isobar (nuclide)
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Isobars are atoms (
nuclide Nuclides (or nucleides, from nucleus, also known as nuclear species) are 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 the A ...
s) of different
chemical element 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: each oxygen atom has 8 protons in its ...
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. Until the 1960s, nucleons were thought to be ele ...
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 its atomic nucleus. For ordinary nuclei composed of protons and neutrons, this is equal to the proton number (''n''p) or the number of pro ...
(or number of
proton A proton is a stable subatomic particle, symbol , Hydron (chemistry), H+, or 1H+ with a positive electric charge of +1 ''e'' (elementary charge). Its mass is slightly less than the mass of a neutron and approximately times the mass of an e ...
s) but have the same
mass number 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 appro ...
. 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 British chemist Alfred Walter Stewart in 1918. It is derived .


Mass

The same mass number implies neither the same
mass Mass is an Intrinsic and extrinsic properties, intrinsic property of a physical body, body. It was traditionally believed to be related to the physical quantity, quantity of matter in a body, until the discovery of the atom and particle physi ...
of nuclei, nor equal atomic masses of corresponding nuclides. From the Weizsäcker formula for the mass of a nucleus: : m(A,Z) = Z m_p + N m_n - a_ A + a_ A^ + a_ \frac + a_ \frac - \delta(A,Z) 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 polytop ...
(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 an atomic nucleus emits a beta particle (fast energetic electron or positron), transforming into an isobar of that nuclide. For example, beta decay of a neutron ...
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 disintegration, or nuclear disintegration) is the process by which an unstable atomic nucleus loses energy by radiation. A material containing unstable nuclei is conside ...
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(A,Z) = (-1)^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 do not have 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 models 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 numbers of either neutrons or protons, giving it excess nuclear energy, and making it unstable. This excess energy can be used in one of three ...
(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. For instance, radioactive iodine-126 has almost equal probabilities for two decay modes:
positron emission Positron emission, beta plus decay, or β+ decay is a subtype of radioactive decay called beta decay, in which a proton inside a radionuclide nucleus is converted into a neutron while releasing a positron and an electron neutrino (). Positron emi ...
, leading to tellurium-126, and beta emission, leading to xenon-126. No observationally stable 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 consi ...
plus a
proton A proton is a stable subatomic particle, symbol , Hydron (chemistry), H+, or 1H+ with a positive electric charge of +1 ''e'' (elementary charge). Its mass is slightly less than the mass of a neutron and approximately times the mass of an e ...
or
neutron The neutron is a subatomic particle, symbol or , that has no electric charge, and a mass slightly greater than that of a proton. The Discovery of the neutron, neutron was discovered by James Chadwick in 1932, leading to the discovery of nucle ...
), 8 (decays to two helium-4 nuclei), 147, 151, as well as for 209 and above (noting primordial but not stable 147Sm, 151Eu, and 209Bi). 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 (including a meta state), 192, 196, 198 and 204.via
stable isotope Stable nuclides are Isotope, isotopes of a chemical element whose Nucleon, nucleons are in a configuration that does not permit them the surplus energy required to produce a radioactive emission. The Atomic nucleus, nuclei of such isotopes are no ...
; observationally stable; primordial radionuclide (some of whose radioactivity was discovered within the last two decades)
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 an atomic nucleus emits a beta particle (fast energetic electron or positron), transforming into an isobar of that nuclide. For example, beta decay of a neutron ...
and double beta decay), 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 radioactive decay in which an atomic nucleus emits an alpha particle (helium nucleus). The parent nucleus transforms or "decays" into a daughter product, with a mass number that is reduced by four and an a ...
.


See also

*
Isotope Isotopes are distinct nuclear species (or ''nuclides'') of the same chemical element. They have the same atomic number (number of protons in their Atomic nucleus, nuclei) and position in the periodic table (and hence belong to the same chemica ...
s (nuclides having the same number of protons) * Isotones (nuclides having the same number of neutrons) * Nuclear isomers (different excited states of the same nuclide) * Magic number (physics) *
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. Th ...


Bibliography


References

{{DEFAULTSORT:Isobar (Nuclide) Nuclear physics