March 24, 192 1] 



NATURE 



107 



the questions here discussed will be treated in greater 

 detail. In this letter it is my intention only to direct 

 attention to the possibilities which the elaboration of 

 the principles underlying the spectral applications of 

 the quantum theory seems to open for the interpreta- 

 tion of other properties of the elements. In this con- 

 nection I should also like to mention that it seems 

 possible, from the examination of the change of the 

 spectra of the elements in the presence of magnetic 

 fields, to develop an argument which promises to 

 throw light on the difficulties which have hitherto 

 been involved in the explanation of the characteristic 

 magnetic properties of the elements, and have been 

 discussed in various recent letters in Nature. 



N. Bohr. 

 Copenhagen, February 14. 



The Dimensions of Atoms and Molecules. 



Certain relations which are to be traced between 

 the distances separating atoms in a crystal make it 

 possible to estimate the distance between their centres 

 when linked together in chemical combination. On 

 the Lewis-Langmuir theory of atomic constitution, 

 two electro-negative elements when combined hold 

 one or more pairs of electrons in common, so that 

 the outer electron shell of one atom may be 

 regarded as coincident with that of the other at the 

 point where the atoms are linked together. From 

 this point of view, estimates may be made (W. L. 

 Bragg, Phil. Mag., vol. xi., August, 1920) ' from 

 crystal data of the diameters of these outer shells. 

 The outer shell of neon, for example, was estimated 

 from the apparent diameters of the carbon, nitrogen, 

 oxygen, and fluorine atoms, which show a gradual 

 approximation to a minimum value of 1-30x10-' cm. 

 The diameters of the inert gases as found in this 

 wav are given in the second column of the following 

 table : 



In the third column are given Rankine's values 

 (A. O. Rankine, Proc. Roy. Soc, A, vol. xcviii., 693, 

 pp. 360-74, February, 192 1) for the diameters of the 

 inert gases calculated from their viscosities by Chap- 

 man's formula (S. Chapman, Phil. Trans. Roy. Soc, 

 A, vol. ccxvi., pp. 279-348, December, 1915). These 

 are considerably greater than the diameters calculated 

 from crystals, but this is not surprising in view of 

 our ignorance both of the field of force surrounding 

 the outer electron shells and of the nature of the 

 electron-sharing which links the atoms together, for 

 it is quite possible that their structures might 

 coalesce to a considerable extent. The constancy of 

 the differences between the two estimates given in 

 the fourth column shows that the increase in the 

 size of the atom as each successive electron shell 

 is added is nearly^ the same (except in the case of 

 neon), whether measured by viscosity lOr by the 

 crystal data. Further, Rankine has shown that the 

 molecule CU behaves as regards its viscosity like two 

 argon atoms with a distance between their centres 

 very closely equal to that calculated from crystals, 

 and that the same is true for the pairs Brj and 

 krvpton, L and xenon. 



We see, therefore, that the evidence both of crystals 

 and viscosity measurements indicates that (a) the ele- 

 ments at the end of any one period in the periodic 

 table are very nearly identical as regards the diameters 



NO. 2682, VOL. 107] 



of their outer electron shells, and (b) in passing from 

 one period to the next there is a definite increase in the 

 dimensions of the outer electron shell, the absolute 

 amount of this increase estimated by viscosity agree- 

 ing closely with that determined from crystal 

 measurements. 



A further check on these measurements is afforded 

 by the infra-red absorption spectra of HF, HCl, and 

 HBr. The wave-number difference Sv between sue 

 cessive absorption lines determines the moment of 

 inertia I of the molecule in each case, the formula 

 being 



8u = 



47r-Vl' 



where h is Planck's constant and c the velocity of 

 light. 



It is therefore possible to calculate the distances 

 between the centres of the nuclei in each molecule, 

 for 



2_m + m' h 



mm' ' \-n^cm^v 



where t»z and m' are the atomic weights relative to 

 hydrogen and tn^ the mass of the hydrogen atom. 

 The following table gives these distances (E. S. Imes, 

 Astroph. Journal, vol. 1., p. 251, 1919). It will be 

 seen that there are again increases in passing from 

 F to CI and CI to Br, which agree closely with the 

 increases in the radii o- of the electron shells given 

 by the crystal and viscosity data. 



The increase from fluorine to chlorine of 

 0-35x10-' cm. confirms the estimate given by 

 crystals of 0-37x10-* cm., as against the estimate 

 0-26x10-' cm. given by viscosity data. It follows 

 from the above that the distance between the hydrogen 

 nucleus and the centre of an electro-negative atom to 

 which it is attached is obtained by adding 

 0-26x10-' cm. to the radius of the electro-negative 

 atom as given by crystal structures. TTie radius of 

 the inner electron orbit, according to Bohr's theory, 

 is 0-53 X10-' cm., double this value. The crystal 

 data, therefore, predict the value 8v = i3-o cm.-' for 

 the HI molecule, corresponding to a distance 

 I-6IXIO-* cm. between their atomic centres. 



This evidence is interesting as indicating that the 

 forces binding the atoms together are localised at that 

 part of the electron shell where linking takes place. 



W. L. Bragg. 

 H. Bell. 



Manchester University, March 16. 



The International Research Council. 



The object of this council, says Sir Arthur Schuster 

 in Nature of March 17, is "to reorganise international 

 work which had come to a standstill through the 

 war, and to extend it where found desirable." It 

 may be worth while to consider for a moment how 

 the council has set to work to promote these innocent 

 and laudable ends. 



