Stable isotope

Stable isotope ratio

Small differences in the relative abundance of two isotopes of one element have wide scientific and technological applications. The relative abundance is expressed as a ratio and compared to reference standards. These stable isotope ratios can be used to determine the West African Monsoon over the last 155,000 years, the feeding patterns of moulting seabirds, determine the style and country of origin of beer, mapping out ecological relationships and nutrient dynamics in aquatic ecosystems, and a wide variety of applications in isotope geochemistry.

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.

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 electrons 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 it 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.

Rare 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 but have not been observed 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) to 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, which is theoretically possible for the nuclides with atomic mass numbers ≥ 93, that is all those with atomic numbers ≥ 41.

Besides spontaneous fission, 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).

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.

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.

Lists of stable nuclides

The list of nuclides includes all stable nuclides as well as primordial radionuclides, and radionuclides of various half-lifes, totaling 991 nuclides in order of stability, all with half-lives over one hour. The table is based on the standard NUBASE 2020.