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In mathematics and physics, the term generator or generating set may refer to any of a number of related concepts. The underlying concept in each case is that of a smaller set of objects, together with a set of operations that can be applied to it, that result in the creation of a larger collection of objects, called the generated set .
In atomic physics, a term symbol is an abbreviated description of the total spin and orbital angular momentum quantum numbers of the electrons in a multi-electron atom. So while the word symbol suggests otherwise, it represents an actual value of a physical quantity .
Element Group Electron configuration electron configuration (P8000) Term symbol note 1, 2, S, P, 1 H hydrogen: 1 1s 1: 1s¹ : 2 S 1/2: S: 2 He helium: 18 1s 2: 1s² : 1 S 0: S: 3 Li lithium
The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics. Additionally, the subsequent columns contains an informal explanation, a short example, the Unicode location, the name for use in HTML documents, [1] and the LaTeX symbol.
We need to consider only the outer 3p 2 electrons, for which it can be shown (see term symbols) that the possible terms allowed by the Pauli exclusion principle are 1 D , 3 P , and 1 S. Hund's first rule now states that the ground state term is 3 P, which has S = 1. The superscript 3 is the value of the multiplicity = 2S + 1 = 3.
This notation is used to specify electron configurations and to create the term symbol for the electron states in a multi-electron atom. When writing a term symbol, the above scheme for a single electron's orbital quantum number is applied to the total orbital angular momentum associated to an electron state. [4]
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In universal algebra and mathematical logic, a term algebra is a freely generated algebraic structure over a given signature. [1] [2] For example, in a signature consisting of a single binary operation, the term algebra over a set X of variables is exactly the free magma generated by X.