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In mathematics, an isotopy from a possibly non-associative algebra A to another is a triple of bijective linear maps (a, b, c) such that if xy = z then a(x)b(y) = c(z).This is similar to the definition of an isotopy of loops, except that it must also preserve the linear structure of the algebra.
Homotopy#Isotopy, a continuous path of homeomorphisms connecting two given homeomorphisms is an isotopy of the two given homeomorphisms in homotopy; Regular isotopy of a link diagram, an equivalence relation in knot theory
A nuclide is a species of an atom with a specific number of protons and neutrons in the nucleus, for example, carbon-13 with 6 protons and 7 neutrons. The nuclide concept (referring to individual nuclear species) emphasizes nuclear properties over chemical properties, whereas the isotope concept (grouping all atoms of each element) emphasizes chemical over nuclear.
A chart or table of nuclides maps the nuclear, or radioactive, behavior of nuclides, as it distinguishes the isotopes of an element.It contrasts with a periodic table, which only maps their chemical behavior, since isotopes (nuclides that are variants of the same element) do not differ chemically to any significant degree, with the exception of hydrogen.
This is a list of radioactive nuclides (sometimes also called isotopes), ordered by half-life from shortest to longest, in seconds, minutes, hours, days and years. Current methods make it difficult to measure half-lives between approximately 10 −19 and 10 −10 seconds.
No odd-neutron-number isotope is the most naturally abundant isotope in its element, except for beryllium-9 (which is the only stable beryllium isotope), nitrogen-14, and platinum-195. No stable nuclides have a neutron number of 19, 21, 35, 39, 45, 61, 89, 115, 123, or ≥ 127.
All isotopes of a given element have the same number of protons in each atom. The term isotope is formed from the Greek roots isos (ἴσος "equal") and topos (τόπος "place"), meaning "the same place"; thus, the meaning behind the name is that different isotopes of a single element occupy the same position on the periodic table.
They have shorter half-lives than primordial radionuclides. They arise in the decay chain of the primordial isotopes thorium-232, uranium-238, and uranium-235. Examples include the natural isotopes of polonium and radium. Cosmogenic isotopes, such as carbon-14, are present because they are continually being formed in the atmosphere due to ...