588 



NA TURE 



[October 



1 (-' 



Letters to the Editor. 



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A Calculation of the Atomic Weights of Isotopes. 



Some months ago, when engaged on a study of 

 radioactive disintegration series, the results of which 

 appeared in tlie October issue of the Philosophical 

 Magazine, I was able to formulate simple rules from 

 radioactive data which enabled me to calculate a 

 list of the atomic weights of the principal isotopes 

 of both common and radioactive elements. This list, 

 which will be published in due course, agreed closely, 

 although not identically, with all the experimental 

 values of the atomic weights of the isotopes of the 

 common elements determined up to that date (June 

 1923) by Aston and others. Since then, in a recent 

 issue of Nature (September 22, p. 449), Aston has 

 published some further results with which my 

 predictions agree so exactly that I feel constrained 

 to give here a brief account of how my list was arrived 

 at, and to state some results which have yet to be 

 verified or disproved experimentally. 



The main supposition is that there are four separate 

 radioactive series the members of which have atomic 

 weights given respectively by 4«+3, ^n+2, 4«+i, 

 and 4n, where n is an integer. In the paper mentioned 

 above I give reasons for supposing that the first of 

 these is the actinium series, the second the uranium 

 series, the third a hypothetical series the end-products 

 of which may be bismuth {a =209) and thallium 

 {a =205), and the fourth the thorium series. It is 

 known that in the uranium and in the thorium series 

 successive changes are principally of two kinds : a 

 succession of o-particles, and the succession a, fi, fi 

 and a ; it is probable, and I assume it to be so, that 

 in the two other series the characteristic successive 

 changes are a succession of a-particles and the 

 succession a, /3, a, fi. 1 next imagine that radio- 

 activity continues below the so-called end-products 

 of the series, the uranium and thorium series being 

 continued by the elements of even atomic number 

 and the two other ones by the elements of odd 

 atomic number. There is no experimental evidence 

 for this, nor does it matter. The point is merely that 

 isotopes, which on radioactive evidence would be 

 presumed stable, would be found experimentally to 

 be the isotopes of common elements, and those 

 presumed instable (bodies which supposedly expel 

 /!i-particles, for example) would not be found. This 

 is reasonable. 



An arrangement of this kind yields a surprising 

 amount of information, and it may be claimed that 

 solely from radioactive evidence the following points 

 may be deduced : (i) It is probable, but not im- 

 possible, that isotopes do not differ by more than 

 8 units of atomic weight ; (2) only end-products 

 of radioactive series or radio-elements emitting a- 

 particles should be considered when a comparison is 

 made between common and radioactive isotopes ; 

 (3) all elements are limited to two isotopes of odd 

 atomic weight (odd isotopes), and these differ by 

 2 units of atomic weight only ; (4) odd elements 

 {i.e. elements of odd atomic number) have odd 

 isotopes only, and, if there be two, the lighter one is 

 likelier to be the more stable and consequently the 

 more abundant in Nature ; (5) even elements may 

 have both even and odd isotopes, but the former 

 should be as a rule at least twice as numerous as the 



NO. 2816, VOL. I 12] 



latter, and an odd isotope should not be either the 

 lightest or the heaviest o! all : (6) isobarcs of common 

 elements may be of even atomic weight only ; (7) 

 an element the atomic number of which is given by 

 4*1 -f 3 has an isotope of atomic weight 4n-f i, and 

 vice versa ; and (8) an even element has always one 

 isotope a unit of atomic weight higher than one of 

 the isotopes of the element next below it. 



Several of the above rules have already been pointed 

 out by Aston from his results on comi 

 They are indeed the common ground of 

 and radioactive isotopes. They do not ;ij)im\ m 

 their entirety to the elements below nickel and 

 cobalt. It is not to be expected that the Hgh*'- t 

 elements with their simple structure would Ix' 

 exactly like the heavier ones. In addition, it is p 

 able from atomic weight evidence and certain vvv 1 

 from Aston's results that the series 4« -f-2 and 4/. i 

 do not run continuously below the limit of cobalt 

 and nickel. 



If the radioactive evidence were decisive in r< 

 to which mass - numbers are unstable, and v. 

 are possible isobares, the determination by calcula- 

 tion of all the isotopes of all the elements would not 

 be difficult, but this does not apf>ear to be so. The 

 evidence does not give a complete solution because, 

 among other things, I have not considered possible 

 branching in any of the series. Branching no doubt 

 occurs according to some plan, but up to date I have 

 not discovered what that plan is. Consetiuently on 

 one or two occasions I have failed to agree entirely 

 with Aston's experimental results. For example, my 

 calculations give two isotopes to calcium, 44 and 40, 

 and two to argon, 40 and 36, but they indicate that 

 36 is the more abundant, whereas Aston's results 

 (and the atomic weight) contradict this. 



For the elements from hydrogen to ^-ttrium my 

 list is identical with Aston's list, which covers this 

 range completely, except that I say that scandium 

 has a second isotope at 47. Zirconium has an 

 isotope at 92 and possibly a third at 94, but no 

 others in addition to its principal one at 90 alreadv 

 established by Aston. Niobium has 93 and 95, 

 molybdenum is simple and 96. Element 43 would 

 have 97 or 99 if either existed, but they do not. 

 (Presumably a missing odd element is one which 

 occurs at a place where two successive odd mass- 

 numbers happen to be unstable.) Ruthenium has 

 100, loi, 102, and 104, possibly 98, but not 106. 

 Rhodium is principally, and probably only, 103. 

 Palladium is certainly 104, 106, and loS, not 105 but 

 possibly 102 and no. Silver is as given by Aston. 

 Cadmium is no, in, 112, 114, with perhaps 108 and 

 '116, but not 106. Indium is 115 only. Tin and 

 antimony are as given by .\ston. Tellurium is 

 mainly 128 and 126, with possibly 130 and 124 

 but not 122. (Were it not that 128 is greater than 

 the atomic weight of iodine I should be inclined 

 to say that, notwithstanding its atomic weight, 

 tellurium was mainly 128.) Iodine and cassium are 

 simple as given by Aston. Xenon is as given by 

 Aston, except that I drop 126 or 124. Lanthanum 

 and praesodymium are simple, 139 and 141 respect- 

 ively. It is more probable that cenum is simple 

 and 140 than complex and 140, 142, and 144. 

 Barium is complex, having 134, 136, and 138 but 

 not, if cerium be simple, 140, and it has no odd 

 isotopes. 



The rare earths are not difficult to do in spite of 

 the uncertainty of their atomic weights. Each of 

 the even rare earths is complex. Element 61 would 

 have 147 and 149 if either existed ; europium is 

 151 and 153, holmium 163 and 155, and thulium 169 

 and 171. In spite of their atomic weights, terbium is 

 159 only and lutecium only 177. Hafnium is mainly 



