202 



NATURE 



[April 14, 192 1 



to another is recognised as splendid exercise in the 

 process of "initiation "; but for the uninitiated there 

 should be only one system of units, and that the very 

 best there is. Comprehension soon follows when 

 principles are really sound and scientific in the best 

 sense. That is the real advantage of "a normal 

 constant " of 200, which means in this case counting 

 degrees upwards continuously from —273° C. 



In order to meet the objection that temperatures 

 expressed in this way are not, strictly speaking, in 

 the absolute scale, I suggested in Nature some years 

 ago that the scale of Centigrade degrees measured 

 from —273 should be called " tercentesimal." 



April 2. Napier Shaw. 



Isotopes: Their Number and Classification. 



One of the most remarkable characteristics of 

 atoms is their predilection for the number 2 or for 

 even numbers. The nuclei of atoms are now con- 

 sidered to be built up from hydrogen nuclei, which 

 may be called positive electrons or protons. Suppose 

 these to be P in number. Combined with these are 

 N negative electrons. Since these N negative elec- 

 trons may for most purposes be considered to 

 neutralise the charge of N protons, the net positive 

 charge on the nucleus is equal to P-N or M, the 

 Moseley or atomic number. Now it is most rerhark- 

 able that in about 97-98 per cent, of all atoms N is 

 even ; in 90-95 per cent. P is even ; and M or P-N 

 is also even in 89 per cent, of the atoms in the 

 surface of the earth and in 98 per cent, of the atoms 

 in thie meteorities. 



According to the theory of nuclear building pub- 

 lished by the writer in 1915 and 1917, not only are 

 the above facts to be expected, but also, as was 

 pointed out specifically by N. F. Hall in the latter 

 year, the number of isotopes should be considerably 

 greater for elements of even than for those of odd 

 atomic number. The recent remarkable positive-ray 

 work of Aston, together with the investigation of 

 magnesium by Dempster, show that eleven elements 

 of even number consist of about three isotopes each, 

 while those of odd number average only 1-44, or more 

 than twice as many when the atomic number is even. 

 The contrast should be very marked in the region of 

 abundant isotopes between atomic numbers 28 and 83, 

 or from nickel to bismuth. Keeping in mind this 

 distinction between odd and even numbers, it may 

 be predicted that nearlv three hundred atomic species 

 will be found when all the ninety-two elements are 

 investigated fully, using methods of the present 

 delicacy. An increase in the delicacy of the method 

 of detection will naturally increase the number of 

 isotopes discovered. 



The number 2 occurs in another fundamental con- 

 nection, since in no known permanently existing 

 species of atoms in which the nucleus is complex 

 is the number of protons more than twice the 

 number of electrons, or the ratio N/P is never less 

 than 1/2. This fundamental law was fully discussed 

 in an earlier paper by the writer ("The Stability of 

 Atoms as Related to the Positive and Negative Elec- 

 trons in their Nuclei," Journ. Amer. Chem. Soc, 

 vol. xlii., pp. 1956-97, 1919). It is of great interest 

 that for 85 per cent, of the atoms of the earth's crust 

 and 80 per cent, of those in the meteorites N/P is 

 neither less nor more than 1/2. Thus most atom 

 nuclei have the formula (p^e)^, and for such atoms 

 M is almost ^ always a multiple of 2 or an even 

 number, but is odd in the very rare lower isotopes 

 of lithium, boron, and also in nitrogen, which is a 

 moderately rare element on earth, since it makes"^ up 

 onlv a very small fraction of the material of the 

 earth's crust. 



Let us specify the atoms of this important class as 

 those of isoto-pic nuinber o. Then the isotopes of 

 magnesium of atomic weights 24, 25, and 26 will 

 have isotopic numbers o, i, and 2, and may be 

 specified as Mg i2n", i2o", and i2g'\ where 12 is the 

 atomic number. It is easily seen that the isotopic 

 number n is the number which, when added to twice 

 the atomic number, gives the atomic weight (P). The 

 Harkins-Wilson equation for atomic weights is 

 P = 2M+2/, where / has values o to 27 for complex 

 nuclei and —1/2 for hydrogen. It is now proposed to 

 change this classification of atoms by their / values 

 (loc. cit.) into a classification according to their n 

 values, where n, the isotopic number, takes the place 

 of 2/ in the above equation. The isotopic number 

 of uranium is 54, the isotopes of krypton are 6, 8, 10, 

 II, 12, and 14, those of chlorine are i and 3, that of 

 arsenic is 9, those of bromine are 9 and 11, that of 



NO. 2685, VOL. 107] 



AT. NO, 



Fig. j. — The abundance of Uo^opes as a function of the isotopic number, 

 .^nd as a function of the atomic number. While this figure exhibits the 

 relations in the meteorite*;, the similar figure for the earth's crust is 

 almo.st identical, except that the peak for aluminium is higher, and those 

 for magnesium \o«rer. 



iodine is 21, etc. It is of interest to note that the 

 isotopic numbers of elements of even atomic number 

 are mostly even, while those of odd atomic number 

 are mostly odd. 



The isotopic number may be defined as the number 

 of neutrons (pe) which would have to be added to 

 the atom of the same atomic number, but of zero 

 isotopic number, to give the composition of the 

 nucleus. Thus the formula of any nucleus would be 

 (/a<?)M( /<?)„• 



It is of interest to note that most atoms have an 

 isotopic number o, but that their abundance decreases 

 rapidly to isotopic number i, which includes sodium, 

 aluminium, and silicon, decreases again to isotopic 

 number 2, and becomes almost zero in isotopic 

 number 3. With isotopic number 4 the abundance 

 rises again to a secondary maximum, and then 

 decreases again (Fig. i.). Thus there is a certain 



