TERM SYMBOLS N. W. GREGORY University of Washington, Seattle, Washington
INA senior or first-year-graduate introductory course treating atomic structure, it is valuable and satisfying for the student to correlate assigned electronic configurations with spectroscopic evidence in the form of term symbols for the ground states of various atoms or monatomic ions. At this level the majority of students above. This gives a total spin C m , = S of 3/2 and have insufficient background to understand and apply E m l = 0. Hence, L = 0 and the ground state term 1, and ,, showing a multiplicity 2S the methods of spectroscopy for derivation of all the symbol is 4SS. J = I L S (J = I L S I when the orbital is more possible terms arising from coupling of several equivalent electrons (for example, see Hersberg'). Based on than half-filled). Similarly, the assumption of RussellSaunders coupling, the AI 18%ZS= zps392 3p1 o isP2s12p4 author hm used a relatively simple system in which Hund's rules are applied to any given configuration in a formal manner which leads directly to the ground state term svmbol. It will be recalled that this tvoe of couplin"g considers the quantum designation fh'r the atom, L, to be calculated as the vector sum of the li for the electrons. Similarly, the S is the sum of the s, assigned to the electrons. The J designation for the atom is then calculated from the L and S for the atom rather than from the summation of jl established for each electron independently. Although the method here outlined may well have been used by others, a description of i t has not been noted in standard texts on the subject. One first writes down the possible m, values msociated with the orbital type (s, p, d, etc.) being filled in the valence shell. The available electrons are then placed (symbolically) in these suborbitals, one a t a time, keeping spins parallel until pairing becomes necessary in accord with the greatest multiplicity rule. For a given number of unpaired electrons, Hund's rule asserts that the state with largest L will have the lowest energy. This value may be derived by filling the ml levels in The ease of handling attoms with large numbers of d or such a way that the sum of ms: for all electrons has the felectrons is illustrated for Co, Cr, and Dy. One need largest possible absolute value. This sum will be not derive all poszible terms, which is quite tedious, identical with L (the maximum value of MZ)for the but can proceed directly to the ground state term. Assignment of electrons in other ways, using only combined atom. The simplicity of the method will be the valence orbitals and following the Panli exclusion made evident in the following examples. In N with a configuration of ls2 2s2 2p3, the 1s and principle, leads to M , and M , values which are either 2s orbitals are filled completely and do not contribute component parts of the ground state term or of perto low-lying spectral lines. For p orbitals, m, may mitted low-lying excited states. For some of the assume values of f l , 0, -1. One may construct a simpler cases the better student can verify that contable and assign the three 2 p electrons as described sideration of all permitted arrangements leads to the same set of terms derived by the usual method (Her5 IHERZBERG, G., "Atomic Spectra and Atomic Structure," berg'). Prentice-Ball, Inc., New York, 1937, p. 133.
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