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 (nucleon number).
Until the 1960s, nucleons were ...
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 ever ...
(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
The mass number (symbol ''A'', from the German word ''Atomgewicht'' tomic 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 approxima ...
. 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
Alfred Walter Stewart (5 September 1880 – 1 July 1947) was a British chemist and part-time novelist who wrote seventeen detective novels and a pioneering science fiction work between 1923 and 1947 under the pseudonym of JJ Connington. He create ...
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 property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different ele ...
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 (symbol: kg), atomic mass is often expressed in the non-SI unit dalton (symbol: Da) – equivalently, unified atomic mass unit (u). 1&n ...
es of corresponding nuclides. From the
Weizsäcker formula for the mass of a nucleus:
:
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
Odd means unpaired, occasional, strange or unusual, or a person who is viewed as eccentric.
Odd may also refer to:
Acronym
* ODD (Text Encoding Initiative) ("One Document Does it all"), an abstracted literate-programming format for describing X ...
, 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 a beta particle (fast energetic electron or positron) is emitted from an atomic nucleus, transforming the original nuclide to an isobar of that nuclide. For ...
is energetically favorable for
neutron-rich nuclides, and
positron decay
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 ...
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 consid ...
s do not change the mass number, hence an original nucleus and its
daughter
A daughter is a female offspring; a girl or a woman in relation to her parents. Daughterhood is the state of being someone's daughter. The male counterpart is a son. Analogously the name is used in several areas to show relations between groups ...
nucleus are isobars. In both aforementioned cases, a heavier nucleus decays to its lighter isobar.
For
even
Even may refer to:
General
* Even (given name), a Norwegian male personal name
* Even (surname)
* Even (people), an ethnic group from Siberia and Russian Far East
**Even language, a language spoken by the Evens
* Odd and Even, a solitaire game wh ...
the term has the form:
:
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 protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford based on the 1909 Geiger–Marsden gold foil experiment. After the discovery of the neutron in ...
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; transfer ...
(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
In particle physics and nuclear physics, the branching fraction (or branching ratio) for a decay is the fraction of particles which decay by an individual decay mode or with respect to the total number of particles which decay. It applies to eithe ...
of the middle isobar may occur: e.g. radioactive
iodine-126
There are 37 known isotopes of iodine (53I) from 108I to 144I; all undergo radioactive decay except 127I, which is stable. Iodine is thus a monoisotopic element.
Its longest-lived radioactive isotope, 129I, has a half-life of 15.7 million year ...
has almost equal probabilities for two decay modes, which lead to different daughter isotopes:
tellurium-126
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 bee ...
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.
Th ...
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 cons ...
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.
Th ...
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 of that nuclide. For ...
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 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 four and an at ...
.
See also
*
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 num ...
s (nuclides having the same number of protons)
*
Isotones (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 higher energy levels than in the ground state of the same nucleus. "Metastable" describes nuclei whose excited states have ...
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. ...
Bibliography
References
{{DEFAULTSORT:Isobar (Nuclide)
Nuclear physics