Stable nuclide

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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

(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

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 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

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 (

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

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.

Still-unobserved decay

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

.

Isotopes that are theoretically believed to be unstable but have not been observed to decay are termed as 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 "

.

146 nuclides from 62 elements with

For processes other than spontaneous fission, other theoretical decay routes for heavier elements include:[10]

• 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.

The positivity of energy release in these processes means that they are allowed kinematically (they do not violate the conservation of energy) and, thus, in principle, can occur.[10] 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. 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 known decay modes, including isomeric transition, and double beta decay	146	146	Contains 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; also, 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[2][11]	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 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.