Primordial nuclide

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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.

All of the known 251 stable nuclides, plus another 35 nuclides that have half-lives long enough to have survived from the formation of the Earth, occur as primordial nuclides. These 35 primordial radionuclides represent isotopes of 28 separate elements. Cadmium, tellurium, xenon, neodymium, samarium, osmium, and uranium each have two primordial radioisotopes (¹¹³
Cd
, ¹¹⁶
Cd
; ¹²⁸
Te
, ¹³⁰
Te
; ¹²⁴
Xe
, ¹³⁶
Xe
; ¹⁴⁴
Nd
, ¹⁵⁰
Nd
; ¹⁴⁷
Sm
, ¹⁴⁸
Sm
; ¹⁸⁴
Os
, ¹⁸⁶
Os
; and ²³⁵
U
, ²³⁸
U
).

Because the age of the Earth is 4.58×10⁹ years (4.6 billion years), the half-life of the given nuclides must be greater than about 10⁸ years (100 million years) for practical considerations. For example, for a nuclide with half-life 6×10⁷ years (60 million years), this means 77 half-lives have elapsed, meaning that for each mole (6.02×10²³ atoms) of that nuclide being present at the formation of Earth, only 4 atoms remain today.

The seven shortest-lived primordial nuclides (i.e., the nuclides with the shortest half-lives) to have been experimentally verified are ⁸⁷
Rb
(5.0×10¹⁰ years), ¹⁸⁷
Re
(4.1×10¹⁰ years), ¹⁷⁶
Lu
(3.8×10¹⁰ years), ²³²
Th
(1.4×10¹⁰ years), ²³⁸
U
(4.5×10⁹ years), ⁴⁰
K
(1.25×10⁹ years), and ²³⁵
U
(7.0×10⁸ years).

These are the seven nuclides with half-lives comparable to, or somewhat less than, the estimated age of the universe. (⁸⁷Rb, ¹⁸⁷Re, ¹⁷⁶Lu, and ²³²Th have half-lives somewhat longer than the age of the universe.) For a complete list of the 35 known primordial radionuclides, including the next 28 with half-lives much longer than the age of the universe, see the complete list below. For practical purposes, nuclides with half-lives much longer than the age of the universe may be treated as if they were stable. ⁸⁷Rb, ¹⁸⁷Re, ¹⁷⁶Lu, ²³²Th, and ²³⁸U have half-lives long enough that their decay is limited over geological time scales; ⁴⁰K and ²³⁵U have shorter half-lives and are hence severely depleted, but are still long-lived enough to persist significantly in nature.

The longest-lived isotope not proven to be primordial^[1] is ¹⁴⁶
Sm
, which has a half-life of 1.03×10⁸ years, followed by ²⁴⁴
Pu
(8.08×10⁷ years) and ⁹²
Nb
(3.5×10⁷ years). ²⁴⁴Pu was reported to exist in nature as a primordial nuclide in 1971,^[2] but this detection could not be confirmed by further studies in 2012 and 2022.^[3][4]

Taking into account that all these nuclides must exist for at least 4.6×10⁹ years, ¹⁴⁶Sm must survive 45 half-lives (and hence be reduced by 2⁴⁵ ≈ 4×10¹³), ²⁴⁴Pu must survive 57 (and be reduced by a factor of 2⁵⁷ ≈ 1×10¹⁷), and ⁹²Nb must survive 130 (and be reduced by 2¹³⁰ ≈ 1×10³⁹). Mathematically, considering the likely initial abundances of these nuclides, primordial ¹⁴⁶Sm and ²⁴⁴Pu should persist somewhere within the Earth today, even if they are not identifiable in the relatively minor portion of the Earth's crust available to human assays, while ⁹²Nb and all shorter-lived nuclides should not. Nuclides such as ⁹²Nb that were present in the primordial solar nebula but have long since decayed away completely are termed extinct radionuclides if they have no other means of being regenerated.^[5] As for ²⁴⁴Pu, calculations suggest that as of 2022, sensitivity limits were about one order of magnitude away from detecting it as a primordial nuclide.^[4]

Because primordial chemical elements often consist of more than one primordial isotope, there are only 83 distinct primordial chemical elements. Of these, 80 have at least one observationally stable isotope and three additional primordial elements have only radioactive isotopes (bismuth, thorium, and uranium).

Some unstable isotopes which occur naturally (such as ¹⁴
C
, ³
H
, and ²³⁹
Pu
) are not primordial, as they must be constantly regenerated. This occurs by cosmic radiation (in the case of cosmogenic nuclides such as ¹⁴
C
and ³
H
), or (rarely) by such processes as geonuclear transmutation (neutron capture of uranium in the case of ²³⁷
Np
and ²³⁹
Pu
). Other examples of common naturally occurring but non-primordial nuclides are isotopes of radon, polonium, and radium, which are all radiogenic nuclide daughters of uranium decay and are found in uranium ores. The stable argon isotope ⁴⁰Ar is actually more common as a radiogenic nuclide than as a primordial nuclide, forming almost 1% of the Earth's atmosphere, which is regenerated by the beta decay of the extremely long-lived radioactive primordial isotope ⁴⁰K, whose half-life is on the order of a billion years and thus has been generating argon since early in the Earth's existence. (Primordial argon was dominated by the alpha process nuclide ³⁶Ar, which is significantly rarer than ⁴⁰Ar on Earth.)

A similar radiogenic series is derived from the long-lived radioactive primordial nuclide ²³²Th. These nuclides are described as geogenic, meaning that they are decay or fission products of uranium or other actinides in subsurface rocks.^[6] All such nuclides have shorter half-lives than their parent radioactive primordial nuclides. Some other geogenic nuclides do not occur in the decay chains of ²³²Th, ²³⁵U, or ²³⁸U but can still fleetingly occur naturally as products of the spontaneous fission of one of these three long-lived nuclides, such as ¹²⁶Sn, which makes up about 10⁻¹⁴ of all natural tin.^[7] Another, ⁹⁹Tc, has also been detected.^[8] There are five other long-lived fission products known.

A primordial element is a chemical element with at least one primordial nuclide. There are 251 stable primordial nuclides and 35 radioactive primordial nuclides, but only 80 primordial stable elements—hydrogen through lead, atomic numbers 1 to 82, with the exceptions of technetium (43) and promethium (61)—and three radioactive primordial elements—bismuth (83), thorium (90), and uranium (92). If plutonium (94) turns out to be primordial (specifically, the long-lived isotope ²⁴⁴Pu), then it would be a fourth radioactive primordial, though practically speaking it would still be more convenient to produce synthetically. Bismuth's half-life is so long that it is often classed with the 80 primordial stable elements instead, since its radioactivity is not a cause for serious concern. The number of elements is smaller than the number of nuclides, because many of the primordial elements are represented by multiple isotopes. See chemical element for more information.

As noted, these number about 251. For a list, see the article list of elements by stability of isotopes. For a complete list noting which of the "stable" 251 nuclides may be in some respect unstable, see list of nuclides and stable nuclide. These questions do not impact the question of whether a nuclide is primordial, since all "nearly stable" nuclides, with half-lives longer than the age of the universe, are also primordial.

Although it is estimated that about 35 primordial nuclides are radioactive (list below), it becomes very difficult to determine the exact total number of radioactive primordials, because the total number of stable nuclides is uncertain. There exist many extremely long-lived nuclides whose half-lives are still unknown, in fact, all nuclides heavier than dysprosium-164 are theoretically radioactive. For example, it is predicted theoretically that all isotopes of tungsten, including those indicated by even the most modern empirical methods to be stable, must be radioactive and can decay by alpha emission, but as of 2013^[update] this could only be measured experimentally for ¹⁸⁰
W
.^[9] Similarly, all four primordial isotopes of lead are expected to decay to mercury, but the predicted half-lives are so long (some exceeding 10¹⁰⁰ years) that such decays could hardly be observed in the near future. Nevertheless, the number of nuclides with half-lives so long that they cannot be measured with present instruments—and are considered from this viewpoint to be stable nuclides—is limited. Even when a "stable" nuclide is found to be radioactive, it merely moves from the stable to the unstable list of primordial nuclides, and the total number of primordial nuclides remains unchanged. For practical purposes, these nuclides may be considered stable for all purposes outside specialized research.^{[citation needed]}

These 35 primordial nuclides represent radioisotopes of 28 distinct chemical elements (cadmium, neodymium, osmium, samarium, tellurium, uranium, and xenon each have two primordial radioisotopes). The radionuclides are listed in order of stability, with the longest half-life beginning the list. These radionuclides in many cases are so nearly stable that they compete for abundance with stable isotopes of their respective elements. For three chemical elements, indium, tellurium, and rhenium, a very long-lived radioactive primordial nuclide is found in greater abundance than a stable nuclide.

The longest-lived radionuclide known, ¹²⁸Te, has a half-life of 2.2×10²⁴ years, which is 160 trillion times the age of the Universe. Only four of these 35 nuclides have half-lives shorter than, or equal to, the age of the universe. Most of the remaining 30 have half-lives much longer. The shortest-lived primordial isotope, ²³⁵U, has a half-life of 703.8 million years, about one sixth of the age of the Earth and the Solar System. Many of these nuclides decay by double beta decay, although some like ²⁰⁹Bi decay by other methods such as alpha decay.

At the end of the list, two more nuclides have been added: ¹⁴⁶Sm and ²⁴⁴Pu. They have not been confirmed as primordial, but their half-lives are long enough that minute quantities should persist today.

No. (number)

A running positive integer for reference. These numbers may change slightly in the future since there are 251 nuclides now classified as stable, but which are theoretically predicted to be unstable (see Stable nuclide § Still-unobserved decay), so that future experiments may show that some are in fact unstable. The number starts at 252, to follow the 251 (observationally) stable nuclides.

Nuclide

Nuclide identifiers are given by their mass number A and the symbol for the corresponding chemical element (implies a unique proton number).

Energy

Mass of the average nucleon of this nuclide relative to the mass of a neutron (so all nuclides get a positive value) in MeV/c², formally: m_n − m_nuclide / A.

Half-life

All times are given in years.

Decay mode

α	α decay
β−	β− decay
K	electron capture
KK	double electron capture
β+	β+ decay
SF	spontaneous fission
2 β−	double β− decay
2 β+	double β+ decay
I	isomeric transition
p	proton emission
n	neutron emission

Decay energy

Multiple values for (maximal) decay energy in MeV are mapped to decay modes in their order.

• Alpha nuclide
• Table of nuclides sorted by half-life
• Table of nuclides
• Isotope geochemistry
• Radionuclide
• Mononuclidic element
• Monoisotopic element
• Stable isotope
• List of nuclides
• List of elements by stability of isotopes
• Big Bang nucleosynthesis