The Mattauch isobar rule, formulated by

Josef Mattauch Josef Mattauch (21 November 1895 – 10 August 1976) was a nuclear physicist and chemist. He was known for the development of the Mattauch-Herzog double-focusing mass spectrometer, for his work on the investigation of isotopic abundances using mas ...

in 1934, states that if two adjacent

elements Element or elements may refer to: Science * Chemical element, a pure substance of one type of atom * Heating element, a device that generates heat by electrical resistance * Orbital elements, parameters required to identify a specific orbit of ...

on the

periodic table The periodic table, also known as the periodic table of the (chemical) elements, is a rows and columns arrangement of the chemical elements. It is widely used in chemistry, physics, and other sciences, and is generally seen as an icon of ch ...

have isotopes of the same mass number, one of these isotopes must be radioactive. Two

nuclide A nuclide (or nucleide, from nucleus, also known as nuclear species) is a class of atoms characterized by their number of protons, ''Z'', their number of neutrons, ''N'', and their nuclear energy state. The word ''nuclide'' was coined by Truman ...

s 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

s 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. However, this rule cannot make predictions on the

half-lives Half-life (symbol ) is the time required for a quantity (of substance) to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable at ...

of these radioisotopes.

Technetium and promethium

A consequence of this rule is that technetium and

promethium Promethium is a chemical element with the 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 Earth's crust at any given time. Promethium is one of onl ...

both have no stable isotopes, as each of the neighboring elements on the periodic table (

molybdenum Molybdenum is a chemical element with the symbol Mo and atomic number 42 which is located in period 5 and group 6. The name is from Neo-Latin ''molybdaenum'', which is based on Ancient Greek ', meaning lead, since its ores were confused with lea ...

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). 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 The mass excess of a nuclide is the difference between its actual mass and its mass number in daltons. It is one of the predominant methods for tabulating nuclear mass. The mass of an atomic nucleus is well approximated (less than 0.1% difference fo ...

or greatest binding energy is shown to be stable to beta decay because

energy conservation Energy conservation is the effort to reduce wasteful energy consumption by using fewer energy services. This can be done by using energy more effectively (using less energy for continuous service) or changing one's behavior to use less service (f ...

forbids a spontaneous transition to a less stable state. Thus no stable nuclides have

proton number The atomic number or nuclear charge number (symbol ''Z'') of a chemical element is the charge number of an atomic nucleus. For ordinary nuclei, this is equal to the proton number (''n''p) or the number of protons found in the nucleus of every ...

43 or 61, and by the same reasoning no stable nuclides have

neutron number The neutron number, symbol ''N'', is the number of neutrons in a nuclide. Atomic number (proton number) plus neutron number equals mass number: . The difference between the neutron number and the atomic number is known as the neutron excess: . ...

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 Antimony (51Sb) occurs in two stable isotope, stable isotopes, 121Sb and 123Sb. There are 35 artificial radioisotope, radioactive isotopes, the longest-lived of which are 125Sb, with a half-life of 2.75856 years; 124Sb, with a half-life of 60.2 da ...

and

tellurium-123 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. Naturally-occurring tellurium on Earth consists of eight isotopes. Two of these have been ...

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 A nuclear isomer is a metastable state of an atomic nucleus, in which one or more nucleons (protons or neutrons) occupy higher energy levels than in the ground state of the same nucleus. "Metastable" describes nuclei whose excited states have ha ...

to ¹⁸⁰Ta, beta decay to ¹⁸⁰W, electron capture to ¹⁸⁰Hf, or alpha decay to ¹⁷⁶Lu, but none of these decay modes have been observed. In addition, beta decay has been seen for neither

curium-247 Curium (96Cm) is an artificial element with an atomic number of 96. Because it is an artificial element, a standard atomic weight cannot be given, and it has no stable isotopes. The first isotope synthesized was 242Cm in 1944, which has 146 neutr ...

nor berkelium-247, though it is expected that the former should decay into the latter. Both nuclides are alpha-unstable.

References

Nuclear physics {{nuclear-stub