Mattauch isobar rule

Under the Mattauch 's Isobarenregel, sometimes Isobarenregel, Mattauch'sche rule or Mattauch usually understood as an empirical rule of radiochemistry. It states that neighboring stable isobar, ie nuclides with the same mass number, do not occur, or in other words, that the difference of atomic numbers of two stable isobars is always greater than one. It is named after the German physicist Joseph Mattauch, who postulated in 1934.

Basics

By β - decay an isobar of the parent nuclide ( nuclide ) forms. Isobars are nuclei with the same number of nucleons, but which differ in the number of protons ( = atomic number Z) and neutrons. As an example, the β was - decay of to shown.

The nucleon number (198 ) remains the same, while the number of protons increases by one, which lowers the neutron by one. It forms the isobaric nuclide Hg.

The Mattauchsche Isobarenregel based on the fact that nuclei are particularly stable with an even number of protons and an even number of neutrons ( so-called G, G - cores, see droplets model). Those in which both odd numbers ( U, U - cores) are destabilized. The u, g and g, u cores lie between these two. In general, u, u - cores are not stable ( see below). If the parent nuclide, a g, g - core so formed by β -decay a u, u - core and vice versa, while incurred g - g cores, u cores u and vice versa:

Near the line of beta stability occurs as decay, apart from γ - decay, which, however, forms only one isomer, only β -decay to. Distance of the line to find no stable nuclides.

Description

The stabilities of the nuclei can be represented as parables, the parable of the unstable u, u - cores on the g, g - cores is. Starting from a core, the remote is the line of beta stability ( in the figure, for example, Z = n-4) is running, from a decay chain, the daughter nuclide of each β - decay is on the other parabola. The row ends when the line of the beta stability is reached, in this case with Z = N. The same is true for the series of β -decays starting at Z = n 4. However, this ends at the nuclide Z = n 2, since the u, u - core Z = n 1 is less stable. Only one double β -decay is the most stable nuclide can be obtained with Z = n.

Since the g, g parabola is always below the u, u - parabola, so can never be two adjacent stable isobars occur. An interesting feature is the core Z = n 1 represents, which can be obtained not by β -decays, but in other ways ( for example, by α -decays ). This core now has the opportunity to by a β - decay to Z = n 2 and stabilize by β decay to Z = n. Often such nuclei have both decay modes:

The Mattauchsche Isobarenregel applies to u, u - cores only for A > 14 For A ≤ 14, however, the parables are so strongly curved that the masses of a, u - nuclide neighboring g, g - nuclides are larger than that of u, u - nuclide itself, and this therefore u is stable. For A ≤ 14, there are four stable u, u - nuclides:

Starts the decay chain with a g, u or u, g - core, so the picture is simplified because both parabolas are congruent. The decay chain begins away from the line of beta stability and ends the most stable core at the minimum of the parabola. Since only the stable end member of this series is formed, also occur in this case no stable neighboring isobars. This rule applies to all nuclei, including those with A ≤ 14

Application

The rule can be used to explain the absence of stable technetium and Promethiumisotope. Because of the surrounding elements many stable isotopes exist, the Isobarenregel would hurt for stable isotopes of these two elements. Only far from the line of beta stability stable isotopes could occur, however, due to their core composition can no longer be stable then. Furthermore helped the Mattauchsche Isobarenregel in locating very long-lived radionuclides. Cores that were considered stable and opposite to the Isobarenregel had stable isobars were investigated in detail on the basis of this fact and proved to be extremely long-lived radionuclides. These include: