PHYSICAL AND CHEMICAL PROPEBTIES OF THE ELE1O5NTS 67
Thus Moseley found for all the elements he investigated that the
frequencies of the strongest line in the L group may be represented
by a formula which with a simplification similar to that employed
in formula (8) can be written
Here again we obtain an expression for the frequency which corre-
sponds to a line in the spectrum which would be emitted by the
binding of an electron to a nucleus, whose charge is Ne.
The fine structure of the hydrogen lines. This similarity be-
tween the structure of the X-ray spectra and the hydrogen spectrum
was still further extended in a very interesting manner by Sommer-
feld's important theory of the fine structure of the hydrogen lines.
The calculation given above of the energy in the stationary states
of the hydrogen system, where each state is characterized by a
single quantnm number, rests upon the assumption that the orbit
of the electron in the atom is simply periodic. This is, however,
only approximately true. It is found that if the change in the mass
of the electron due to its velocity is taken into consideration the
orbit of the electron no longer remains a simple ellipse, bufc its
motion may be described as a central motion obtained by superposing
a slow and uniform rotation upon a simple periodic motion in a
very nearly elliptical orbit. For a central motion of this kind the
stationary states are characterized by two quantum numbers. In the
case under consideration one of these may be so chosen that to a
very close approximation it will determine the energy of the atom
in the same manner as the quantum number previously used
determined the energy in the case of a simple elliptical orbit. This
quantum number which will always be denoted by n will therefore
be called the "principal quantum number." Besides this condition,
which to a very close approximation determines the major axis in the
rotating and almost elliptical orbit, a second condition will be imposed
upon the stationary states of a central orbit, namely that the angular
momentum of the electron about the centre shall be equal to a whole
multiple of Planck's constant divided by STT. The whole number, which
occurs as a factor in this expression, may be regarded as the second
quantum number and will be denoted by k. The latter condition fixes
5—2