Mattauch isobar rule

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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 the isotopes must be radioactive. [1] [2] 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 (at least to beta decay or double beta decay), but many such nuclides which are theoretically unstable to double beta decay have not been observed to decay, e.g. 134Xe. [1] However, this rule cannot make predictions on the half-lives of these radioisotopes. [1]

Contents

Technetium and promethium

A consequence of this rule is that technetium and promethium both have no stable isotopes, as each of the neighboring elements on the periodic table (molybdenum and ruthenium, and neodymium and samarium, respectively) have a beta-stable isotope for each mass number for the range in which the isotopes of the unstable elements usually would be stable to beta decay. (Note that although 147Sm is unstable, it is stable to beta decay; thus 147 is not a counterexample). [1] [2] These ranges can be calculated using the liquid drop model (for example the stability of technetium isotopes), in which the isobar with the lowest mass excess or greatest binding energy is shown to be stable to beta decay [3] because energy conservation forbids a spontaneous transition to a less stable state. [4]

Thus no stable nuclides have proton number 43 or 61, and by the same reasoning no stable nuclides have neutron number 19, 21, 35, 39, 45, 61, 71, 89, 115, or 123.

Exceptions

The only known exceptions to the Mattauch isobar rule are the cases of antimony-123 and tellurium-123 and of hafnium-180 and tantalum-180m, where both nuclei are observationally stable. It is predicted that 123Te would undergo electron capture to form 123Sb, but this decay has not yet been observed; 180mTa should be able to undergo isomeric transition to 180Ta, beta decay to 180W, electron capture to 180Hf, or alpha decay to 176Lu, but none of these decay modes have been observed. [5]

In addition, beta decay has been seen for neither curium-247 nor berkelium-247, though it is expected that the former should decay into the latter. Both nuclides are alpha-unstable.

As mentioned above, the Mattauch isobar rule cannot make predictions as to the half-lives of the beta-unstable isotopes. Hence there are a few cases where isobars of adjacent elements both occur primordially, as the half-life of the unstable isobar is over a billion years. This occurs for the following mass numbers:

See also

Related Research Articles

<span class="mw-page-title-main">Beta decay</span> Type of radioactive decay

In nuclear physics, beta decay (β-decay) is a type of radioactive decay in which an atomic nucleus emits a beta particle, transforming into an isobar of that nuclide. For example, beta decay of a neutron transforms it into a proton by the emission of an electron accompanied by an antineutrino; or, conversely a proton is converted into a neutron by the emission of a positron with a neutrino in what is called positron emission. Neither the beta particle nor its associated (anti-)neutrino exist within the nucleus prior to beta decay, but are created in the decay process. By this process, unstable atoms obtain a more stable ratio of protons to neutrons. The probability of a nuclide decaying due to beta and other forms of decay is determined by its nuclear binding energy. The binding energies of all existing nuclides form what is called the nuclear band or valley of stability. For either electron or positron emission to be energetically possible, the energy release or Q value must be positive.

A chemical element is a chemical substance whose atoms all have the same number of protons. The number of protons is called the atomic number of that element. For example, oxygen has an atomic number of 8, meaning each oxygen atom has 8 protons in its nucleus. Atoms of the same element can have different numbers of neutrons in their nuclei, known as isotopes of the element. Two or more atoms can combine to form molecules. Some elements are formed from molecules of identical atoms, e. g. atoms of hydrogen (H) form diatomic molecules (H2). Chemical compounds are substances made of atoms of different elements; they can have molecular or non-molecular structure. Mixtures are materials containing different chemical substances; that means (in case of molecular substances) that they contain different types of molecules. Atoms of one element can be transformed into atoms of a different element in nuclear reactions, which change an atom's atomic number.

<span class="mw-page-title-main">Promethium</span> Chemical element with atomic number 61 (Pm)

Promethium is a chemical element with symbol Pm and atomic number 61. All of its isotopes are radioactive; it is extremely rare, with only about 500–600 grams naturally occurring in the Earth's crust at any given time. Promethium is one of the only two radioactive elements that are both preceded and followed in the periodic table by elements with stable forms, the other being technetium. Chemically, promethium is a lanthanide. Promethium shows only one stable oxidation state of +3.

<span class="mw-page-title-main">Stable nuclide</span> Nuclide that does not undergo radioactive decay

Stable nuclides are isotopes of a chemical element whose nucleons are in a configuration that does not permit them the surplus energy required to produce a radioactive emission. The nuclei of such isotopes are not radioactive and unlike radionuclides do not spontaneously undergo radioactive decay. When these nuclides are referred to in relation to specific elements they are usually called that element's stable isotopes.

<span class="mw-page-title-main">Electron capture</span> Process in which a proton-rich nuclide absorbs an inner atomic electron

Electron capture is a process in which the proton-rich nucleus of an electrically neutral atom absorbs an inner atomic electron, usually from the K or L electron shells. This process thereby changes a nuclear proton to a neutron and simultaneously causes the emission of an electron neutrino.

<span class="mw-page-title-main">Nuclide</span> Atomic species

Nuclides are a class of atoms characterized by their number of protons, Z, their number of neutrons, N, and their nuclear energy state.

<span class="mw-page-title-main">Magic number (physics)</span> Number of protons or neutrons that make a nucleus particularly stable

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.

<span class="mw-page-title-main">Mass number</span> Number of heavy particles in the atomic nucleus

The mass number (symbol A, from the German word: Atomgewicht, "atomic weight"), also called atomic mass number or nucleon number, is the total number of protons and neutrons (together known as nucleons) in an atomic nucleus. It is approximately equal to the atomic (also known as isotopic) mass of the atom expressed in atomic mass units. Since protons and neutrons are both baryons, the mass number A is identical with the baryon number B of the nucleus (and also of the whole atom or ion). The mass number is different for each isotope of a given chemical element, and the difference between the mass number and the atomic number Z gives the number of neutrons (N) in the nucleus: N = A − Z.

Natural tantalum (73Ta) consists of two stable isotopes: 181Ta (99.988%) and 180m
Ta
 (0.012%).

There are 39 known isotopes and 17 nuclear isomers of tellurium (52Te), with atomic masses that range from 104 to 142. These are listed in the table below.

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.

A table or chart of nuclides is a two-dimensional graph of isotopes of the elements, in which one axis represents the number of neutrons and the other represents the number of protons in the atomic nucleus. Each point plotted on the graph thus represents a nuclide of a known or hypothetical chemical element. This system of ordering nuclides can offer a greater insight into the characteristics of isotopes than the better-known periodic table, which shows only elements and not their isotopes. The chart of the nuclides is also known as the Segrè chart, after the Italian physicist Emilio Segrè.

<span class="mw-page-title-main">Neutron number</span> The number of neutrons in a nuclide

The neutron number is the number of neutrons in a nuclide.

<span class="mw-page-title-main">Isotope</span> Different atoms of the same element

Isotopes are distinct nuclear species of the same chemical element. They have the same atomic number and position in the periodic table, but different 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.

<span class="mw-page-title-main">Primordial nuclide</span> Nuclides predating the Earths formation (found on Earth)

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.

<span class="mw-page-title-main">Beta-decay stable isobars</span> Set of nuclides that cannot undergo beta decay

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.

<span class="mw-page-title-main">Isobar (nuclide)</span> Atoms of different elements with the same number of nucleons

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.

<span class="mw-page-title-main">Even and odd atomic nuclei</span> Nuclear physics classification method

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.

References

  1. 1 2 3 4 Thyssen, Pieter; Binnemans, Koen; Shinohara, Hisanori; Saito, Yahachi; Gulay, Lubomir D.; Daszkiewicz, Marek; Yan, Chun-Hua; Yan, Zheng-Guan; Du, Ya-Ping (2011). Gschneider, Karl A. Jr.; Bünzli, Jean-Claude; Pecharsky, Vitalij K. (eds.). Handbook on the Physics and Chemistry of Rare Earths. Amsterdam, The Netherlands: Elsevier. p. 66. ISBN   978-0-444-53590-0 . Retrieved January 14, 2012.
  2. 1 2 Holleman, Arnold Frederik; Wiberg, Egon (2001), Wiberg, Nils (ed.), Inorganic Chemistry, translated by Eagleson, Mary; Brewer, William, San Diego/Berlin: Academic Press/De Gruyter, p. 84, ISBN   0-12-352651-5
  3. ↑ Wang, M.; Audi, G.; Kondev, F. G.; Huang, W. J.; Naimi, S.; Xu, X. (2017). "The AME2016 atomic mass evaluation (II). Tables, graphs, and references" (PDF). Chinese Physics C. 41 (3): 030003-1–030003-442. doi:10.1088/1674-1137/41/3/030003.
  4. ↑ K.S. Krane (1988). Introductory Nuclear Physics . John Wiley & Sons. p.  381. ISBN   978-0-471-80553-3.
  5. ↑ Sonzogni, Alejandro. "Interactive Chart of Nuclides". National Nuclear Data Center: Brookhaven National Laboratory. Retrieved 27 November 2012.
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