§ 4. The high frequency spectra of the elements.
Reading edition
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 type. The value calculated for this energy was equal to the expression (5) if . In the calculation the repulsion from the other electrons in the ring was neglected. This must result in making the value a little too large, but on account of the complexity of the problem no attempt at that time was made to obtain a more exact determination of the energy.
These considerations have obtained strong support through Moseley’s important researches on the high frequency spectra of the elements[29]. Moseley found that the frequency of the strongest lines in these spectra varied in a remarkably simple way with the atomic number of the corresponding element. For the strongest line in the radiation he found that the frequency for a great number of elements was represented with considerable accuracy by the empirical formula where is the Rydberg constant in the hydrogen spectrum. It will be seen that this result is in approximate agreement with the calculation mentioned above if we assume that the radiation is emitted as a quantum .
Moseley pointed out the analogy between the formula (14) and the formula (3) in section 2, and remarked that the constant was equal to the last factor in this formula, if we put and . He therefore proposed the explanation of the formula (14), that the line was emitted during a transition of the innermost ring between two states in which the angular momentum of each electron was equal to and respectively. From the replacement of by he deduced that the number of electrons in the ring was equal to 4. This view, however, can hardly be maintained. The approximate agreement mentioned above with Whiddington’s measurements for the energy necessary to produce the characteristic radiation indicates very strongly that the spectrum is due to a displacement of a single electron, and not to a whole ring. In the latter case the energy should be several times larger. It is also pointed out by Nicholson[30] that Moseley’s explanation would imply the emission of several quanta at the same time; but this assumption is apparently not necessitated for the explanation of other phenomena. At present it seems impossible to obtain a detailed interpretation of Moseley’s results, but much light seems to be thrown on the whole problem by some recent interesting considerations by W. Kossel[31].
Kossel takes the view of the nucleus atom and assumes that the electrons are arranged in rings, the one outside the other. As in the present theory, it is assumed that any radiation emitted from the atom is due to a transition of the system between two steady states, and that the frequency of the radiation is determined by the relation (1). He considers now the radiation which results from the removal of an electron from one of the rings, assuming that the radiation is emitted when the atom settles down in its original state. The latter process may take place in different ways. The vacant place in the ring may be taken by an electron coming directly from outside the whole system, but it may also be taken by an electron jumping from one of the outer rings. In the latter case a vacant place will be left in that ring to be replaced in turn by another electron, etc. For the sake of brevity, we shall refer to the innermost ring as ring 1, the next one as ring 2, and so on. Kossel now assumes that the radiation results from the removal of an electron from ring 1, and makes the interesting suggestion that the line denoted by Moseley as corresponds to the radiation emitted when an electron jumps from ring 2 to ring 1, and that the line , corresponds to a jump from ring 3 to ring 1. On this view, we should expect that the radiation consists of as many lines as there are rings in the atom, the lines forming a series of rapidly increasing intensities. For the radiation, Kossel makes assumptions analogous to those for the radiation, with the distinction that the radiation is ascribed to the removal of an electron from ring 2 instead of ring 1. A possible radiation is ascribed to ring 3, and so on. The interest of these considerations is that they lead to the prediction of some simple relations between the frequencies of the different lines. Thus it follows as an immediate consequence of the assumption used that we must have It will be seen that these relations correspond exactly to the ordinary principle of combination of spectral lines. By using Moseley’s measurements for and and extrapolating for the values of by the help of Moseley’s. empirical formula, Kossel showed that the first relation was closely satisfied for the elements from calcium to zinc. Recently T. Malmer[32] has measured the wave-length of and for a number of elements of higher atomic weight, and it is therefore possible to test the relation over a wider range and without extrapolation. The table gives Malmer’s values for and Moseley’s values for , all values being multiplied by .
N 40 42 44 46 47 50 51 57
4.6 5.5 6.1 6.6 6.9 8.4 9.0 11.6
4.93 5.53 6.17 6.84 7.19 8.29 8.67 11.21
It is seen that the agreement is close, and probably within the limits of experimental error. A comparison with the second relation is not possible at present, and we meet also here with a difficulty arising from the fact that Moseley observed a greater number of lines in the radiation than should be expected on Kossel’s simple scheme[33].
There is another point in connexion with the above considerations which appears to be of interest. In a recent paper W. H. Bragg[34] has shown that, in order to excite any line of the radiation of an element, the frequency of the exciting radiation must be greater than the frequency of all the lines in the radiation. This result, which is in striking contrast to the ordinary phenomena of selective absorption, can be simply explained on Kossel’s view. The simple reverse of the process corresponding to the emission of, for instance, would necessitate the direct transfer of an electron from ring 1 to ring 2, but this will obviously not be possible unless at the beginning of the process there was a vacant place in the latter ring. For the excitation of any line in the radiation, it is therefore necessary that the electron should be completely removed from the atom. Another consequence of Kossel’s view is that it should be impossible to obtain the series of an element without the simultaneous emission of the series. This seems to be in agreement with some recent experiments of C. G. Barkla[35] on the energy involved in the production of characteristic Röntgen radiation. From these examples it will be seen that even if Kossel’s considerations will need modification in order to account in detail for the high frequency spectra, they seem to offer a basis for a further development.
As in the former section, it is assumed that the spectra considered above are due to the displacement of a single electron. If, however, several electrons should happen to be removed from one of the rings by a violent impact, the considerations at the end of the former section would not apply, since the electrons removed in this case can be replaced by electrons in the other rings. We might therefore possibly expect that the rearrangement of the electrons, consequent to the removal of more than one electron from a ring, would give rise to spectra of still higher frequency than those considered in this section.
University of Manchester, August 1915.