View source for Oddo–Harkins rule

{{Short description|Relative abundance of chemical elements}}
The '''Oddo–Harkins rule''' holds that an [[chemical element|element]] with an [[Even and odd atomic nuclei|even atomic number]] is [[Abundance of the chemical elements|more abundant]] than the elements with immediately adjacent [[Atomic number|atomic numbers]]. For example, [[carbon]], with atomic number 6, is more abundant than [[boron]] (5) and [[nitrogen]] (7). Generally, the relative abundance of an even atomic numbered element is roughly two orders of magnitude greater than the relative abundances of the immediately adjacent odd atomic numbered elements to either side.  This pattern was first reported by [[Giuseppe Oddo]]<ref>{{cite journal | doi = 10.1002/zaac.19140870118 | title = Die Molekularstruktur der radioaktiven Atome | year = 1914 | last1 = Oddo | first1 = Giuseppe | journal = Zeitschrift für Anorganische Chemie | lang = de | volume = 87 | pages = 253–268| url = https://zenodo.org/record/1428150 }}</ref> in 1914 and [[William Draper Harkins]]<ref>{{cite journal | doi = 10.1021/ja02250a002 | year = 1917 | last1 = Harkins | first1 = William D. | title = The Evolution of the Elements and the Stability of Complex Atoms | journal = Journal of the American Chemical Society | volume = 39 | issue = 5 | pages = 856–879| url = https://zenodo.org/record/1429060 }}</ref> in 1917.<ref name="north">{{cite book |last=North |first=John |title=Cosmos an illustrated history of astronomy and cosmology |year=2008 |publisher=Univ. of Chicago Press |isbn=978-0-226-59441-5 |pages=602 |url=https://books.google.com/books?id=qq8Luhs7rTUC&q=%22william+draper+harkins%22+oddo&pg=PA602 |edition=Rev. and updated}}</ref><ref>This secondary reference only calls it Harkins rule. {{Cite journal |last1=Suess |first1=Hans E. |url=https://link.aps.org/doi/10.1103/RevModPhys.28.53 |title=Abundances of the Elements |last2=Urey |first2=Harold C. |journal=Reviews of Modern Physics |date=1956-01-01 |volume=28 |pages=53–74 |language=en |doi=10.1103/RevModPhys.28.53 |issn=0034-6861}}</ref> The Oddo–Harkins rule is true for all elements beginning with carbon produced by [[stellar nucleosynthesis]] but not true for the lightest elements below carbon produced by [[Big Bang nucleosynthesis|big bang nucleosynthesis]] and [[cosmic ray spallation]].{{cn|date=March 2024}}

[[Image:SolarSystemAbundances.svg|thumb|right|600px|Estimated abundances of the chemical elements in the solar system]]

==Definitions==
[[File:Elemental abundances.svg|thumb|Abundance of elements in [[Earth's crust]] per million Si atoms (''y'' axis is logarithmic); the Oddo–Harkins rule is visible for most of the metallic elements.|200x200px]]
All [[atoms]] heavier than [[hydrogen]] are formed in stars or supernovae through [[nucleosynthesis]], when [[gravity]], [[temperature]] and [[pressure]] reach levels high enough to fuse [[protons]] and [[neutrons]] together. Protons and neutrons form the [[atomic nucleus]], which accumulates [[Electron|electrons]] to form atoms. The number of protons in the nucleus, called atomic number, uniquely identifies a chemical element.

== The rule ==
The early form of the rule derived from Harkin's 1917 study of meteorites. He reasoned, as did others at the time, that meteorites are more representative of the cosmological abundance of the elements. Harkins observed that elements with even atomic numbers (''Z'') were about 70 times more abundant than those with odd ''Z''. The most common seven elements, making up almost 99% of the material in a meteorite, all had even ''Z''. In addition, he observed that 90% of the material consisted of only 15 different isotopes, with atomic weights in multiples of four, the approximate weight of [[alpha particles]]. Three years earlier, Oddo made a similar observation for elements in the Earth's crust, speculating that elements are condensation products of [[helium]]. The nuclear core of helium is the same as an alpha particle.<ref name=KraghGeochemsitry>{{Cite journal |last=Kragh |first=Helge |date=2000 |title=An Unlikely Connection: Geochemistry and Nuclear Structure |url=http://link.springer.com/10.1007/s000160050051 |journal=Physics in Perspective |volume=2 |issue=4 |pages=381 |doi=10.1007/s000160050051 |bibcode=2000PhP.....2..381K }}</ref>{{rp|385}}
This early work connecting geochemistry with nuclear physics and cosmology was greatly expanded by the Norwegian group created by [[Victor Goldschmidt]].<ref name=KraghGeochemsitry/>{{rp|389}}

== Relation to stellar nucleosynthesis ==
[[File:Light nuclide abundance and origins hi res.png|thumb|450x450px|Nucleosynthetic origins of light nuclides. The most abundant nuclides have equal numbers of protons and neutrons (box around isotopic symbol). Products of cosmic-ray spallation are the least abundant.]] 
The Oddo–Harkins rule for elements from <sup>12</sup>C to <sup>56</sup>Fe is explained by the [[alpha process]] of [[stellar nucleosynthesis]].<ref>{{Cite book |last=Faure |first=Gunter |title=Introduction to planetary science: the geological perspective |last2=Mensing |first2=Teresa M. |date=2007 |publisher=Springer |isbn=978-1-4020-5544-7 |location=Dordrecht}}</ref>{{rp|42}} The process involves the fusion of alpha particles (helium-4 nuclei) under high temperature and pressure within the stellar environment. Each step in the alpha process adds two protons (and two neutrons), favoring synthesis of even-numbered elements. Carbon itself is a product of a [[triple-alpha process]] from helium, a process that skips Li, Be, and B. These nuclides (and helium-3) are produced by [[cosmic ray spallation]]{{snd}} a type of nuclear fission in which cosmic rays impact larger isotopes and fragment them. Spallation does not require high temperature and pressure of the stellar environment but can occur on Earth. Though the lighter products of spallation are relatively rare, the odd-mass-number isotopes in this class occur in greater relative abundance compared to even-number isotopes, in contravention of the Oddo–Harkins rule.

==Exceptions to the rule==
This postulate, however, does not apply to the universe's most abundant and simplest element: [[hydrogen]], with an atomic number of 1. This may be because, in its ionized form, a hydrogen atom becomes a single proton, of which it is theorized to have been one of the first major conglomerates of [[quarks]] during the initial second of the [[cosmic inflation|Universe's inflation period]], following the [[Big Bang]]. In this period, when inflation of the universe had brought it from an infinitesimal point to about the size of a modern galaxy, temperatures in the particle soup fell from over a trillion [[kelvin]]s to several million kelvins.

This period allowed the [[Nuclear fusion|fusion]] of single protons and [[deuterium]] nuclei to form [[helium]] and [[lithium]] nuclei but was too short for every H<sup>+</sup> ion to be reconstituted into heavier elements. In this case, helium, atomic number 2, remains the even-numbered counterpart to hydrogen. Thus, neutral hydrogen—or hydrogen paired with an [[electron]], the only stable [[lepton]]—constituted the vast majority of the remaining [[annihilation|unannihilated]] portions of matter following the conclusion of inflation.

Another exception to the rule is [[beryllium]], which, despite an even atomic number (4), is rarer than adjacent elements ([[lithium]] and [[boron]]). This is because most of the universe's lithium, beryllium, and boron are made by [[cosmic ray spallation]], not ordinary [[stellar nucleosynthesis]], and beryllium has only one stable isotope (even that is a [[Borromean nucleus]] near the boundary of stability), causing it to lag in abundance with regard to its neighbors, each of which has two stable isotopes.

== Isotopic abundance ==
[[File:Nucleonic_symmetry_of_the_most_abundant_isotopes.png|thumb|A plot of the stable isotopic compositions of the first 16 elements, which make up 99.9% of ordinary matter in the universe.<ref name=":0">{{Cite journal |last1=Rosman |first1=K. J. R. |last2=Taylor |first2=P. D. P. |date=1998-11-01 |title=Isotopic Compositions of the Elements 1997 |url=https://pubs.aip.org/jpr/article/27/6/1275/241811/Isotopic-Compositions-of-the-Elements-1997 |journal=Journal of Physical and Chemical Reference Data |language=en |volume=27 |issue=6 |pages=1275–1287 |doi=10.1063/1.556031 |issn=0047-2689}}</ref> Isotopes with equal numbers of protons and neutrons [boxes] are particularly abundant.|450x450px]]
The elemental basis of the Oddo–Harkins has direct roots in the isotopic compositions of the elements.<ref name=":0" /> While even-atomic-numbered elements are more abundant than odd, the spirit of Oddo–Harkins rule extends to the most abundant [[isotope]]s as well. Isotopes containing an equal number of protons and neutrons are the most abundant. These include <chem>^{4}_{2}He</chem>, <chem>^{12}_{6}C</chem>, <chem>^{14}_{7}N</chem>, <chem>^{16}_{8}O</chem>, <chem>^{20}_{10}Ne</chem>, <chem>^{24}_{12}Mg</chem>, <chem>^{28}_{14}Si</chem>, and <chem>^{32}_{16}S</chem>. Seven of the eight are [[alpha nuclide]]s containing whole multiples of He-4 nuclei (<chem>^{14}_{7}N</chem> is the exception). Two of the eight (<chem>^{4}_{2}He</chem> and <chem>^{16}_{8}O</chem>) contain [[Magic number (physics)|magic numbers]] of either protons or neutrons (2, 8, 20, 28, 50, 82, and 126) and are therefore predicted by the [[nuclear shell model]] to be unusually abundant. The high abundances of the remaining six (<chem>^{12}_{6}C</chem>, <chem>^{14}_{7}N</chem>, <chem>^{20}_{10}Ne</chem>, <chem>^{24}_{12}Mg</chem>, <chem>^{28}_{14}Si</chem>, and  <chem>^{32}_{16}S</chem>) are not predicted by the shell model. "That nuclei of this type are unusually abundant indicates that the excess stability must have played a part in the process of the creation of elements", stated [[Maria Goeppert Mayer]] in her acceptance lecture for the Nobel Prize in Physics in 1963 for discoveries concerning nuclear shell structure.<ref>{{Cite web |title=The Nobel Prize in Physics 1963 |url=https://www.nobelprize.org/prizes/physics/1963/summary/ |access-date=2024-02-01 |website=NobelPrize.org |language=en-US}}</ref>

The Oddo–Harkins rule may suggest that elements with odd atomic numbers have a single, unpaired proton and may swiftly capture another in order to achieve an even atomic number and proton parity. Protons are paired in elements with even atomic numbers, with each member of the pair balancing the spin of the other, thus enhancing nucleon stability. A challenge to this explanation is posed by <chem>^{14}_{7}N</chem>, which is highly abundant in spite of having an unpaired proton. Additionally, even-parity isotopes that have exactly two more neutrons than protons are not particularly abundant despite their even parity. Each of the light elements oxygen, neon, magnesium, silicon, and sulfur, have two isotopes with even isospin (nucleon) parity. As shown in the plot above, the isotope with an ''equal'' number of protons and neutrons is one to two orders of magnitude more abundant than the isotope with even parity but two additional neutrons. This may leave open the role of parity in abundance. The structural or subatomic basis of the unusual abundances of equinucleonic isotopes in baryonic matter is one of the simplest and most profound unsolved mysteries of the atomic nucleus.{{cn|date=May 2024}}

===Relationship to fusion===
Depending on the mass of a star, the Oddo–Harkins pattern arises from the burning of progressively more massive elements within a collapsing dying  star by fusion processes such as the [[proton–proton chain]], the [[CNO cycle]], and the [[triple-alpha process]]. The newly formed elements are ejected slowly as [[stellar wind]] or in the explosion of a [[supernova]] and eventually join the rest of the galaxy's [[interstellar medium]].

==See also==
* {{annotated link|Abundance of elements in Earth's crust}}
* {{annotated link|List of elements by stability of isotopes}}
* {{annotated link|Nuclear chemistry}}

==References==
{{reflist}}

{{DEFAULTSORT:Oddo-Harkins rule}}
[[Category:Eponymous chemical rules]]
[[Category:Nuclear chemistry]]