Term symbol: Difference between revisions

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For historical reasons, the term symbol is somewhat inconsistent in the sense that the quantum numbers ''L'' and ''J'' are indicated directly, by a letter and a number, respectively, while the spin ''S'' is indicated by its multiplicity 2''S''+1. The eigenstates labeled by a term symbol are obtained in the [[Russell-Saunders coupling]] scheme.
For historical reasons, the term symbol is somewhat inconsistent in the sense that the quantum numbers ''L'' and ''J'' are indicated directly, by a letter and a number, respectively, while the spin ''S'' is indicated by its multiplicity 2''S''+1. The eigenstates labeled by a term symbol are obtained in the [[Russell-Saunders coupling]] scheme.
 
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==Examples==
==Examples==
A few ground state atoms are listed.
A few ground state atoms are listed.

Revision as of 16:16, 5 January 2008

In atomic spectroscopy, a term symbol gives the total spin-, orbital-, and spin-orbital angular momentum of the atom. The term symbol has the following form:

where S is the total spin angular momentum and 2S+1 is the spin multiplicity. The symbol X represents the total orbital angular momentum. For historical reasons it is coded by a letter as follows (between brackets the L quantum number designated by the letter):

and further up the alphabet (excluding P and S). The value J is the quantum number of the spin-orbital angular momentum: JL + S. The value J satisfies the triangular conditions:

.

Sometimes the parity of the state is added, as in

which indicates that the state has odd parity. This is the case if the sum of the one-electron orbital angular momenta is odd.

For historical reasons, the term symbol is somewhat inconsistent in the sense that the quantum numbers L and J are indicated directly, by a letter and a number, respectively, while the spin S is indicated by its multiplicity 2S+1. The eigenstates labeled by a term symbol are obtained in the Russell-Saunders coupling scheme.

[edit intro]

Examples

A few ground state atoms are listed.

  • Hydrogen atom: . Spin angular momentum: S = 1/2. Orbital angular momentum: L = 0. Spin-orbital angular momentum: J = 1/2. Electronic configuration: 1s. Parity: even.
  • Carbon atom: . Spin angular momentum: S = 1. Orbital angular momentum: L = 1. Spin-orbital angular momentum: J = 0. Electronic configuration: [He]2s22p2. Parity even.
  • Aluminium atom: . Spin angular momentum: S = 1/2. Orbital angular momentum: L = 1. Spin-orbital angular momentum: J = 1/2. Electronic configuration: [Ne]3s23p1. Parity odd.
  • Scandium atom: . Spin angular momentum: S = 1/2. Orbital angular momentum: L = 2. Spin-orbital angular momentum: J = 3/2. Electronic configuration: [Ne]3s23p63d14s2. Parity even.