. This agrees very closely with the value calculated on the present theory for the energy necessary to remove one electron from the helium atom, viz., 29.3 volts. On the other hand, the later value is considerably larger than the ionization potential in helium (20.5 volts) measured directly by Franck and Hertz[23]. This apparent disagreement, however, may possibly be explained by the assumption, that the ionization potential measured does not correspond to the removal of the electron from the atom but only to a transition from the normal state of the atom to some other stationary state where the one electron rotates outside the other, and that the ionization observed is produced by the radiation emitted when the electron falls back to its original position. This radiation would be of a sufficiently high frequency to ionize any impurity which may be present in the helium gas, and also to liberate electrons from the metal part of the apparatus. The frequency of the radiation would be
, which is of the same order of magnitude as the characteristic frequency calculated from experiments on dispersion in helium, viz.,
[24].
Similar considerations may possibly apply also to the recent remarkable experiments of Franck and Hertz on ionization in mercury vapour[25]. These experiments show strikingly that an electron does not lose energy by collision with a mercury atom if its energy is smaller than a certain value corresponding to 4.9 volts, but as soon as the energy is equal to this value the electron has a great probability of losing all its energy by impact with the atom. It was further shown that the atom, as the result of such an impact, emits a radiation consisting only of the ultraviolet mercury line of wave-length 2536, and it was pointed out that if the frequency of this line is multiplied by Planck’s constant, we obtain a value which, within the limit of experimental error, is equal to the energy acquired by an electron by a fall through a potential difference of 4.9 volts. Franck and Hertz assume that 4.9 volts corresponds to the energy necessary to remove an electron from the mercury atom, but it seems that their experiments may possibly be consistent with the assumption that this voltage corresponds only to the transition from the normal state to some other stationary state of the neutral atom. On the present theory we should expect that the value for the energy necessary to remove an electron from the mercury atom could be calculated from the limit of the single line series of Paschen, 1850, 1403, 1269[26]. For since mercury vapour absorbs light of wave-length 1850[27], the lines of this series as well as the line 2536 must correspond to a transition from the normal state of the atom to other stationary states of the neutral atom (see I. p. 16). Such a calculation gives 10.5 volts for the ionization potential instead of 4.9 volts[28]. If the above considerations are correct it will be seen that Franck and Hertz’s measurements give very strong support to the theory considered in this paper. If, on the other hand, the ionization potential of mercury should prove to be as low as assumed by Franck and Hertz, it would constitute a serious difficulty for the above interpretation of the Rydberg constant, at any rate for the mercury spectrum, since this spectrum contains lines of greater frequency than the line 2536.
It will be remarked that it is assumed that all the spectra considered in this section are essentially connected with the displacement of a single electron. This assumption—which is in contrast to the assumptions used by Nicholson in his criticism of the present theory—does not only seem supported by the measurements of the energy necessary to produce the spectra, but it is also strongly advocated by general reasons if we base our considerations on the assumption of stationary states. Thus it may happen that the atom loses several electrons by a violent impact, but the probability that the electrons will be removed to exactly the same distance from the nucleus or will fall back into the atom again at exactly the same time would appear to be very small. For molecules, i. e. systems containing more than one nucleus, we have further to take into consideration that if the greater part of the electrons are removed there is nothing to keep the nuclei together, and that we must assume that the molecules in such cases will split up into single atoms (comp. III. p. 2).
§ 4. The high frequency spectra of the elements.
In paper II. it was shown that the assumption E led to an estimate of the energy necessary to remove an electron from the innermost ring of an atom which was in approximate agreement with Whiddington’s measurements of the minimum kinetic energy of cathode rays required to produce the characteristic Röntgen radiation of the
