Hund's rules
In atomic spectroscopy Hund's rules predict which atomic energy level with quantum numbers L, S and J is lowest. The rules are called after Friedrich Hund who formulated them in 1925.[1] A group of atomic energy levels, obtained in the Russell-Saunders coupling, is concisely indicated by a term symbol. A term (also known as multiplet) is a set of simultaneous eigenfunctions of L2 (total orbital angular momentum squared) and S2 (total spin angular momentum squared) with given quantum numbers L and S, respectively. If there is no spin-orbit coupling, the functions of one term are degenerate (have the same energy).
Hund's rules are:
- Of the Russell-Saunders states arising from a given electronic configuration those with the largest spin quantum number S lie lowest, those with the next largest next, and so on; in other words, the states with largest spin multiplicity are the most stable.
- Of the group of terms with a given value of S, that with the largest value of L lies lowest.
- Of the states with given values of S and L in an electronic configuration consisting of less than half the electrons in a closed subshell, the state with the smallest value of J is usually the most stable, and for a configuration consisting of more than half the electrons in a closed subshell the state with largest J is the most stable.
The levels of the second sort, largest J most stable, can be seen as arising from holes in the closed subshell.
References
- ↑ F. Hund, Zur Deutung verwickelter Spektren, insbesondere der Elemente Scandium bis Nickel. [On the interpretation of complicated spectra, in particular scandium through nickel]. Zeitschrift f. Physik, vol. 33, pp. 345-371 (1925).