76

THE STRUCTUBE OF THE ATOM AND THE

be regarded as occurring in N stages, corresponding with the suc-
cessive binding of JV electrons in the field of the nucleus. A spectrum
must be assumed to correspond to each of these binding processes;
but only for the first two elements, hydrogen and helium, do we
possess a detailed knowledge of these spectra. For other elements
of higher atomic number, where several spectra will be connected
with the formation of the atom, we axe at present acquainted with
only two types, called the "arc" and " spark " spectra respectively,
according to the experimental conditions of excitation. Although
these spectra show a much more complicated structure than the
hydrogen spectrum, given by formula (2) and the helium spectrum
given by formula (7), nevertheless in many cases it has been
possible to find simple laws for the frequencies exhibiting a close
analogy with the laws expressed by these formulae.

Are and spark spectra. If for the sake of simplicity we dis-
regard the complex structure shown by the lines of most spectra
(occurrence of doublets, triplets etc.), the frequency of the lines of
many arc spectra can be represented to a close approximation by
the Rydberg formula

. ' K Jg

where <nf and n" are integral numbers, K the same constant as in
the hydrogen spectrum, while a# and aw are two constants be-
longing to a set characteristic of the element. A spectrum with a
structure of this kind is, like the hydrogen spectrum, called a series
spectrum, since the lines can be arranged into series in which the
frequencies converge to definite limiting values. These series are
for example represented by formula (12) if, using two definite
constants for «#/ and a^, n" remains unaltered, while n' assumes a
series of successive, gradually increasing integral values.

Formula (12) applies only approximately, but it is always found
that the frequencies of the spectral lines can be written, as in
formulae (2) and (12), as a difference of two functions of integral
numbers. Thus the latter formula applies accurately, if the
quantities a^ are not considered as constants, but as representatives
of a set of series of numbers a& (n) characteristic of the element,
whose values for increasing n within each series quickly approachicles. Langmuir, who has attempted to develop Lewis' con-