Stable isotope

Stable nuclides are isotopes of a chemical element whose nucleons are in a configuration that does not permit them the surplus energy required to produce a radioactive emission. The nuclei of such isotopes are not radioactive and unlike radionuclides do not spontaneously undergo radioactive decay. When these nuclides are referred to in relation to specific elements they are usually called that element's stable isotopes.

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.

The 80 elements with one or more stable isotopes comprise a total of 251 nuclides that have not been shown to decay using current equipment. Of these 80 elements, 26 have only one stable isotope and are called monoisotopic. The other 56 have more than one stable isotope. Tin has ten stable isotopes, the largest number of any 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 long enough 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. Primordial 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 10¹⁸ years or more). 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

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 2024, there are 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. 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

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 >10⁹ years: potassium-40, vanadium-50, lanthanum-138, and lutetium-176. Odd–odd primordial nuclides are rare because most odd–odd nuclei beta-decay, because the decay products are even–even, and are therefore more strongly bound, due to nuclear pairing effects.

Yet another effect of the instability of an odd number of either type of nucleon is that odd-numbered elements tend to have fewer stable isotopes. Of the 26 monoisotopic elements (those with only one 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 is beryllium.

The end of the stable elements occurs after lead, largely because nuclei with 128 neutrons—two neutrons above the magic number 126—are extraordinarily unstable and almost immediately alpha-decay. This contributes to the very short half-lives of astatine, radon, and francium. A similar phenomenon occurs to a much lesser extent with 84 neutrons—two neutrons above the magic number 82—where various isotopes of lanthanide elements alpha-decay.

Nuclear isomers, including a "stable" one

The 251 known stable nuclides include tantalum-180m, since even though its decay is automatically implied by its being "metastable", this has not been observed. All "stable" isotopes (stable by observation, not theory) are the ground states of nuclei, except for tantalum-180m, which is a nuclear isomer or excited state. The ground state, tantalum-180, is radioactive with half-life 8 hours; in contrast, the decay of the nuclear isomer is extremely strongly forbidden by spin-parity selection rules. It has been reported by direct observation that the half-life of ^180mTa to gamma decay must be >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

It is expected that improvement of experimental sensitivity will allow discovery of very mild radioactivity of some isotopes now considered stable. For example, in 2003 it was reported that bismuth-209 (the only primordial isotope of bismuth) is very mildly radioactive, with half-life (1.9 ± 0.2) × 10¹⁹ yr, confirming earlier theoretical predictions from nuclear physics that bismuth-209 would very slowly alpha decay.

Isotopes that are theoretically believed to be unstable but have not been observed to decay are termed observationally stable. Currently there are 105 "stable" isotopes which are theoretically unstable, 40 of which have been observed in detail with no sign of decay, the lightest in any case being ³⁶Ar. Many "stable" nuclides are "metastable" in that they would release energy if they were to decay, and are expected to undergo very rare kinds of radioactive decay, including double beta decay.

146 nuclides from 62 elements with atomic numbers from 1 (hydrogen) through 66 (dysprosium) except 43 (technetium), 61 (promethium), 62 (samarium), and 63 (europium) are theoretically stable to any kind of nuclear decay — except for the theoretical possibility of proton decay, which has never been observed despite extensive searches for it; and spontaneous fission (SF), which is theoretically possible for the nuclides with atomic mass numbers ≥ 93.

Besides SF, other theoretical decay routes for heavier elements include:

• alpha decay – 70 heavy nuclides (the lightest two are cerium-142 and neodymium-143)
• double beta decay – 55 nuclides
• beta decay – tantalum-180m
• electron capture – tellurium-123, tantalum-180m
• double electron capture
• isomeric transition – tantalum-180m

These include all nuclides of mass 165 and greater. Argon-36 is the lightest known "stable" nuclide which is theoretically unstable.

The positivity of energy release in these processes means they are allowed kinematically (they do not violate conservation of energy) and, thus, in principle, can occur. They are not observed due to strong but not absolute suppression, by spin-parity selection rules (for beta decays and isomeric transitions) or by the thickness of the potential barrier (for alpha and cluster decays and spontaneous fission).

Summary table for numbers of each class of nuclides

This is a summary table from List of nuclides. 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 known decay modes, including alpha decay, beta decay, isomeric transition, and double beta decay	146	146	All the first 66 elements, except 43, 61, 62, and 63. If spontaneous fission is possible for the nuclides with mass numbers ≥ 93, then all such nuclides are unstable, so that only the first 40 elements would be stable. If protons decay, then there are no stable nuclides.
Energetically unstable to one or more known decay modes, but no decay yet seen. Considered stable until radioactivity confirmed.	105	251	Total is the observationally stable nuclides. All elements up to lead (except technetium and promethium) are included.
Radioactive primordial nuclides.	35	286	Includes bismuth, thorium, and uranium
Radioactive nonprimordial, but occur naturally 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 are included for comparison; they are italicized and offset from the list of stable nuclides proper.

1. Hydrogen-1
2. Hydrogen-2 (deuterium)
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 (α, 2B)*
172. Praseodymium-141
173. Neodymium-142
174. Neodymium-143 (α)
     Neodymium-144 (α) – long-lived primordial radionuclide
175. Neodymium-145 (α)*
176. Neodymium-146 (α, 2B)*
     no mass number 147^§
177. Neodymium-148 (α, 2B)*
     Neodymium-150 (2B) – long-lived primordial radionuclide
     Promethium - no stable isotopes
178. Samarium-144 (2E)
     Samarium-146 (α) – probable long-lived primordial radionuclide
     Samarium-147 (α) – long-lived primordial radionuclide
     Samarium-148 (α) – long-lived primordial radionuclide
179. Samarium-149 (α)*
180. Samarium-150 (α)
     no mass number 151^§
181. Samarium-152 (α)
182. Samarium-154 (2B)*
     Europium-151 (α) – long-lived primordial radionuclide
183. Europium-153 (α)*
     Gadolinium-152 (α) – long-lived primordial radionuclide (2E also predicted possible)
184. Gadolinium-154 (α)
185. Gadolinium-155 (α)
186. Gadolinium-156
187. Gadolinium-157
188. Gadolinium-158
189. Gadolinium-160 (2B)*
190. Terbium-159
191. Dysprosium-156 (α, 2E)*
192. Dysprosium-158 (α)
193. Dysprosium-160 (α)
194. Dysprosium-161 (α)
195. Dysprosium-162 (α)
196. Dysprosium-163
197. Dysprosium-164
198. Holmium-165 (α)
199. Erbium-162 (α, 2E)*
200. Erbium-164 (α, 2E)
201. Erbium-166 (α)
202. Erbium-167 (α)
203. Erbium-168 (α)
204. Erbium-170 (α, 2B)*
205. Thulium-169 (α)
206. Ytterbium-168 (α, 2E)*
207. Ytterbium-170 (α)
208. Ytterbium-171 (α)
209. Ytterbium-172 (α)
210. Ytterbium-173 (α)
211. Ytterbium-174 (α)
212. Ytterbium-176 (α, 2B)*
213. Lutetium-175 (α)
     Lutetium-176 (B) – long-lived primordial radionuclide (α, E also predicted possible)
     Hafnium-174 (α) – long-lived primordial radionuclide (2E also predicted possible)
214. Hafnium-176 (α)
215. Hafnium-177 (α)
216. Hafnium-178 (α)
217. Hafnium-179 (α)
218. Hafnium-180 (α)
219. Tantalum-180m (α, B, E, IT)* ^
220. Tantalum-181 (α)
     Tungsten-180 (α) – long-lived primordial radionuclide (2E also predicted possible)
221. Tungsten-182 (α)*
222. Tungsten-183 (α)*
223. Tungsten-184 (α)*
224. Tungsten-186 (α, 2B)*
225. Rhenium-185 (α)
     Rhenium-187 (B) – long-lived primordial radionuclide (A also predicted possible)
     Osmium-184 (α) – long-lived primordial radionuclide (2E also predicted possible)
     Osmium-186 (α) – long-lived primordial radionuclide
226. Osmium-187 (α)
227. Osmium-188 (α)
228. Osmium-189 (α)
229. Osmium-190 (α)
230. Osmium-192 (α, 2B)*
231. Iridium-191 (α)
232. Iridium-193 (α)
     Platinum-190 (α) – long-lived primordial radionuclide (2E also predicted possible)
233. Platinum-192 (α)*
234. Platinum-194 (α)
235. Platinum-195 (α)*
236. Platinum-196 (α)
237. Platinum-198 (α, 2B)*
238. Gold-197 (α)
239. Mercury-196 (α, 2E)*
240. Mercury-198 (α)
241. Mercury-199 (α)
242. Mercury-200 (α)
243. Mercury-201 (α)
244. Mercury-202 (α)
245. Mercury-204 (2B)
246. Thallium-203 (α)
247. Thallium-205 (α)
248. Lead-204 (α)*
249. Lead-206 (α)*
250. Lead-207 (α)*
251. Lead-208 (α)*
     Bismuth ^^ and above –

     no stable isotopes

     no mass number 209 and above
     Bismuth-209 (α) – long-lived primordial radionuclide
     Thorium-232 (α, SF) – long-lived primordial radionuclide (2B also predicted possible)
     Uranium-235 (α, SF) – long-lived primordial radionuclide
     Uranium-238 (α, 2B, SF) – long-lived primordial radionuclide
     Plutonium-244 (α, SF) – probable long-lived primordial radionuclide (2B also predicted possible)

Abbreviations for predicted unobserved decay:

α 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 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 is an "observationally stable" primordial nuclide, a rare isotope of tantalum. This is the only nuclear isomer with a half-life so long that it has never been observed to decay. It is thus included in this list.

^^ Bismuth-209 was long believed to be stable, due to its 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 4.62×10¹⁸ years and 1.066×10¹¹ years, respectively.

See also

• Isotope geochemistry
• List of elements by stability of isotopes
• List of nuclides (991 nuclides in order of stability, all with half-lives over one hour)
• Mononuclidic element
• Periodic table
• Primordial nuclide
• Radionuclide
• Stable isotope ratio
• Table of nuclides
• Valley of stability

References

1. "DOE explains ... Isotopes". Department of Energy, United States. Archived from the original on 14 April 2022. Retrieved 11 January 2023.
2. 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. Bibcode:2016JPhG...43j5102K. 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. "NNDC – Atomic Masses". www.nndc.bnl.gov. Archived from the original on 2019-01-11. Retrieved 2009-01-17.
10. Nucleonica website
11. 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.
12. "Nucleonica :: Web driven nuclear science".

Book references

• 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.

External links

• The LIVEChart of Nuclides – IAEA
• AlphaDelta: Stable Isotope fractionation calculator
• National Isotope Development Center Reference information on isotopes, and coordination and management of isotope production, availability, and distribution
• Isotope Development & Production for Research and Applications (IDPRA) U.S. Department of Energy program for isotope production and production research and development
• Isosciences Archived 2021-01-18 at the Wayback Machine Use and development of stable isotope labels in synthetic and biological molecules