Beta-decay stable isobars are the set of nuclides which cannot undergo beta decay, that is, the transformation of a neutron to a proton or a proton to a neutron within the nucleus. A subset of these nuclides are also stable with regards to double beta decay or theoretically higher simultaneous beta decay, as they have the lowest energy of all isobars with the same mass number.
This set of nuclides is also known as the line of beta stability, a term already in common use in 1965. [1] [2] This line lies along the bottom of the nuclear valley of stability.
The line of beta stability can be defined mathematically by finding the nuclide with the greatest binding energy for a given mass number, by a model such as the classical semi-empirical mass formula developed by C. F. Weizsäcker. These nuclides are local maxima in terms of binding energy for a given mass number.
βDS | One | Two | Three |
---|---|---|---|
2-34 | 17 | ||
36-58 | 6 | 6 | |
60-72 | 5 | 2 | |
74-116 | 2 | 20 | |
118-154 | 2 | 12 | 5 |
156-192 | 5 | 14 | |
194-210 | 6 | 3 | |
212-262 | 7 | 19 | |
Total | 50 | 76 | 5 |
All odd mass numbers have only one beta decay stable nuclide.
Among even mass number, five (124, 130, 136, 150, 154) have three beta-stable nuclides. None have more than three; all others have either one or two.
All primordial nuclides are beta decay stable, with the exception of 40K, 50V, 87Rb, 113Cd, 115In, 138La, 176Lu, and 187Re. In addition, 123Te and 180mTa have not been observed to decay, but are believed to undergo beta decay with an extremely long half-life (over 1015 years). (123Te can only undergo electron capture to 123Sb, whereas 180mTa can decay in both directions, to 180Hf or 180W.) Among non-primordial nuclides, there are some other cases of theoretically possible but never-observed beta decay, notably including 222Rn and 247Cm (the most stable isotopes of their elements considering all decay modes). Finally, 48Ca and 96Zr have not been observed to undergo beta decay (which is theoretically possible for both), but double beta decay is known for both. All elements up to and including nobelium, except technetium and promethium, are known to have at least one beta-stable isotope.
350 beta-decay stable nuclides are currently known. [3] [4] Theoretically predicted or experimentally observed double beta-decay is shown by arrows, i.e. arrows point towards the lightest-mass isobar. This is sometimes dominated by alpha decay or spontaneous fission, especially for the heavy elements. Possible decay modes are listed as α for alpha decay, SF for spontaneous fission, and n for neutron emission in the special case of 5He. For mass 5 there are no bound isobars at all; there are bound isobars for mass 8, but the beta-stable one 8Be is unbound. [5]
Two beta-decay stable nuclides exist for odd neutron numbers 1 (2H and 3He), 3 (5He and 6Li – the former having an extremely short half-life), 5 (9Be and 10B), 7 (13C and 14N), 55 (97Mo and 99Ru), and 85 (145Nd and 147Sm); the first four cases involve very light nuclides where odd-odd nuclides are more stable than their surrounding even-even isobars, and the last two surround the proton numbers 43 and 61 which have no beta-stable isotopes. Also, two beta-decay stable nuclides exist for odd proton numbers 1, 3, 5, 7, 17, 19, 29, 31, 35, 47, 51, 63, 77, 81, and 95; the first four cases involve very light nuclides where odd-odd nuclides are more stable than their surrounding even-even isobars, and the other numbers surround the neutron numbers 19, 21, 35, 39, 45, 61, 71, 89, 115, 123, 147 which have no beta-stable isotopes. (For N = 21 the long-lived primordial 40K exists, and for N = 71 there is 123Te whose electron capture has not yet been observed, but neither are beta-stable.)
All even proton numbers 2 ≤ Z ≤ 102 have at least two beta-decay stable nuclides, with exactly two for Z = 4 (8Be and 9Be – the former having an extremely short half-life) and 6 (12C and 13C). Also, the only even neutron numbers with only one beta-decay stable nuclide are 0 (1H) and 2 (4He); at least two beta-decay stable nuclides exist for even neutron numbers in the range 4 ≤ N ≤ 160, with exactly two for N = 4 (7Li and 8Be), 6 (11B and 12C), 8 (15N and 16O), 66 (114Cd and 116Sn, noting also primordial but not beta-stable 115In), 120 (198Pt and 200Hg), and 128 (212Po and 214Rn – both very unstable to alpha decay). Seven beta-decay stable nuclides exist for the magic N = 82 (136Xe, 138Ba, 139La, 140Ce, 141Pr, 142Nd, and 144Sm) and five for N = 20 (36S, 37Cl, 38Ar, 39K, and 40Ca), 50 (86Kr, 88Sr, 89Y, 90Zr, and 92Mo, noting also primordial but not beta-stable 87Rb), 58 (100Mo, 102Ru, 103Rh, 104Pd, and 106Cd), 74 (124Sn, 126Te, 127I, 128Xe, and 130Ba), 78 (130Te, 132Xe, 133Cs, 134Ba, and 136Ce), 88 (148Nd, 150Sm, 151Eu, 152Gd, and 154Dy – the last not primordial), and 90 (150Nd, 152Sm, 153Eu, 154Gd, and 156Dy).
For A ≤ 209, the only beta-decay stable nuclides that are not primordial nuclides are 5He, 8Be, 146Sm, 150Gd, and 154Dy. (146Sm has a half-life long enough that it should barely survive as a primordial nuclide, but has never been experimentally confirmed as such.)
Even N | Odd N | |
---|---|---|
Even Z | Even A | Odd A |
Odd Z | Odd A | Even A |
Odd A | Even A | Odd A | Even A | Odd A | Even A | Odd A | Even A |
---|---|---|---|---|---|---|---|
1H | 2H | 3He | 4He | 5He (n) | 6Li | 7Li | 8Be (α) |
9Be | 10B | 11B | 12C | 13C | 14N | 15N | 16O |
17O | 18O | 19F | 20Ne | 21Ne | 22Ne | 23Na | 24Mg |
25Mg | 26Mg | 27Al | 28Si | 29Si | 30Si | 31P | 32S |
33S | 34S | 35Cl | 36S ← 36Ar | 37Cl | 38Ar | 39K | 40Ar ← 40Ca |
41K | 42Ca | 43Ca | 44Ca | 45Sc | 46Ca → 46Ti | 47Ti | 48Ti [lower-alpha 1] |
49Ti | 50Ti ← 50Cr | 51V | 52Cr | 53Cr | 54Cr ← 54Fe | 55Mn | 56Fe |
57Fe | 58Fe ← 58Ni | 59Co | 60Ni | 61Ni | 62Ni | 63Cu | 64Ni ← 64Zn |
65Cu | 66Zn | 67Zn | 68Zn | 69Ga | 70Zn → 70Ge | 71Ga | 72Ge |
73Ge | 74Ge ← 74Se | 75As | 76Ge → 76Se | 77Se | 78Se ← 78Kr | 79Br | 80Se → 80Kr |
81Br | 82Se → 82Kr | 83Kr | 84Kr ← 84Sr | 85Rb | 86Kr → 86Sr | 87Sr | 88Sr |
89Y | 90Zr | 91Zr | 92Zr ← 92Mo | 93Nb | 94Zr → 94Mo | 95Mo | 96Mo ← 96Ru [lower-alpha 2] |
97Mo | 98Mo → 98Ru | 99Ru | 100Mo → 100Ru | 101Ru | 102Ru ← 102Pd | 103Rh | 104Ru → 104Pd |
105Pd | 106Pd ← 106Cd | 107Ag | 108Pd ← 108Cd | 109Ag | 110Pd → 110Cd | 111Cd | 112Cd ← 112Sn |
113In | 114Cd → 114Sn | 115Sn | 116Cd → 116Sn | 117Sn | 118Sn | 119Sn | 120Sn ← 120Te |
121Sb | 122Sn → 122Te | 123Sb | 124Sn → 124Te ← 124Xe | 125Te | 126Te ← 126Xe | 127I | 128Te → 128Xe |
129Xe | 130Te → 130Xe ← 130Ba | 131Xe | 132Xe ← 132Ba | 133Cs | 134Xe → 134Ba | 135Ba | 136Xe → 136Ba ← 136Ce |
137Ba | 138Ba ← 138Ce | 139La | 140Ce | 141Pr | 142Ce → 142Nd | 143Nd | 144Nd (α) ← 144Sm |
145Nd | 146Nd → 146Sm (α) | 147Sm (α) | 148Nd → 148Sm (α) [lower-alpha 3] | 149Sm | 150Nd → 150Sm ← 150Gd (α) | 151Eu (α) | 152Sm ← 152Gd (α) |
153Eu | 154Sm → 154Gd ← 154Dy (α) | 155Gd | 156Gd ← 156Dy | 157Gd | 158Gd ← 158Dy | 159Tb | 160Gd → 160Dy |
161Dy | 162Dy ← 162Er | 163Dy | 164Dy ← 164Er | 165Ho | 166Er | 167Er | 168Er ← 168Yb |
169Tm | 170Er → 170Yb | 171Yb | 172Yb | 173Yb | 174Yb ← 174Hf (α) | 175Lu | 176Yb → 176Hf |
177Hf | 178Hf | 179Hf | 180Hf ← 180W (α) | 181Ta | 182W | 183W | 184W ← 184Os (α) |
185Re | 186W → 186Os (α) | 187Os | 188Os | 189Os | 190Os ← 190Pt (α) | 191Ir | 192Os → 192Pt |
193Ir | 194Pt | 195Pt | 196Pt ← 196Hg | 197Au | 198Pt → 198Hg | 199Hg | 200Hg |
201Hg | 202Hg | 203Tl | 204Hg → 204Pb | 205Tl | 206Pb | 207Pb | 208Pb |
209Bi (α) | 210Po (α) | 211Po (α) | 212Po (α) ← 212Rn (α) | 213Po (α) | 214Po (α) ← 214Rn (α) | 215At (α) | 216Po (α) → 216Rn (α) |
217Rn (α) | 218Rn (α) ← 218Ra (α) | 219Fr (α) | 220Rn (α) → 220Ra (α) | 221Ra (α) | 222Ra [lower-alpha 4] (α) | 223Ra (α) | 224Ra (α) ← 224Th (α) |
225Ac (α) | 226Ra (α) → 226Th (α) | 227Th (α) | 228Th (α) | 229Th (α) | 230Th (α) ← 230U (α) | 231Pa (α) | 232Th (α) → 232U (α) |
233U (α) | 234U (α) | 235U (α) | 236U (α) ← 236Pu (α) | 237Np (α) | 238U (α) → 238Pu (α) | 239Pu (α) | 240Pu (α) |
241Am (α) | 242Pu (α) ← 242Cm (α) | 243Am (α) | 244Pu (α) → 244Cm (α) | 245Cm (α) | 246Cm (α) | 247Bk (α) | 248Cm (α) → 248Cf (α) |
249Cf (α) | 250Cf (α) | 251Cf (α) | 252Cf (α) ← 252Fm (α) | 253Es (α) | 254Cf (SF) → 254Fm (α) | 255Fm (α) | 256Cf (SF) → 256Fm (SF) |
257Fm (α) | 258Fm (SF) ← 258No (SF) | 259Md (SF) | 260Fm (SF) → 260No (SF) | [lower-alpha 5] | 262No (SF) |
All beta-decay stable nuclides with A ≥ 209 are known to undergo alpha decay, though for some, spontaneous fission is the dominant decay mode. Cluster decay is sometimes also possible, but in all known cases it is a minor branch compared to alpha decay or spontaneous fission. Alpha decay is energetically possible for all beta-stable nuclides with A ≥ 165 with the single exception of 204Hg, but in most cases the Q-value is small enough that such decay has never been seen. [11] With the exception of 262No, no nuclides with A > 260 have been definitively identified as beta-stable. 260Fm and 262No are unconfirmed. [4] Moreover, the known beta-stable nuclei for individual masses A > 257 may not represent the complete set. [10] [12]
The general patterns of beta-stability are expected to continue into the region of superheavy elements, though the exact location of the center of the valley of stability is model dependent. It is widely believed that an island of stability exists along the beta stability line for isotopes of elements around copernicium that are stabilized by shell closures in the region; such isotopes would decay primarily through alpha decay or spontaneous fission. [13] Beyond the island of stability, various models that correctly predict many known beta-stable isotopes also predict anomalies in the beta-stability line that are unobserved in any known nuclides, such as the existence of two beta-stable nuclides with the same odd mass number. [10] [14] This is a consequence of the fact that a semi-empirical mass formula must consider shell correction and nuclear deformation, which become far more pronounced for heavy nuclides. [14] [15]
Beta decay generally causes nuclides to decay toward the isobar with the lowest mass (which is often, but not always, the one with highest binding energy) with the same mass number. Thus, those with lower atomic number and higher neutron number than the minimum-mass isobar undergo beta-minus decay, while those with higher atomic number and lower neutron number undergo beta-plus decay or electron capture. However, there are several nuclides that are exceptions, in that the majority of their decays are in the opposite direction:
Nuclide | Mass | Nuclide | Mass | Nuclide | Mass | Nuclide | Mass | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Parent | Cl-36 | 35.96830698 | K-40 | 39.96399848 | Ag-108 | 107.905956 | Eu-150m | 149.919747 | ||||
Minority decay (β+/EC) | 2% to S-36 | 35.96708076 | 11.2% to Ar-40 | 39.9623831225 | 3% to Pd-108 | 107.903892 | 11% to Sm-150 | 149.9172755 | ||||
Majority decay (β−) | 98% to Ar-36 | 35.967545106 | 89% to Ca-40 | 39.96259098 | 97% to Cd-108 | 107.904184 | 89% to Gd-150 | 149.918659 | ||||
Nuclide | Mass | Nuclide | Mass | Nuclide | Mass | Nuclide | Mass | |||||
Parent | Eu-152m1 | 151.9217935 | Tb-158m1 | 157.9255315 | Am-242 | 242.0595474 | ||||||
Minority decay (β+/EC) | 28% to Sm-152 | 151.9197324 | 0.01% to Gd-158 | 157.9241039 | 17.3% to Pu-242 [ electron capture, not beta+ ] | 242.0587426 | ||||||
Majority decay (β−) | 72% to Gd-152 | 151.9197910 | 0.6% to Dy-158 | 157.924409 | 82.7% to Cm-242 | 242.0588358 | ||||||
Nuclide | Mass | Nuclide | Mass | Nuclide | Mass | Nuclide | Mass | |||||
Parent | Pm-146 | 145.914696 | Es-254 | 254.088022 | ||||||||
Minority decay (β−) | 37% to Sm-146 | 145.913041 | 1.74×10−6% to Fm-254 | 254.0868544 | ||||||||
Majority decay (β+/EC) | 63% to Nd-146 [ citation needed ] | 145.9131169 | 10−4% to Cf-254 [ citation needed ] | 254.087323 |
Stable nuclides are nuclides that are not radioactive and so do not spontaneously undergo radioactive decay. When such nuclides are referred to in relation to specific elements, they are usually termed stable isotopes.
In nuclear physics, the island of stability is a predicted set of isotopes of superheavy elements that may have considerably longer half-lives than known isotopes of these elements. It is predicted to appear as an "island" in the chart of nuclides, separated from known stable and long-lived primordial radionuclides. Its theoretical existence is attributed to stabilizing effects of predicted "magic numbers" of protons and neutrons in the superheavy mass region.
Flerovium is a superheavy synthetic chemical element; it has symbol Fl and atomic number 114. It is an extremely radioactive synthetic element, named after the Flerov Laboratory of Nuclear Reactions of the Joint Institute for Nuclear Research in Dubna, Russia, where the element was discovered in 1999. The lab's name, in turn, honours Russian physicist Georgy Flyorov. IUPAC adopted the name on 30 May 2012. The name and symbol had previously been proposed for element 102 (nobelium), but was not accepted by IUPAC at that time.
A nuclide is a class of atoms characterized by their number of protons, Z, their number of neutrons, N, and their nuclear energy state.
In nuclear engineering, fissile material is material that can undergo nuclear fission when struck by a neutron of low energy. A self-sustaining thermal chain reaction can only be achieved with fissile material. The predominant neutron energy in a system may be typified by either slow neutrons or fast neutrons. Fissile material can be used to fuel thermal-neutron reactors, fast-neutron reactors and nuclear explosives.
In nuclear science, the decay chain refers to a series of radioactive decays of different radioactive decay products as a sequential series of transformations. It is also known as a "radioactive cascade". The typical radioisotope does not decay directly to a stable state, but rather it decays to another radioisotope. Thus there is usually a series of decays until the atom has become a stable isotope, meaning that the nucleus of the atom has reached a stable state.
In nuclear physics, a magic number is a number of nucleons such that they are arranged into complete shells within the atomic nucleus. As a result, atomic nuclei with a "magic" number of protons or neutrons are much more stable than other nuclei. The seven most widely recognized magic numbers as of 2019 are 2, 8, 20, 28, 50, 82, and 126.
Naturally occurring samarium (62Sm) is composed of five stable isotopes, 144Sm, 149Sm, 150Sm, 152Sm and 154Sm, and two extremely long-lived radioisotopes, 147Sm (half life: 1.06×1011 y) and 148Sm (6.3×1015 y), with 152Sm being the most abundant (26.75% natural abundance). 146Sm is also fairly long-lived, but is not long-lived enough to have survived in significant quantities from the formation of the Solar System on Earth, although it remains useful in radiometric dating in the Solar System as an extinct radionuclide. A 2012 paper revising the estimated half-life of 146Sm from 10.3(5)×107 y to 6.8(7)×107 y was retracted in 2023. It is the longest-lived nuclide that has not yet been confirmed to be primordial.
Technetium (43Tc) is one of the two elements with Z < 83 that have no stable isotopes; the other such element is promethium. It is primarily artificial, with only trace quantities existing in nature produced by spontaneous fission or neutron capture by molybdenum. The first isotopes to be synthesized were 97Tc and 99Tc in 1936, the first artificial element to be produced. The most stable radioisotopes are 97Tc, 98Tc, and 99Tc.
Calcium (20Ca) has 26 known isotopes, ranging from 35Ca to 60Ca. There are five stable isotopes, plus one isotope (48Ca) with such a long half-life that it is for all practical purposes stable. The most abundant isotope, 40Ca, as well as the rare 46Ca, are theoretically unstable on energetic grounds, but their decay has not been observed. Calcium also has a cosmogenic isotope, 41Ca, with half-life 99,400 years. Unlike cosmogenic isotopes that are produced in the air, 41Ca is produced by neutron activation of 40Ca. Most of its production is in the upper metre of the soil column, where the cosmogenic neutron flux is still strong enough. 41Ca has received much attention in stellar studies because it decays to 41K, a critical indicator of solar system anomalies. The most stable artificial isotopes are 45Ca with half-life 163 days and 47Ca with half-life 4.5 days. All other calcium isotopes have half-lives of minutes or less.
In nuclear physics, the valley of stability is a characterization of the stability of nuclides to radioactivity based on their binding energy. Nuclides are composed of protons and neutrons. The shape of the valley refers to the profile of binding energy as a function of the numbers of neutrons and protons, with the lowest part of the valley corresponding to the region of most stable nuclei. The line of stable nuclides down the center of the valley of stability is known as the line of beta stability. The sides of the valley correspond to increasing instability to beta decay. The decay of a nuclide becomes more energetically favorable the further it is from the line of beta stability. The boundaries of the valley correspond to the nuclear drip lines, where nuclides become so unstable they emit single protons or single neutrons. Regions of instability within the valley at high atomic number also include radioactive decay by alpha radiation or spontaneous fission. The shape of the valley is roughly an elongated paraboloid corresponding to the nuclide binding energies as a function of neutron and atomic numbers.
The neutron number is the number of neutrons in a nuclide.
Isotopes are distinct nuclear species of the same chemical element. They have the same atomic number and position in the periodic table, but differ in nucleon numbers due to different numbers of neutrons in their nuclei. While all isotopes of a given element have similar chemical properties, they have different atomic masses and physical properties.
In geochemistry, geophysics and nuclear physics, primordial nuclides, also known as primordial isotopes, are nuclides found on Earth that have existed in their current form since before Earth was formed. Primordial nuclides were present in the interstellar medium from which the solar system was formed, and were formed in, or after, the Big Bang, by nucleosynthesis in stars and supernovae followed by mass ejection, by cosmic ray spallation, and potentially from other processes. They are the stable nuclides plus the long-lived fraction of radionuclides surviving in the primordial solar nebula through planet accretion until the present; 286 such nuclides are known.
Isobars are atoms (nuclides) of different chemical elements that have the same number of nucleons. Correspondingly, isobars differ in atomic number but have the same mass number. An example of a series of isobars is 40S, 40Cl, 40Ar, 40K, and 40Ca. While the nuclei of these nuclides all contain 40 nucleons, they contain varying numbers of protons and neutrons.
The nuclear drip line is the boundary beyond which atomic nuclei are unbound with respect to the emission of a proton or neutron.
The Mattauch isobar rule, formulated by Josef Mattauch in 1934, states that if two adjacent elements on the periodic table have isotopes of the same mass number, one of these isotopes must be radioactive. Two nuclides that have the same mass number (isobars) can both be stable only if their atomic numbers differ by more than one. In fact, for currently observationally stable nuclides, the difference can only be 2 or 4, and in theory, two nuclides that have the same mass number cannot be both stable, but many such nuclides which are theoretically unstable to double beta decay have not been observed to decay, e.g. 134Xe. However, this rule cannot make predictions on the half-lives of these radioisotopes.
In nuclear physics, properties of a nucleus depend on evenness or oddness of its atomic number Z, neutron number N and, consequently, of their sum, the mass number A. Most importantly, oddness of both Z and N tends to lower the nuclear binding energy, making odd nuclei generally less stable. This effect is not only experimentally observed, but is included in the semi-empirical mass formula and explained by some other nuclear models, such as the nuclear shell model. This difference of nuclear binding energy between neighbouring nuclei, especially of odd-A isobars, has important consequences for beta decay.