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Hund's rule of maximum multiplicity is a rule based on observation of atomic spectra, which is used to predict the ground state of an atom or molecule with one or more open electronic shells. The rule states that for a given electron configuration , the lowest energy term is the one with the greatest value of spin multiplicity . [ 1 ]
The three rules are: [1] [2] [3] For a given electron configuration, the term with maximum multiplicity has the lowest energy. The multiplicity is equal to + , where is the total spin angular momentum for all electrons. The multiplicity is also equal to the number of unpaired electrons plus one. [4]
The superscript three (read as triplet) indicates that the multiplicity 2S+1 = 3, so that the total spin S = 1. This spin is due to two unpaired electrons, as a result of Hund's rule which favors the single filling of degenerate orbitals. The triplet consists of three states with spin components +1, 0 and –1 along the direction of the total ...
Rules for decomposing the restriction of an irreducible representation into irreducible representations of the subgroup are called branching rules, and have important applications in physics. For example, in case of explicit symmetry breaking , the symmetry group of the problem is reduced from the whole group to one of its subgroups.
Kasha's rule is a principle in the photochemistry of electronically excited molecules. The rule states that photon emission (fluorescence or phosphorescence) occurs in appreciable yield only from the lowest excited state of a given multiplicity. It is named after American spectroscopist Michael Kasha, who proposed it in 1950. [1] [2]
The multiplicity of a prime factor p of n is the largest exponent m for which p m divides n. The tables show the multiplicity for each prime factor. ... 9, 11, 13, 15 ...
With 2-methylpropane, (CH 3) 3 CH, as another example: the CH proton is attached to three identical methyl groups containing a total of 9 identical protons. The C−H signal in the spectrum would be split into 10 peaks according to the n + 1 rule of multiplicity. Below are NMR signals corresponding to several simple multiplets of this type.
The notion of the multiplicity of a module is a generalization of the degree of a projective variety. By Serre's intersection formula, it is linked to an intersection multiplicity in the intersection theory. The main focus of the theory is to detect and measure a singular point of an algebraic variety (cf. resolution of singularities).