th state of the
th series apart from an arbitrary additive constant being given by
This complicated character of the ensemble of stationary states of atoms of higher atomic number is exactly what was to be expected from the relation between the spectra calculated on the quantum theory, and the decomposition of the motions of the atoms into harmonic oscillations. From this point of view we may regard the simple character of the stationary states of the hydrogen atom as intimately connected with the simple periodic character of this atom. Where the neutral atom contains more than one electron, we find much more complicated motions with correspondingly complicated harmonic components. We must therefore expect a more complicated ensemble of stationary states, if we are still to have a corresponding relation between the motions in the atom and the spectrum. In the course of the lecture we shall trace this correspondence in detail, and we shall be led to a simple explanation of the apparent capriciousness in the occurrence of lines predicted by the combination principle.
The following figure gives a survey of the stationary states of the sodium atom deduced from the series terms.
Diagram of the series spectrum of sodium.
The stationary states are represented by black dots whose distance from the vertical line a—a is proportional to the numerical value of the energy in the states. The arrows in the figure indicate the transitions giving those lines of the sodium spectrum which appear under the usual conditions of excitation. The arrangement of the states in horizontal rows corresponds to the ordinary arrangement of the "spectral terms" in the spectroscopic tables. Thus, the states in the first row (
