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The tables of elements are sorted in order of decreasing number of nuclides associated with each element. (For a list sorted entirely in terms of half-lives of nuclides, with mixing of elements, see List of nuclides.) Stable and unstable (marked decays) nuclides are given, with symbols for unstable (radioactive) nuclides in italics. Note that ...
Monoisotopic elements are characterized, except in one case, by odd numbers of protons (odd Z), and even numbers of neutrons. Because of the energy gain from nuclear pairing, the odd number of protons imparts instability to isotopes of an odd Z , which in heavier elements requires a completely paired set of neutrons to offset this tendency into ...
11 elements have 5 stable isotopes apiece; 9 elements have 4 stable isotopes apiece; 5 elements have 3 stable isotopes apiece; 16 elements have 2 stable isotopes apiece; 26 elements have 1 single stable isotope. These last 26 are thus called monoisotopic elements. [3] The mean number of stable isotopes for elements which have at least one ...
is asymptotically stable (in fact, exponentially stable) if all the eigenvalues of have a modulus smaller than one. This latter condition has been generalized to switched systems: a linear switched discrete time system (ruled by a set of matrices {, …,})
A chemical element, often simply called an element, is a type of atom which has a specific number of protons in its atomic nucleus (i.e., a specific atomic number, or Z). [ 1 ] The definitive visualisation of all 118 elements is the periodic table of the elements , whose history along the principles of the periodic law was one of the founding ...
A Lyapunov function for an autonomous dynamical system {: ˙ = ()with an equilibrium point at = is a scalar function: that is continuous, has continuous first derivatives, is strictly positive for , and for which the time derivative ˙ = is non positive (these conditions are required on some region containing the origin).
A consequence of this rule is that technetium and promethium both have no stable isotopes, as each of the neighboring elements on the periodic table (molybdenum 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.
Each chemical element has a unique atomic number (Z— for "Zahl", German for "number") representing the number of protons in its nucleus. [4] Each distinct atomic number therefore corresponds to a class of atom: these classes are called the chemical elements. [5] The chemical elements are what the periodic table classifies and organizes.