thermal and fast neutrons.[25][26]
Uranium-233
Uranium-233 is a fissile isotope of uranium that is bred from thorium-232 as part of the thorium fuel cycle. 233U was investigated for use in nuclear weapons and as a reactor fuel. It was occasionally tested but never deployed in nuclear weapons and has not been used commercially as a nuclear fuel.[27] It has been used successfully in experimental nuclear reactors and has been proposed for much wider use as a nuclear fuel. It has a half-life of around 160,000 years.
Uranium-233 is produced by the neutron irradiation of thorium-232. When thorium-232 absorbs a neutron, it becomes thorium-233, which has a half-life of only 22 minutes. Thorium-233 beta decays into protactinium-233. Protactinium-233 has a half-life of 27 days and beta decays into uranium-233; some proposed molten salt reactor designs attempt to physically isolate the protactinium from further neutron capture before beta decay can occur.
Uranium-233 usually fissions on neutron absorption but sometimes retains the neutron, becoming uranium-234. The capture-to-fission ratio is smaller than the other two major fissile fuels, uranium-235 and plutonium-239; it is also lower than that of short-lived plutonium-241, but bested by very difficult-to-produce neptunium-236.
Uranium-234
234U occurs in natural uranium as an indirect decay product of uranium-238, but makes up only 55 parts per million of the uranium because its half-life of just 245,500 years is only about 1/18,000 that of 238U. The path of production of 234U is this: 238U alpha decays to thorium-234. Next, with a short half-life, 234Th beta decays to protactinium-234. Finally, 234Pa beta decays to 234U.[28][29]
234U alpha decays to thorium-230, except for the small percentage of nuclei that undergo spontaneous fission.
Extraction of rather small amounts of 234U from natural uranium would be feasible using isotope separation, similar to normal uranium-enrichment. However, there is no real demand in chemistry, physics, or engineering for isolating 234U. Very small pure samples of 234U can be extracted via the chemical ion-exchange process, from samples of plutonium-238 that have aged somewhat to allow some decay to 234U via alpha emission.
Enriched uranium contains more 234U than natural uranium as a byproduct of the uranium enrichment process aimed at obtaining uranium-235, which concentrates lighter isotopes even more strongly than it does 235U. The increased percentage of 234U in enriched natural uranium is acceptable in current nuclear reactors, but (re-enriched) reprocessed uranium might contain even higher fractions of 234U, which is undesirable.[30] This is because 234U is not fissile, and tends to absorb slow neutrons in a nuclear reactor—becoming 235U.[29][30]
234U has a neutron capture cross section of about 100 barns for thermal neutrons, and about 700 barns for its resonance integral—the average over neutrons having various intermediate energies. In a nuclear reactor, non-fissile isotopes capture a neutron breeding fissile isotopes. 234U is converted to 235U more easily and therefore at a greater rate than uranium-238 is to plutonium-239 (via neptunium-239), because 238U has a much smaller neutron-capture cross section of just 2.7 barns.
Uranium-235
Uranium-235 makes up about 0.72% of natural uranium. Unlike the predominant isotope uranium-238, it is fissile, i.e., it can sustain a fission chain reaction. It is the only fissile isotope that is a primordial nuclide or found in significant quantity in nature.
Uranium-235 has a half-life of 703.8 million years. It was discovered in 1935 by Arthur Jeffrey Dempster. Its (fission) nuclear cross section for slow thermal neutron is about 504.81 barns. For fast neutrons it is on the order of 1 barn. At thermal energy levels, about 5 of 6 neutron absorptions result in fission and 1 of 6 result in neutron capture forming uranium-236.[31] The fission-to-capture ratio improves for faster neutrons.
Uranium-236
Uranium-236 has a half-life of about 23 million years; and is neither fissile with thermal neutrons, nor very good fertile material, but is generally considered a nuisance and long-lived radioactive waste. It is found in spent nuclear fuel and in the reprocessed uranium made from spent nuclear fuel.
Uranium-237
Uranium-237 has a half-life of about 6.75 days. It decays into neptunium-237 by beta decay. It was discovered by Japanese physicist Yoshio Nishina in 1940, who in a near-miss discovery, inferred the creation of element 93, but was unable to isolate the then-unknown element or measure its decay properties.[32]
Uranium-238
Uranium-238 (238U or U-238) is the most common isotope of uranium found in nature. It is not fissile, but is fertile: it can capture a slow neutron and after two beta decays become fissile plutonium-239. Uranium-238 is fissionable by fast neutrons, but cannot support a chain reaction because inelastic scattering reduces neutron energy below the range where fast fission of one or more next-generation nuclei is probable. Doppler broadening of 238U's neutron absorption resonances, increasing absorption as fuel temperature increases, is also an essential negative feedback mechanism for reactor control.
About 99.284% of natural uranium is uranium-238, which has a half-life of 1.41×1017 seconds (4.468×109 years). Depleted uranium has an even higher concentration of 238U, and even low-enriched uranium (LEU) is still mostly 238U. Reprocessed uranium is also mainly 238U, with about as much uranium-235 as natural uranium, a comparable proportion of uranium-236, and much smaller amounts of other isotopes of uranium such as uranium-234, uranium-233, and uranium-232.
Uranium-239
Uranium-239 is usually produced by exposing 238U to neutron radiation in a nuclear reactor. 239U has a half-life of about 23.45 minutes and beta decays into neptunium-239, with a total decay energy of about 1.29 MeV.[33] The most common gamma decay at 74.660 keV accounts for the difference in the two major channels of beta emission energy, at 1.28 and 1.21 MeV.[34]
239Np then, with a half-life of about 2.356 days, beta-decays to plutonium-239.
Uranium-241
In 2023, in a paper published in Physical Review Letters, a group of researchers based in Korea reported that they had found uranium-241 in an experiment involving 238U+198Pt multinucleon transfer reactions.[35][36] Its half-life is about 40 minutes.[35]
References
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- ^ "Standard Atomic Weights: Uranium". CIAAW. 1999.
- ^ Prohaska, Thomas; Irrgeher, Johanna; Benefield, Jacqueline; Böhlke, John K.; Chesson, Lesley A.; Coplen, Tyler B.; Ding, Tiping; Dunn, Philip J. H.; Gröning, 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.
- ^ "Uranium Isotopes". GlobalSecurity.org. Retrieved 14 March 2012.
- ^ Wang, Meng; Huang, W.J.; Kondev, F.G.; Audi, G.; Naimi, S. (2021). "The AME 2020 atomic mass evaluation (II). Tables, graphs and references*". Chinese Physics C. 45 (3): 030003. doi:10.1088/1674-1137/abddaf.
- ^ Zhang, Z. Y.; Yang, H. B.; Huang, M. H.; Gan, Z. G.; Yuan, C. X.; Qi, C.; Andreyev, A. N.; Liu, M. L.; Ma, L.; Zhang, M. M.; Tian, Y. L.; Wang, Y. S.; Wang, J. G.; Yang, C. L.; Li, G. S.; Qiang, Y. H.; Yang, W. Q.; Chen, R. F.; Zhang, H. B.; Lu, Z. W.; Xu, X. X.; Duan, L. M.; Yang, H. R.; Huang, W. X.; Liu, Z.; Zhou, X. H.; Zhang, Y. H.; Xu, H. S.; Wang, N.; Zhou, H. B.; Wen, X. J.; Huang, S.; Hua, W.; Zhu, L.; Wang, X.; Mao, Y. C.; He, X. T.; Wang, S. Y.; Xu, W. Z.; Li, H. W.; Ren, Z. Z.; Zhou, S. G. (2021). "New α-Emitting Isotope U214 and Abnormal Enhancement of α-Particle Clustering in Lightest Uranium Isotopes". Physical Review Letters. 126 (15): 152502. arXiv:2101.06023. Bibcode:2021PhRvL.126o2502Z. doi:10.1103/PhysRevLett.126.152502. PMID 33929212. S2CID 231627674.
- ^ a b Zhang, M. M.; Tian, Y. L.; Wang, Y. S.; Zhang, Z. Y.; Gan, Z. G.; Yang, H. B.; Huang, M. H.; Ma, L.; Yang, C. L.; Wang, J. G.; Yuan, C. X.; Qi, C.; Andreyev, A. N.; Huang, X. Y.; Xu, S. Y.; Zhao, Z.; Chen, L. X.; Wang, J. Y.; Liu, M. L.; Qiang, Y. H.; Li, G. S.; Yang, W. Q.; Chen, R. F.; Zhang, H. B.; Lu, Z. W.; Xu, X. X.; Duan, L. M.; Yang, H. R.; Huang, W. X.; Liu, Z.; Zhou, X. H.; Zhang, Y. H.; Xu, H. S.; Wang, N.; Zhou, H. B.; Wen, X. J.; Huang, S.; Hua, W.; Zhu, L.; Wang, X.; Mao, Y. C.; He, X. T.; Wang, S. Y.; Xu, W. Z.; Li, H. W.; Niu, Y. F.; Guo, L.; Ren, Z. Z.; Zhou, S. G. (4 August 2022). "Fine structure in the α decay of the 8+ isomer in 216, 218U". Physical Review C. 106 (2): 024305. doi:10.1103/PhysRevC.106.024305. ISSN 2469-9985. S2CID 251359451.
- ^ Gan, ZaiGuo; Jiang, Jian; Yang, HuaBin; Zhang, ZhiYuan; Ma, Long; Yu, Lin; Wang, JianGuo; Tian, YuLin; Ding, Bing; Huang, TianHeng; Wang, YongSheng; Guo, Song; Sun, MingDao; Wang, KaiLong; Zhou, ShanGui; Ren, ZhongZhou; Zhou, XiaoHong; Xu, HuShan (1 August 2016). "α decay studies of the neutron-deficient uranium isotopes 215-217U". Chinese Science Bulletin. 61 (22): 2502–2511. doi:10.1360/N972015-01316. Retrieved 24 June 2023.
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- ^ 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.
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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]." - ^ 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.
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