July 8, 1922] 



NA TURE 



37 



Letters to the Editor. 



[The " Editor does not hold liimself responsible for 

 opinions expressed by his correspondents. Neither 

 can he undertake to return, or to correspond -with 

 the writers of, rejected manuscripts intended for 

 this or any other part of NATURE. No notice is 

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The Difference between Series Spectra of Isotopes. 



Prof. P. Ehrenfest and Prof. N. Bohr, in their 

 letters to Nature of June 10, have raised the inter- 

 esting question of the difference to be expected 

 between the spectra of isotopes. Much confusion, 

 as their letters clearly indicate, exists on the subject, 

 and while not in disagreement with any of their 

 conclusions, I should like to make a few remarks 

 which may tend to elucidate the matter somewhat 

 further. 



Prof. Ehrenfest raised the question in relation to 

 the spectra of the isotopes of lithium — the subject of 

 an investigation by Prof. Zeeman — and pointed out 

 that the factor M./(m +M) in the Rydberg constant 

 was only deduced by Bohr — L and subsequently used 

 by Fowler to obtain the best estimate we have for the 

 ratio w/M, in his Bakerian lecture — for the case of 

 an atom with a single electron. He justifiably rejects 

 anv conclusions founded on its application to atoms 

 with more than one electron, and Prof. Bohr entirely 

 concurs. Ehrenfest 's illustration of an atom in which 

 the mass of the nucleus, on account of symmetry, 

 does not enter into the spectrum at all, is perhaps a 

 sufficient indication of the difficulty of the problem, 

 if such symmetrical atoms can exist, a matter which 

 appears improbable. 



The spectra of the lithium isotopes are at present 

 peculiarly interesting since the announcement that 

 Prof. M'Lennan has isolated them and found a differ- 

 ence which is greater than that calculated by the Bohr 

 formula, and in fact three times this value, while 3 

 is the accepted atomic number of lithium. The 

 quantum theory is unable to explain this large 

 separation, and its exponents must doubt the fact 

 that M'Lennan 's new series is the spectrum of an 

 isotope. There are two alternatives — it may be 

 a combination series or a spark series. In an investi- 

 gation which the present writer made a year ago, on 

 some of the simpler possible orbits in a lithium 

 atom with only two electrons, a specially simple class 

 of orbits was found. Although the work is not yet 

 published, it is possible to state that its result gave, 

 as the principal spark-line of lithium, a value very 

 close to X 6708, the red line shown in the ordinary 

 spectrum. This line had already been suspected, by 

 several spectroscopists, to have a spark component. 



In these simple orbits of a lithium atom positively 

 charged, the two electrons are behaving very differ- 

 ently. The orbit of one of them is only about -,'.-. the 

 linear dimensions of that of the other, so that the 

 Bohr formula for one electron is nearly applicable. 

 In fact, the orbits are very closely analogous to those 

 now generally accepted for the neutral helium atom, 

 which can take two forms, in both of which the orbit 

 of one electron is very small compared with that 

 of the other ; the orbits differ mainly in the fact that 

 in ortho - helium they are practically coplanar, and 

 in parhelium practically perpendicular. 



I have found it possible by a choice of the simpler 

 orbits, and by the supposition made by Sommerfeld 

 and others as to the invariability of the energy W 

 for all possible orbits, to show that the inner orbit 

 has a radius only about -,V of that of the outer. 

 Thus the Bohr formula is again nearly true, and the 

 Tvydberg constant in the ordinary helium series is not 

 very different from its value in the Pickering series. 



NO. 2749, VOL. I IO] 



Such results are suggestive, and appear to indicate 

 that when there are many electrons in an atom, 

 a ratio roughly of order tV exists between the orbital 

 radii of the two outer consecutive electrons. An 

 immediate consequence is that the Bohr formula 

 would never be very far wrong in its use for a rough 

 determination of the separation to be looked for in 

 the spectra of isotopes. If the correspondence with 

 these results does not, however, extend to heavier 

 atoms, we are precluded from making any prediction 

 without the knowledge of the general position — 

 on the average — of the centre of mass of an atom. 

 In a problem of this nature no general treatment is 

 possible, and no general simple law of separation 

 down the Periodic Table is to be expected. 



J. W. Nicholson. 

 Balliol College, Oxford, June 12. 



A Possible Reconciliation of the Atomic Models 

 of Bohr and of Lewis and Langmuir. 



Broadly -speaking, the merits of Bohr's atomic 

 model lie in its very accurate explanation of the 

 reaction of atoms and molecules with radiation, 

 while those of the Lewis-Langmuir model lie in its 

 very satisfactory representation of the mechanism 

 of chemical combination, but the merits of either 

 model are lacking in the other. Both must therefore 

 possess properties which are accurate representations 

 of the truth, and the problem remains to devise a 

 third model which will incorporate those properties 

 in its structure. The following considerations lead 

 to a modification of the Lewis-Langmuir model, 

 which appears to be a satisfactory solution of the 

 problem — so far as I am aware it is new. 



Consider first the well-known Lewis-Langmuir 

 model for any atom. It is built up of the central 

 nucleus and its surrounding electrons the mean posi- 

 tions of which are fixed with respect to one another 

 and to the position of the nucleus. Now in order to 

 account for the reaction between the atom and 

 radiant energy it is necessary to assume that these 

 electrons possess acceleration of some kind. The 

 particular kind most agreeable with the results of 

 experiment is the orbital acceleration assumed by 

 Bohr. But since the electrons are fixed (or can be 

 assumed to move but very slightly from their fixed 

 mean positions) in the Lewis-Langmuir model, 

 orbital acceleration is impossible. 



Now, apparently, a way out of this difficulty is to 

 assume that the electron shells are fixed and the 

 nucleus rotates on an axis. 



By the Theory of Relativity it is immaterial whether 

 — viewing a given atom — we regard the electrons as 

 describing orbits around a fixed nucleus (not fixed in 

 position only) or whether we regard the nucleus as 

 rotating inside the electron shell or shells with each 

 electron fixed relatively to the others. That is, the 

 nucleus possesses acceleration with respect to the 

 electrons, or what is the same thing, the electrons 

 possess acceleration with respect to the nucleus in 

 spite of the fact that they are fixed relatively to outside 

 systems such as other electron shells. Therefore this 

 model when viewed with respect to the electron shells 

 is precisely the same as the Lewis-Langmuir model, 

 and, furthermore, with respect to the whole atom it 

 possesses all the merits of Bohr's model. That is, it 

 appears to be a satisfactory reconciliation of the two 

 atomic models. 



Furthermore, the proposed model possesses the 

 further merit that by its aid we can predict the exist- 

 ence of isotopes. Thus if the nucleus of a given atom 

 possesses more than one stable axis of rotation with 

 respect to itself, or to its surrounding shells of elec- 



