isobar (nuclide)

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Isobars are atoms (
nuclide A nuclide (or nucleide, from atomic nucleus, 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 co ...
s) of different
chemical element A chemical element is a species of atoms that have a given number of protons in their atomic nucleus, nuclei, including the pure Chemical substance, substance consisting only of that species. Unlike chemical compounds, chemical elements canno ...
s that have the same number of
nucleon In physics and chemistry, a nucleon is either a proton or a neutron, considered in its role as a component of an atomic nucleus. The number of nucleons in a nucleus defines the atom's mass number, mass number (nucleon number). Until the 1960s, n ...
s. Correspondingly, isobars differ in
atomic 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 ...
(or number of
proton A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' elementary charge. Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron mass ...
s) 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. The term "isobars" (originally "isobares") for nuclides was suggested by Alfred Walter Stewart in 1918. It is derived from the
Greek Greek may refer to: Greece Anything of, from, or related to Greece, a country in Southern Europe: *Greeks, an ethnic group. *Greek language, a branch of the Indo-European language family. **Proto-Greek language, the assumed last common ancestor ...
word ''isos'', meaning "equal" and ''baros'', meaning "weight".

# Mass

The same mass number implies neither the same
mass Mass is an Intrinsic and extrinsic properties, intrinsic property of a body. It was traditionally believed to be related to the physical quantity, quantity of matter in a Physical object, physical body, until the discovery of the atom and par ...
of nuclei, nor equal
atomic mass The atomic mass (''m''a or ''m'') is the mass of an atom. Although the SI unit of mass is the kilogram (unit), kilogram (symbol: kg), atomic mass is often expressed in the non-SI unit dalton (unit), dalton (symbol: Da) – equivalently, unif ...
es of corresponding nuclides. From the Weizsäcker formula for the mass of a nucleus: : $m\left(A,Z\right) = Z m_p + N m_n - a_ A + a_ A^ + a_ \frac + a_ \frac - \delta\left(A,Z\right)$ where mass number  equals to the sum of atomic number  and number of neutrons , and , , , , , are constants, one can see that the mass depends on and non-linearly, even for a constant mass number. For odd , it is admitted that and the mass dependence on  is
convex Convex or convexity may refer to: Science and technology * Convex lens, in optics Mathematics * Convex set, containing the whole line segment that joins points ** Convex polygon, a polygon which encloses a convex set of points ** Convex polytope, ...
(or on  or , it does not matter for a constant ). This explains that
beta decay In nuclear physics, beta decay (β-decay) is a type of radioactive decay in which a beta particle (fast energetic electron or positron) is emitted from an atomic nucleus, transforming the original nuclide to an isobar (nuclide), isobar of that ...
is energetically favorable for neutron-rich nuclides, and positron decay is favorable for strongly neutron-deficient nuclides. Both
decay mode Radioactive decay (also known as nuclear decay, radioactivity, radioactive Decay chain, disintegration, or nuclear disintegration) is the process by which an unstable atomic nucleus loses energy by radiation. A material containing unstable nucl ...
s do not change the mass number, hence an original nucleus and its daughter nucleus are isobars. In both aforementioned cases, a heavier nucleus decays to its lighter isobar. For even  the  term has the form: :$\delta\left(A,Z\right) = \left(-1\right)^Z a_P A^$ where is another constant. This term, subtracted from the mass expression above, is positive for even-even nuclei and negative for odd-odd nuclei. This means that even-even nuclei, which have not a strong neutron excess or neutron deficiency, have higher
binding energy In physics and chemistry, binding energy is the smallest amount of energy required to remove a particle from a system of particles or to disassemble a system of particles into individual parts. In the former meaning the term is predominantly use ...
than their odd-odd isobar neighbors. It implies that even-even nuclei are (relatively) lighter and more stable. The difference is especially strong for small . This effect is also predicted (qualitatively) by other
nuclear model The atomic nucleus is the small, dense region consisting of proton A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' elementary charge. Its mass is slightly less than that of a neu ...
s and has important consequences.

# Stability

The Mattauch isobar rule states that if two adjacent elements on the periodic table have isotopes of the same mass number, at least one of these isobars must be a
radionuclide A radionuclide (radioactive nuclide, radioisotope or radioactive isotope) is a nuclide that has excess nuclear energy, making it unstable. This excess energy can be used in one of three ways: emitted from the nucleus as gamma radiation; transfe ...
(radioactive). In cases of three isobars of sequential elements where the first and last are stable (this is often the case for even-even nuclides, see above), branched decay of the middle isobar may occur: e.g. radioactive iodine-126 has almost equal probabilities for two decay modes, which lead to different daughter isotopes: tellurium-126 and xenon-126. No
observationally stable Stable nuclides are nuclides that are not radioactive and so (unlike radionuclides) do not spontaneously undergo radioactive decay. When such nuclides are referred to in relation to specific elements, they are usually termed stable isotopes. The ...
isobars exist for mass numbers 5 (decays to
helium-4 Helium-4 () is a stable isotope of the element helium. It is by far the more abundant of the two naturally occurring isotopes of helium, making up about 99.99986% of the helium on Earth. Its nucleus is identical to an alpha particle, and consis ...
plus a
proton A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' elementary charge. Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron mass ...
or
neutron The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the atomic nucleus, nuclei of atoms. Since protons and ...
), 8 (decays to two helium-4 nuclei), 147, 151, as well as for 209 and above. Two observationally stable isobars exist for 36, 40, 46, 50, 54, 58, 64, 70, 74, 80, 84, 86, 92, 94, 96, 98, 102, 104, 106, 108, 110, 112, 114, 120, 122, 123, 124, 126, 132, 134, 136, 138, 142, 154, 156, 158, 160, 162, 164, 168, 170, 176, 180, 192, 196, 198 and 204.via
Stable isotope The term stable isotope has a meaning similar to stable nuclide, but is preferably used when speaking of nuclides of a specific element. Hence, the plural form stable isotopes usually refers to isotopes of the same element. The relative abundanc ...
; cf.
observationally stable Stable nuclides are nuclides that are not radioactive and so (unlike radionuclides) do not spontaneously undergo radioactive decay. When such nuclides are referred to in relation to specific elements, they are usually termed stable isotopes. The ...
and note also more recently discovered decays: Eu-151, Os-186, and Bi-209
In theory, no two stable nuclides have the same mass number (since no two nuclides that have the same mass number are both stable to
beta decay In nuclear physics, beta decay (β-decay) is a type of radioactive decay in which a beta particle (fast energetic electron or positron) is emitted from an atomic nucleus, transforming the original nuclide to an isobar (nuclide), isobar of that ...
and
double beta decay In nuclear physics, double beta decay is a type of radioactive decay in which two neutrons are simultaneously transformed into two protons, or vice versa, inside an atomic nucleus. As in single beta decay, this process allows the atom to move clos ...
), and no stable nuclides exist for mass numbers 5, 8, 143–155, 160–162, and ≥ 165, since in theory, the beta-decay stable nuclides for these mass numbers can undergo
alpha decay Alpha decay or α-decay is a type of radioactivity, radioactive decay in which an atomic nucleus emits an alpha particle (helium nucleus) and thereby transforms or 'decays' into a different atomic nucleus, with a mass number that is reduced by fo ...
.

*
Isotope Isotopes are two or more types of atoms that have the same atomic number (number of protons in their nuclei) and position in the periodic table (and hence belong to the same chemical element), and that differ in nucleon numbers (mass numbe ...
s (nuclides having the same number of protons) *
Isotone Two nuclides are isotones if they have the same neutron number ''N'', but different proton number ''Z''. For example, Isotopes of boron, boron-12 and carbon-13 nuclei both contain 7 neutrons, and so are isotones. Similarly, 36S, 37Cl, 38Ar, 39 ...
s (nuclides having the same number of neutrons) *
Nuclear isomer A nuclear isomer is a metastable state of an atomic nucleus, in which one or more nucleons (protons or neutrons) occupy excited state, higher energy levels than in the ground state of the same nucleus. "Metastable" describes nuclei whose excited ...
s (different excited states of the same nuclide) *
Magic number (physics) In nuclear physics, a magic number is a number of nucleons (either protons or neutrons, separately) such that they are arranged into complete Nuclear shell model, shells within the atomic nucleus. As a result, atomic nuclei with a 'magic' number o ...
*
Electron capture Electron capture (K-electron capture, also K-capture, or L-electron capture, L-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. Thi ...

# References

{{DEFAULTSORT:Isobar (Nuclide) Nuclear physics