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The number of nucleons in the nucleus must be smaller than the number of available states, otherwise the nucleus cannot hold all of its nucleons. There are thus several ways to choose Z (or N) states among the n possible. In combinatorial mathematics, the number of choices of Z objects among n is the binomial coefficient C Z n.
The Bohr model of the hydrogen atom (Z = 1) or a hydrogen-like ion (Z > 1), where the negatively charged electron confined to an atomic shell encircles a small, positively charged atomic nucleus and where an electron jumps between orbits, is accompanied by an emitted or absorbed amount of electromagnetic energy (hν). [1]
The atomic nucleus is a bound system of protons and neutrons. The spatial extent and shape of the nucleus depend not only on the size and shape of discrete nucleons, but also on the distance between them (the inter-nucleon distance). (Other factors include spin, alignment, orbital motion, and the local nuclear environment (see EMC effect).)
In mathematics, and especially in category theory, a commutative diagram is a diagram of objects, also known as vertices, and morphisms, also known as arrows or edges, such that when selecting two objects any directed path through the diagram leads to the same result by composition.
For an axially symmetric shape with the axis of symmetry being the z axis, the Hamiltonian is = + (+) ( ). Here m is the mass of the nucleon, N is the total number of harmonic oscillator quanta in the spherical basis, is the orbital angular momentum operator, is its square (with eigenvalues (+)), = (/) (+) is the average value of over the N shell, and s is the intrinsic spin.
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.
The atomic nucleus shown expanded more than 10,000 times its size relative to the atom; electrons have no measurable diameter. The Rutherford model is a name for the first model of an atom with a compact nucleus. The concept arose from Ernest Rutherford discovery of the nucleus.
Nuclear fission is the opposite process, causing a nucleus to split into two smaller nuclei—usually through radioactive decay. The nucleus can also be modified through bombardment by high energy subatomic particles or photons. If this modifies the number of protons in a nucleus, the atom changes to a different chemical element. [47] [48]