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Stable nuclide

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Graph of nuclides (isotopes) by type of decay. Orange and blue nuclides are unstable, with the black squares between these regions representing stable nuclides. The continuous line passing below most of the nuclides comprises the positions on the graph of the (mostly hypothetical) nuclides for which proton number would be the same as neutron number. The graph reflects the fact that elements with more than 20 protons either have more neutrons than protons or are unstable.

Stable nuclides are nuclides that are not radioactive and so (unlike radionuclides) do not spontaneously undergo radioactive decay.[1] When such nuclides are referred to in relation to specific elements, they are usually termed stable isotopes.

The 80 elements with one or more stable isotopes comprise a total of 251 nuclides that have not been known to decay using current equipment (see list at the end of this article). Of these 80 elements, 26 have only one stable isotope; they are thus termed monoisotopic. The rest have more than one stable isotope. Tin has ten stable isotopes, the largest number of stable isotopes known for an element.

Definition of stability, and naturally occurring nuclides

Most naturally occurring nuclides are stable (about 251; see list at the end of this article), and about 35 more (total of 286) are known to be radioactive with sufficiently long half-lives (also known) to occur primordially. If the half-life of a nuclide is comparable to, or greater than, the Earth's age (4.5 billion years), a significant amount will have survived since the formation of the Solar System, and then is said to be primordial. It will then contribute in that way to the natural isotopic composition of a chemical element. Primordially present radioisotopes are easily detected with half-lives as short as 700 million years (e.g., 235U). This is the present limit of detection,[citation needed] as shorter-lived nuclides have not yet been detected undisputedly in nature except when recently produced, such as decay products or cosmic ray spallation.

Many naturally occurring radioisotopes (another 53 or so, for a total of about 339) exhibit still shorter half-lives than 700 million years, but they are made freshly, as daughter products of decay processes of primordial nuclides (for example, radium from uranium) or from ongoing energetic reactions, such as cosmogenic nuclides produced by present bombardment of Earth by cosmic rays (for example, 14C made from nitrogen).

Some isotopes that are classed as stable (i.e. no radioactivity has been observed for them) are predicted to have extremely long half-lives (sometimes as high as 1018 years or more).[2] If the predicted half-life falls into an experimentally accessible range, such isotopes have a chance to move from the list of stable nuclides to the radioactive category, once their activity is observed. For example, 209Bi and 180W were formerly classed as stable, but were found to be alpha-active in 2003. However, such nuclides do not change their status as primordial when they are found to be radioactive.

Most stable isotopes on Earth are believed to have been formed in processes of nucleosynthesis, either in the Big Bang, or in generations of stars that preceded the formation of the Solar System. However, some stable isotopes also show abundance variations in the earth as a result of decay from long-lived radioactive nuclides. These decay-products are termed radiogenic isotopes, in order to distinguish them from the much larger group of 'non-radiogenic' isotopes.

Isotopes per element

See also: List of elements by stability of isotopes, List of nuclides, and Beta-decay stable isobars

Of the known chemical elements, 80 elements have at least one stable nuclide. These comprise the first 82 elements from hydrogen to lead, with the two exceptions, technetium (element 43) and promethium (element 61), that do not have any stable nuclides. As of 2023, there were a total of 251 known "stable" nuclides. In this definition, "stable" means a nuclide that has never been observed to decay against the natural background. Thus, these elements have half-lives too long to be measured by any means, direct or indirect.

Stable isotopes:

  • 1 element (tin) has 10 stable isotopes
  • 5 elements have 7 stable isotopes apiece
  • 7 elements have 6 stable isotopes apiece
  • 11 elements have 5 stable isotopes apiece
  • 9 elements have 4 stable isotopes apiece
  • 5 elements have 3 stable isotopes apiece
  • 16 elements have 2 stable isotopes apiece
  • 26 elements have 1 single stable isotope.

These last 26 are thus called monoisotopic elements.[3] The mean number of stable isotopes for elements which have at least one stable isotope is 251/80 = 3.1375.

Physical magic numbers and odd and even proton and neutron count

See also: Even and odd atomic nuclei

Stability of isotopes is affected by the ratio of protons to neutrons, and also by presence of certain magic numbers of neutrons or protons which represent closed and filled quantum shells. These quantum shells correspond to a set of energy levels within the shell model of the nucleus; filled shells, such as the filled shell of 50 protons for tin, confers unusual stability on the nuclide. As in the case of tin, a magic number for Z, the atomic number, tends to increase the number of stable isotopes for the element.

Just as in the case of electrons, which have the lowest energy state when they occur in pairs in a given orbital, nucleons (both protons and neutrons) exhibit a lower energy state when their number is even, rather than odd. This stability tends to prevent beta decay (in two steps) of many even–even nuclides into another even–even nuclide of the same mass number but lower energy (and of course with two more protons and two fewer neutrons), because decay proceeding one step at a time would have to pass through an odd–odd nuclide of higher energy. Such nuclei thus instead undergo double beta decay (or are theorized to do so) with half-lives several orders of magnitude larger than the age of the universe. This makes for a larger number of stable even–even nuclides, which account for 150 of the 251 total. Stable even–even nuclides number as many as three isobars for some mass numbers, and up to seven isotopes for some atomic numbers.

Conversely, of the 251 known stable nuclides, only five have both an odd number of protons and odd number of neutrons: hydrogen-2 (deuterium), lithium-6, boron-10, nitrogen-14, and tantalum-180m. Also, only four naturally occurring, radioactive odd–odd nuclides have a half-life over a billion years: potassium-40, vanadium-50, lanthanum-138, and lutetium-176. Odd–odd primordial nuclides are rare because most odd–odd nuclei are unstable with respect to beta decay, because the decay products are even–even, and are therefore more strongly bound, due to nuclear pairing effects.[4]

Yet another effect of the instability of an odd number of either type of nucleons is that odd-numbered elements tend to have fewer stable isotopes. Of the 26 monoisotopic elements (those with only a single stable isotope), all but one have an odd atomic number, and all but one has an even number of neutrons—the single exception to both rules being beryllium.

The end of the stable elements in the periodic table occurs after lead, largely due to the fact that nuclei with 128 neutrons—two neutrons above the magic number 126—are extraordinarily unstable and almost immediately shed alpha particles.[5] This also contributes to the very short half-lives of astatine, radon, and francium relative to heavier elements. A similar phenomenon occurs to a much lesser extent with 84 neutrons—two neutrons above the magic number 82—where various isotopes of elements in the lanthanide series exhibit alpha decay.

Nuclear isomers, including a "stable" one

The count of 251 known stable nuclides includes tantalum-180m, since even though its decay and instability is automatically implied by its notation of "metastable", this has still not yet been observed. All "stable" isotopes (stable by observation, not theory) are the ground states of nuclei, with the exception of tantalum-180m, which is a nuclear isomer or excited state. The ground state of this particular nucleus, tantalum-180, is radioactive with a comparatively short half-life of 8 hours; in contrast, the decay of the excited nuclear isomer is extremely strongly forbidden by spin-parity selection rules. It has been reported experimentally by direct observation that the half-life of 180mTa to gamma decay must be more than 1015 years. Other possible modes of 180mTa decay (beta decay, electron capture, and alpha decay) have also never been observed.

Binding energy per nucleon of common isotopes.

Still-unobserved decay

Further information: List of nuclides

It is expected that some continual improvement of experimental sensitivity will allow discovery of very mild radioactivity (instability) of some isotopes that are considered to be stable today. For example, in 2003 it was reported that bismuth-209 (the only primordial isotope of bismuth) is very mildly radioactive, with the half-life time of (1.9 ± 0.2) × 1019 yr,[6][7] confirming earlier theoretical predictions[8] from nuclear physics that bismuth-209 would decay very slowly by alpha emission.

Isotopes that are theoretically believed to be unstable but have not been observed to decay are termed as observationally stable. Currently there are 161 theoretically unstable isotopes, 45 of which have been observed in detail with no sign of decay, the lightest in any case being 36Ar.

Summary table for numbers of each class of nuclides

This is a summary table from List of nuclides. Note that numbers are not exact and may change slightly in the future, as nuclides are observed to be radioactive, or new half-lives are determined to some precision.

Type of nuclide by stability class Number of nuclides in class Running total of nuclides in all classes to this point Notes
Theoretically stable according to the Standard Model 90 90 Includes first 40 elements. If protons decay, then there are no stable nuclides.
Theoretically stable to alpha decay, beta decay, isomeric transition, and double beta decay but not spontaneous fission, which is possible for "stable" nuclides ≥ niobium-93.[citation needed] 56[citation needed] 146 Contains the first 66 elements, except 43, 61, 62, and 63. Note that spontaneous fission has never been observed for nuclides with mass number < 230.
Energetically unstable to one or more known decay modes, but no decay yet seen. Considered stable until radioactivity confirmed. 105[2][9] 251 Total is the observationally stable nuclides.
Radioactive primordial nuclides. 35 286 Includes Bi, Th, U
Radioactive nonprimordial, but naturally occurring on Earth. ~61 significant ~347 significant Cosmogenic nuclides from cosmic rays; daughters of radioactive primordials such as francium, etc.

List of stable nuclides

The primordial radionuclides have been included for comparison; they are italicised and offset from the list of stable nuclides proper.

  1. Hydrogen-1
  2. Hydrogen-2
  3. Helium-3
  4. Helium-4
    no mass number 5
  5. Lithium-6
  6. Lithium-7
    no mass number 8
  7. Beryllium-9
  8. Boron-10
  9. Boron-11
  10. Carbon-12
  11. Carbon-13
  12. Nitrogen-14
  13. Nitrogen-15
  14. Oxygen-16
  15. Oxygen-17
  16. Oxygen-18
  17. Fluorine-19
  18. Neon-20
  19. Neon-21
  20. Neon-22
  21. Sodium-23
  22. Magnesium-24
  23. Magnesium-25
  24. Magnesium-26
  25. Aluminium-27
  26. Silicon-28
  27. Silicon-29
  28. Silicon-30
  29. Phosphorus-31
  30. Sulfur-32
  31. Sulfur-33
  32. Sulfur-34
  33. Sulfur-36
  34. Chlorine-35
  35. Chlorine-37
  36. Argon-36 (2E)
  37. Argon-38
  38. Argon-40
  39. Potassium-39
    Potassium-40 (B, E) – long-lived primordial radionuclide
  40. Potassium-41
  41. Calcium-40 (2E)*
  42. Calcium-42
  43. Calcium-43
  44. Calcium-44
  45. Calcium-46 (2B)*
    Calcium-48 (2B) – long-lived primordial radionuclide (B also predicted possible)
  46. Scandium-45
  47. Titanium-46
  48. Titanium-47
  49. Titanium-48
  50. Titanium-49
  51. Titanium-50
    Vanadium-50 (B, E) – long-lived primordial radionuclide
  52. Vanadium-51
  53. Chromium-50 (2E)*
  54. Chromium-52
  55. Chromium-53
  56. Chromium-54
  57. Manganese-55
  58. Iron-54 (2E)*
  59. Iron-56
  60. Iron-57
  61. Iron-58
  62. Cobalt-59
  63. Nickel-58 (2E)*
  64. Nickel-60
  65. Nickel-61
  66. Nickel-62
  67. Nickel-64
  68. Copper-63
  69. Copper-65
  70. Zinc-64 (2E)*
  71. Zinc-66
  72. Zinc-67
  73. Zinc-68
  74. Zinc-70 (2B)*
  75. Gallium-69
  76. Gallium-71
  77. Germanium-70
  78. Germanium-72
  79. Germanium-73
  80. Germanium-74
    Germanium-76 (2B) – long-lived primordial radionuclide
  81. Arsenic-75
  82. Selenium-74 (2E)
  83. Selenium-76
  84. Selenium-77
  85. Selenium-78
  86. Selenium-80 (2B)
    Selenium-82 (2B) – long-lived primordial radionuclide
  87. Bromine-79
  88. Bromine-81
    Krypton-78 (2E) – long-lived primordial radionuclide
  89. Krypton-80
  90. Krypton-82
  91. Krypton-83
  92. Krypton-84
  93. Krypton-86 (2B)
  94. Rubidium-85
    Rubidium-87 (B) – long-lived primordial radionuclide
  95. Strontium-84 (2E)*
  96. Strontium-86
  97. Strontium-87
  98. Strontium-88
  99. Yttrium-89
  100. Zirconium-90
  101. Zirconium-91
  102. Zirconium-92
  103. Zirconium-94 (2B)*
    Zirconium-96 (2B) – long-lived primordial radionuclide (B also predicted possible)
  104. Niobium-93
  105. Molybdenum-92 (2E)*
  106. Molybdenum-94
  107. Molybdenum-95
  108. Molybdenum-96
  109. Molybdenum-97
  110. Molybdenum-98 (2B)*
    Molybdenum-100 (2B) – long-lived primordial radionuclide
    Technetium - no stable isotopes
  111. Ruthenium-96 (2E)*
  112. Ruthenium-98
  113. Ruthenium-99
  114. Ruthenium-100
  115. Ruthenium-101
  116. Ruthenium-102
  117. Ruthenium-104 (2B)
  118. Rhodium-103
  119. Palladium-102 (2E)
  120. Palladium-104
  121. Palladium-105
  122. Palladium-106
  123. Palladium-108
  124. Palladium-110 (2B)*
  125. Silver-107
  126. Silver-109
  127. Cadmium-106 (2E)*
  128. Cadmium-108 (2E)*
  129. Cadmium-110
  130. Cadmium-111
  131. Cadmium-112
    Cadmium-113 (B) – long-lived primordial radionuclide
  132. Cadmium-114 (2B)*
    Cadmium-116 (2B) – long-lived primordial radionuclide
  133. Indium-113
    Indium-115 (B) – long-lived primordial radionuclide
  134. Tin-112 (2E)*
  135. Tin-114
  136. Tin-115
  137. Tin-116
  138. Tin-117
  139. Tin-118
  140. Tin-119
  141. Tin-120
  142. Tin-122 (2B)*
  143. Tin-124 (2B)*
  144. Antimony-121
  145. Antimony-123
  146. Tellurium-120 (2E)*
  147. Tellurium-122
  148. Tellurium-123 (E)*
  149. Tellurium-124
  150. Tellurium-125
  151. Tellurium-126
    Tellurium-128 (2B) – long-lived primordial radionuclide
    Tellurium-130 (2B) – long-lived primordial radionuclide
  152. Iodine-127
    Xenon-124 (2E) – long-lived primordial radionuclide
  153. Xenon-126 (2E)
  154. Xenon-128
  155. Xenon-129
  156. Xenon-130
  157. Xenon-131
  158. Xenon-132
  159. Xenon-134 (2B)*
    Xenon-136 (2B) – long-lived primordial radionuclide
  160. Caesium-133
    Barium-130 (2E) – long-lived primordial radionuclide
  161. Barium-132 (2E)*
  162. Barium-134
  163. Barium-135
  164. Barium-136
  165. Barium-137
  166. Barium-138
    Lanthanum-138 (B, E) – long-lived primordial radionuclide
  167. Lanthanum-139
  168. Cerium-136 (2E)*
  169. Cerium-138 (2E)*
  170. Cerium-140
  171. Cerium-142 (A, 2B)*
  172. Praseodymium-141
  173. Neodymium-142
  174. Neodymium-143 (A)
    Neodymium-144 (A) – long-lived primordial radionuclide
  175. Neodymium-145 (A)*
  176. Neodymium-146 (A, 2B)*
    no mass number 147§
  177. Neodymium-148 (A, 2B)*
    Neodymium-150 (2B) – long-lived primordial radionuclide
    Promethium - no stable isotopes
  178. Samarium-144 (2E)
    Samarium-146 (A) – probable long-lived primordial radionuclide
    Samarium-147 (A) – long-lived primordial radionuclide
    Samarium-148 (A) – long-lived primordial radionuclide
  179. Samarium-149 (A)*
  180. Samarium-150 (A)
    no mass number 151§
  181. Samarium-152 (A)
  182. Samarium-154 (2B)*
    Europium-151 (A) – long-lived primordial radionuclide
  183. Europium-153 (A)*
    Gadolinium-152 (A) – long-lived primordial radionuclide (2E also predicted possible)
  184. Gadolinium-154 (A)
  185. Gadolinium-155 (A)
  186. Gadolinium-156
  187. Gadolinium-157
  188. Gadolinium-158
  189. Gadolinium-160 (2B)*
  190. Terbium-159
  191. Dysprosium-156 (A, 2E)*
  192. Dysprosium-158 (A)
  193. Dysprosium-160 (A)
  194. Dysprosium-161 (A)
  195. Dysprosium-162 (A)
  196. Dysprosium-163
  197. Dysprosium-164
  198. Holmium-165 (A)
  199. Erbium-162 (A, 2E)*
  200. Erbium-164 (A, 2E)
  201. Erbium-166 (A)
  202. Erbium-167 (A)
  203. Erbium-168 (A)
  204. Erbium-170 (A, 2B)*
  205. Thulium-169 (A)
  206. Ytterbium-168 (A, 2E)*
  207. Ytterbium-170 (A)
  208. Ytterbium-171 (A)
  209. Ytterbium-172 (A)
  210. Ytterbium-173 (A)
  211. Ytterbium-174 (A)
  212. Ytterbium-176 (A, 2B)*
  213. Lutetium-175 (A)
    Lutetium-176 (B) – long-lived primordial radionuclide (A, E also predicted possible)
    Hafnium-174 (A) – long-lived primordial radionuclide (2E also predicted possible)
  214. Hafnium-176 (A)
  215. Hafnium-177 (A)
  216. Hafnium-178 (A)
  217. Hafnium-179 (A)
  218. Hafnium-180 (A)
  219. Tantalum-180m (A, B, E, IT)* ^
  220. Tantalum-181 (A)
    Tungsten-180 (A) – long-lived primordial radionuclide (2E also predicted possible)
  221. Tungsten-182 (A)*
  222. Tungsten-183 (A)*
  223. Tungsten-184 (A)*
  224. Tungsten-186 (A, 2B)*
  225. Rhenium-185 (A)
    Rhenium-187 (B) – long-lived primordial radionuclide (A also predicted possible)
    Osmium-184 (A) – long-lived primordial radionuclide (2E also predicted possible)
    Osmium-186 (A) – long-lived primordial radionuclide
  226. Osmium-187 (A)
  227. Osmium-188 (A)
  228. Osmium-189 (A)
  229. Osmium-190 (A)
  230. Osmium-192 (A, 2B)*
  231. Iridium-191 (A)
  232. Iridium-193 (A)
    Platinum-190 (A) – long-lived primordial radionuclide (2E also predicted possible)
  233. Platinum-192 (A)*
  234. Platinum-194 (A)
  235. Platinum-195 (A)*
  236. Platinum-196 (A)
  237. Platinum-198 (A, 2B)*
  238. Gold-197 (A)
  239. Mercury-196 (A, 2E)*
  240. Mercury-198 (A)
  241. Mercury-199 (A)
  242. Mercury-200 (A)
  243. Mercury-201 (A)
  244. Mercury-202 (A)
  245. Mercury-204 (2B)
  246. Thallium-203 (A)
  247. Thallium-205 (A)
  248. Lead-204 (A)*
  249. Lead-206 (A)*
  250. Lead-207 (A)*
  251. Lead-208 (A)*
    Bismuth ^^ and above –
    no stable isotopes
    no mass number 209 and above
    Bismuth-209 (A) – long-lived primordial radionuclide
    Thorium-232 (A, SF) – long-lived primordial radionuclide (2B also predicted possible)
    Uranium-235 (A, SF) – long-lived primordial radionuclide
    Uranium-238 (A, 2B, SF) – long-lived primordial radionuclide
    Plutonium-244 (A, SF) – probable long-lived primordial radionuclide (2B also predicted possible)

Abbreviations for predicted unobserved decay:[10][2][9]

A for alpha decay, B for beta decay, 2B for double beta decay, E for electron capture, 2E for double electron capture, IT for isomeric transition, SF for spontaneous fission, * for the nuclides whose half-lives have lower bound. Double beta decay has only been listed when beta decay is not also possible.

^ Tantalum-180m is a "metastable isotope" meaning that it is an excited nuclear isomer of tantalum-180. See isotopes of tantalum. However, the half-life of this nuclear isomer is so long that it has never been observed to decay, and it thus occurs as an "observationally nonradioactive" primordial nuclide, as a minor isotope of tantalum. This is the only case of a nuclear isomer which has a half-life so long that it has never been observed to decay. It is thus included in this list.

^^ Bismuth-209 had long been believed to be stable, due to its unusually long half-life of 2.01 · 1019 years, which is more than a billion times the age of the universe.

§ Europium-151 and samarium-147 are primordial nuclides with very long half-lives of 5.004 · 1018 years and 1.061 · 1011 years, respectively.

See also

References

  1. ^ "DOE explains ... Isotopes". Department of Energy, United States. Archived from the original on 14 April 2022. Retrieved 11 January 2023.
  2. ^ a b c Belli, P.; Bernabei, R.; Danevich, F. A.; et al. (2019). "Experimental searches for rare alpha and beta decays". European Physical Journal A. 55 (8): 140–1–140–7. arXiv:1908.11458. Bibcode:2019EPJA...55..140B. doi:10.1140/epja/i2019-12823-2. ISSN 1434-601X. S2CID 201664098.
  3. ^ Sonzogni, Alejandro. "Interactive Chart of Nuclides". National Nuclear Data Center: Brook haven National Laboratory. Archived from the original on 2018-10-10. Retrieved 2008-06-06.
  4. ^ Various (2002). Lide, David R. (ed.). Handbook of Chemistry & Physics (88th ed.). CRC. ISBN 978-0-8493-0486-6. OCLC 179976746. Archived from the original on 2017-07-24. Retrieved 2008-05-23.
  5. ^ Kelkar, N. G.; Nowakowski, M. (2016). "Signature of the N = 126 shell closure in dwell times of alpha-particle tunneling". Journal of Physics G: Nuclear and Particle Physics. 43 (105102). arXiv:1610.02069. doi:10.1088/0954-3899/43/10/105102.
  6. ^ "WWW Table of Radioactive Isotopes".[permanent dead link‍]
  7. ^ Marcillac, Pierre de; Noël Coron; Gérard Dambier; Jacques Leblanc & Jean-Pierre Moalic (2003). "Experimental detection of α-particles from the radioactive decay of natural bismuth". Nature. 422 (6934): 876–878. Bibcode:2003Natur.422..876D. doi:10.1038/nature01541. PMID 12712201. S2CID 4415582.
  8. ^ de Carvalho H. G., de Araújo Penna M. (1972). "Alpha-activity of 209Bi". Lett. Nuovo Cimento. 3 (18): 720–722. doi:10.1007/BF02824346.
  9. ^ a b Tretyak, V.I.; Zdesenko, Yu.G. (2002). "Tables of Double Beta Decay Data — An Update". At. Data Nucl. Data Tables. 80 (1): 83–116. Bibcode:2002ADNDT..80...83T. doi:10.1006/adnd.2001.0873.
  10. ^ "Nucleonica :: Web driven nuclear science".

Book references

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