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In atomic physics and quantum chemistry, the Aufbau principle (/ ˈ aʊ f b aʊ /, from German: Aufbauprinzip, lit. 'building-up principle'), also called the Aufbau rule, states that in the ground state of an atom or ion, electrons first fill subshells of the lowest available energy, then fill subshells of higher energy.
The order of an element of a group (also called period length or period) is the order of the subgroup generated by the element. If the group operation is denoted as a multiplication , the order of an element a of a group, is thus the smallest positive integer m such that a m = e , where e denotes the identity element of the group, and a m ...
A proof of concept (POC or PoC), also known as proof of principle, is an inchoate realization of a certain idea or method in order to demonstrate its feasibility [1] or viability. [2] A proof of concept is usually small and may or may not be complete, but aims to demonstrate in principle that the concept has practical potential without needing ...
The most fundamental concept in chemistry is the law of conservation of mass, which states that there is no detectable change in the quantity of matter during an ordinary chemical reaction. Modern physics shows that it is actually energy that is conserved, and that energy and mass are related; a concept which becomes important in nuclear chemistry.
In this case the order of the ion electronic states corresponds to the order of the orbital energies. Excited-state ionization energies can be measured by photoelectron spectroscopy . For H 2 O, the near-Hartree–Fock orbital energies (with sign changed) of these orbitals are 1a 1 559.5, 2a 1 36.7 1b 2 19.5, 3a 1 15.9 and 1b 1 13.8 eV .
Besides structural order, one may consider charge ordering, spin ordering, magnetic ordering, and compositional ordering. Magnetic ordering is observable in neutron diffraction. It is a thermodynamic entropy concept often displayed by a second-order phase transition. Generally speaking, high thermal energy is associated with disorder and low ...
The proof-theoretic ordinal of such a theory is the supremum of the order types of all ordinal notations (necessarily recursive, see next section) that the theory can prove are well founded—the supremum of all ordinals for which there exists a notation in Kleene's sense such that proves that is an ordinal notation.
Conjugacy classes may be referred to by describing them, or more briefly by abbreviations such as "6A", meaning "a certain conjugacy class with elements of order 6", and "6B" would be a different conjugacy class with elements of order 6; the conjugacy class 1A is the conjugacy class of the identity which has order 1.