126 BELL SYSTEM TECHNICAL JOURNAL 



systems of odd niulliplicity. Thus to produce a singlet system it is 

 necessary to put P/? = ^ (Ji /2Tr) always; to set Pv equal to i (/i/27r) for 

 all ^-states, to 4 (/?/27r) for all P-states, and so forth; and to suppose 

 that the two whirling parts of the atom are constrained to take only 

 such relative orientations as yield values for Pa, the angular momen- 

 tum of the entire atom, which are odd integer multiples of | {h/2ir). 

 It is easy to see that there is but one such orientation for an s-state, 

 one for a ^-state, and one for any other kind of state. To produce a 

 triplet, or a quintet, or a septet system, it is necessary to put Pr = 

 f (^/27r), or 4(^/27r), or ^ (/?/27r), respectively; and to retain the 

 just-stated assumptions about Pv and Pa- 



The question whether these models have any intrinsic truthfulness 

 has now become acute. If there is any doctrine in contemporary 

 atomic theory which appears to be multiply tested and approved, it is 

 surely the doctrine that the angular momentum of the valence-electron 

 is always an integer multiple of h/2T. Yet in this passage I have 

 spoken as if this principle had been indifferently and casually dis- 

 carded, and replaced by a new principle to the effect that the angular 

 momentum of the valence-electron is always an odd-integer multiple 

 of I /7/27r. It is hard to evade or mitigate this arrant contradiction. 



A way out may possibly be found by suggesting that the partition 

 of an atom into "residue" and "valence-electron," while appropriate 

 when calculating energy-values by the method mentioned in Section 

 P, is not appropriate in this instance; that the two whirling parts of 

 the atom are respectively a system composed of a part of the residue, 

 and a system composed of the rest of the residue and the valence- 

 electron. This seems most admissible for such an atom as magnesium, 

 consisting as it is supposed of what I have called a "kernel," and two 

 additional electrons outside. The two whirling parts may be the kernel 

 rotating as a unit, and the pair of outer electrons also rotating as a 

 unit. It may be profitable to push the analysis even further, and to 

 consider the two outer electrons each as an entity possessed of angular 

 momentum, their two angular momenta combining with one another 

 in such a fashion as I have lately described for the two parts of the 

 atom; this resultant angular momentum of the two may then figure 

 as the Pv employed in constructing the atom-model. There are 

 decided possibilities In this way of thinking; but it is doubtful whether 

 the difficulty about half-quantum-numbers can ever quite be removed.* 



8 An unfortunate foature of Landt's model in its original form is that it requires 

 us to believe that the residue of each atom is different from the completed pre- 

 ceding atom. I-'or instance since Mg has a singlet and a triplet system, its residue 

 must have sometimes P,i=\{h/lTr) and sometimes P ii = '\ h/l-w; whereas for the 

 Na atom in its normal state P^ = /i/2:r by the theory. 



