Mattauch's isobar rule

Under Matt's too Isobarenregel , sometimes Isobarenregel , Mattauch'sche rule or Matt also rule , is meant an empirical rule of Radiochemistry . It says that neighboring stable isobars , i.e. nuclides with the same mass number, do not occur, or, in other words, that the difference between the ordinal numbers of two stable isobars is always greater than one. It is named after the Austrian physicist Josef Mattauch , who postulated it in 1934.

Basics

By β ^- decay , an isobar of the starting nuclide (mother nuclide) is formed. Isobars are nuclei with the same number of nucleons , but differ in the number of their protons (= atomic number Z ) and neutrons . The β ^- decay of zu is shown as an example . ${\displaystyle _{\ 79}^{198}\mathrm {Au} }$ ${\displaystyle _{\ 80}^{198}\mathrm {Hg} }$

${\displaystyle _{\ 79}^{198}\mathrm {Au} \;{\xrightarrow {\beta ^{-}}}\;_{\ 80}^{198}\mathrm {Hg} +\mathrm {e} ^{-}+{\overline {\nu }}_{e}}$.

The number of nucleons (198) remains the same, while the number of protons increases by one and that of neutrons decreases by one. The isobaric Hg nuclide is formed.

Conversely, a proton can transform into a neutron during β ⁺ decay and electron capture .

Mattauch's isobar rule is based on the fact that nuclei with an even number of protons and an even number of neutrons are particularly stable (so-called g, g nuclei, see also droplet model ). Those in which both numbers are odd (u, u nuclei) are destabilized. The u, g and g, u nuclei lie between these two. Usually u, u nuclei are not stable (see below). If the mother nuclide is a g, g nucleus, a u, u nucleus is formed through β decay and vice versa, while g, u nuclei develop u, g nuclei and vice versa:

${\displaystyle \mathrm {(g{,}g)\;{\xrightarrow {\beta }}\;(u{,}u)\;{\xrightarrow {\beta }}\;(g{,}g)} }$

${\displaystyle \mathrm {(u{,}g)\;{\xrightarrow {\beta }}\;(g{,}u)\;{\xrightarrow {\beta }}\;(u{,}g)} }$

Near the line of beta stability , apart from γ-decay , which only forms one isomer , only β-decay occurs as a type of decay . No stable nuclides can be found far from the line.

background

Energy parabolas for u, u and g, g nuclei with possible nuclides: According to Mattauch's isobar rule, the most stable nuclide with Z = n lies in the minimum of the parabola.

The binding energies of the atomic nuclei can be described according to the droplet model. If the number of nucleons is odd (u, g and g, u nuclei), the binding energy of the nuclides depending on the number of protons (atomic number) can be represented by a parabola. The nuclide at the apex of the parabola is stable, the neighboring nuclides can transform through β ^- decay or β ⁺ decay and electron capture. With an even number of nucleons there are two parabolas, the parabola of the more unstable u, u nuclei being above that of the g, g nuclei.

Starting from a nucleus that is far from the line of beta stability (e.g. Z = n − 4 in the figure), a decay series now runs, with the daughter nuclide of each β ^- decay on the other parabola. The series ends when the line of beta stability has been reached, here at Z = n. The same applies to the series of β ⁺ decays beginning at Z = n + 4. However, this ends with the nuclide Z = n + 2, since the u, u nucleus Z = n + 1 is less stable.

Since the g, g parabola always lies below the u, u parabola, two neighboring stable isobars can never appear. An interesting peculiarity is the nucleus Z = n + 1, which cannot be obtained by β-decays, but only in another way (for example by α-decays ). This nucleus now has the possibility of stabilizing itself through a β ^- decay to Z = n + 2 and through β ⁺ + decay to Z = n. Such nuclei often show both types of decay:

${\displaystyle \mathrm {^{40}K\;{\xrightarrow {\beta ^{-}}}\;^{40}Ca} }$

${\displaystyle \mathrm {^{40}K\;{\xrightarrow {\beta ^{+}}}\;^{40}Ar} }$

The nuclide Z = n + 2 cannot decay through β-decay , but the most stable nuclide with Z = n can still be achieved through a double β-decay . However, this type of decay is so extremely unlikely (e.g. half-life ^10-20 years for ⁸² Se) that the affected nucleus is usually referred to as stable with Z = n + 2.

Mattauch's isobar rule applies to u, u nuclei only for A> 14. For A≤14, on the other hand, the parabolas are so strongly curved that the masses of the g, g-nuclides adjacent to a u, u-nuclide are greater than those of the u, u-nuclide itself and this is therefore stable. For A≤14 there are four stable u, u nuclides:

${\displaystyle _{1}^{2}\mathrm {H} }$, , And ${\displaystyle _{3}^{6}\mathrm {Li} }$ ${\displaystyle _{\ 5}^{10}\mathrm {B} }$ ${\displaystyle _{\ 7}^{14}\mathrm {N} }$

If the decay series begins with a g, u or u, g kernel, the picture is simplified because both parabolas are congruent. The decay series begins far from the line of beta stability and ends at the most stable core at the minimum of the parabola. Since only the stable end link of this series is formed, no stable neighboring isobars occur in this case either. This rule applies to all cores, including those with A≤14.

application

The rule can be used to explain the absence of stable technetium and promethium isotopes . Since there are many stable isotopes of the surrounding elements , the isobar rule would be violated for stable isotopes of these two elements. Only far away from the line of beta stability could stable isotopes occur, which, however, can no longer be stable due to their core composition.

Furthermore, Mattauch's isobar rule helped to find very long-lived radionuclides. Cores that were considered stable and, contrary to the isobar rule, had stable isobars, were examined more closely on the basis of this fact and turned out to be extremely long-lived radionuclides. These include:

${\displaystyle _{19}^{40}\mathrm {K} }$, , , And ${\displaystyle _{23}^{50}\mathrm {V} }$ ${\displaystyle _{\ 48}^{113}\mathrm {Cd} }$ ${\displaystyle _{\ 57}^{138}\mathrm {La} }$ ${\displaystyle _{\ 71}^{176}\mathrm {Lu} }$

Exceptions

The only exceptions to this rule are antimony-123 and tellurium-123, as well as hafnium-180 and tantalum-180m, where both nuclides are apparently stable or no decay has yet been observed.

swell

• Karl Heinrich Lieser: Introduction to Nuclear Chemistry . 3rd edition, VCH, Weinheim 2000.
• Cornelius Keller: Radiochemistry . 2nd edition, Diesterweg, Frankfurt / Main 1981.

Individual evidence

1. ↑ Josef Mattauch: On the systematics of isotopes. In: Journal of Physics . Volume 91, No. 5-6, 1934, ISSN  0939-7922 , pp. 361-371 ( doi: 10.1007 / BF01342557 ).
2. ↑ Mikael Hult, JS Elisabeth Wieslander, Gerd Marissens, Jo l Gasparro, Uwe Waetjen, Marcin Misiaszek: Search for the radioactivity of ^180m Ta using an underground HPGe sandwich spectrometer. In: Applied Radiation and Isotopes . 67, 2009, pp. 918-921, doi: 10.1016 / j.apradiso.2009.01.057 .

Web links

• German Mineralogical Society (PDF file; 5.14 MB)