332 BELL SYSTEM TECHNICAL JOURNAL 



Third — -and now comes a surprise, for you will probably expect me 

 to say of the magnetic moment that it is ehjAirm-c multiplied either by 

 an integer or a half-integer; but this is not so. The actual state of 

 affairs is described by a formula which is called the g-formula, because 

 it gives g in terms of the moments, both spin and orbit, of the individual 

 electrons. It was discovered by Lande and interpreted in terms of 

 the spinning electron by Goudsmit. The ^-formula gives unity, as of 

 course it must, in the special cases where the electron-spins cancel 

 each other and only the orbital moments are left over, and it gives 2 

 in the special cases where the orbital moments are neutralized with 

 only the spins left over. In the other cases it may give any one of a 

 large variety of values: mostly one gets simple-looking fractions such 

 as 9/8 and 4/3 and 5/6. The magnetic moments are then computed 

 by multiplying the appropriate ^^'-values times ejlmc, into the existing 

 values of angular momentum.^ 



I now turn to that component of the atom of which the spin remains 

 to be discussed — to the nucleus. 



As I have already intimated, the values of p and n and // for the 

 electron-family of any atom are mostly ascertained by analyzing their 

 spectra and utilizing the great general theory of spectra. Such 

 magnetic experiments as I used for my examples are relatively few, 

 and feasible for relatively few substances. The reason for making 

 this remark at this late moment is, that by analyzing spectra we may 

 also learn something about the spins of nuclei; for nuclei also are 

 invested with these properties of angular momentum and of magnetic 

 moment. I take in particular the case of the proto?i — that lightest of 

 all nuclei, the nucleus of the lightest known kind of atom which is 

 ordinary hydrogen, so called to distinguish it from "heavy" hydrogen. 

 Analysis of the spectrum of hydrogen shows us that the proton is 

 capable of taking two permitted orientations in a field; thus, our first 

 piece of information about the proton-spin is conveyed by writing 

 n = 2. 



Now that we have this piece of information, we deduce that as the 



spinning electron has an «-value of 2 and an angular momentum of 



^(h/lir), so the proton with its w-value of 2 must have an angular 



momentum of \{hl2ir). Continuing along this line of thought, we 



are further tempted to infer that the proton should have a g-value of 



2 and a magnetic moment of {ehj^irmc). But what shall we suppose 



^ Should any reader intend to proceed from this article to a thorough study ot 

 atomic theory, he should be warned in advance that according to the latest form of 

 quantal theory, the />- values and the /u-values here given are the values of the projec- 

 tions of these vectors upon the field-direction, the magnitudes of the vectors them- 

 selves being somewhat greater: I have given details as to this in "Contemporary 

 Advances in Physics, XXIX, . . ." This Journal, 14, pp. 293 ff.(1935). 



