436 



SCIENCE 



[N. S. Vol. LII. No. 1349 



as before Tf = 2.270 F„ we find for l, the 

 distance from the nuclei to the center of the 

 molecule, the value 0.190 X 10-^ cm. The 

 moment of inertia is thus 1.20 X 10"*^ g. cm.^ 

 Since this value does not agree at all well 

 with the value 1.85 X 10"*^ calculated from 

 the spectrum it is improbable that this model 

 corresponds to the true structure of the 

 hydrogen molecule in its normal state. It 

 may be however that such a model with a dif- 

 ferent value for h may apply to a disturbed 

 state of the molecule. 



According to Bohr's theory in which the 

 paths of electrons are circular, a hydrogen ion 

 consisting of two hydrogen nuclei with one 

 electron, should not be capable of existing, for 

 the value of W for such a structure (0.88 W^) 

 is less than that for the hydrogen atom and 

 the ion should therefore break up into an 

 electron and a hydrogen atom. There seems 

 to be considerable experimental evidence^ that 

 the positive H, ion is stable and is formed 

 from ordinary molecular hydrogen when an 

 ionizing voltage of about 11 volts is applied. 



Since the H,"* ion has two nuclei there is no 

 obvious necessity for assuming a circular 

 path for the electron. I have therefore con- 

 sidered a model in which the electron oscil- 

 lates along a rectilinear path passing through 

 the center of the ion and perpendicular to the 

 line joining the nuclei. By the methods of 

 the classical mechanics it can be shown that 

 if we take h, the distance between the center 

 of the ion and the nuclei, as unity, then the 

 maximum displacement of the electron from 

 the center (i. e., at the end of its path) is 

 2.214. The velocity of the electron when it 

 passes the center of the ion is such that if it 

 should continue to move with this velocity it 

 would travel a distance 5.148 during the time 

 that it actually takes to move from the center 

 to the point furthest from the center. The 

 total energy W of the ion is 0.6468 W^a^^l. 

 As soon as 6 is known the ionizing potential 

 of hydrogen corresponding to this model can 

 be calculated. 



1 have tried to apply the quantum theory 



2 See particularly Franek, Knipping and Krilger, 

 Beut. Phys. Ges. Verh., 21, 728 (1919). 



in two difierent ways, although without cer- 

 tainty that either way is correct. According 

 to the first method I have assumed that the 

 angular momentum (or the moment of mo- 

 mentum) of the electron about each of the 

 nuclei is /i/2t when the electron passes through 

 the center. Of course the angular momentum 

 about one of the nuclei decreases as the elec- 

 tron moves further from the center but this 

 is due to the fact that the momentum is im- 

 parted to the other nucleus. A consideration 

 of Lande's models for the octet, as well as 

 the model which I previously proposed for the 

 helimn atom, suggests that in structures 

 having more than one electron and one 

 nucleus, we are concerned not with the 

 momentum possessed by any electron, but 

 rather with the momentura which is trans- 

 ferred from one electron to another or from 

 an electron to a nucleus. On the basis of this 

 assumption, it can be readily calculated that 

 the value of 6, the distance of the nuclei from 

 the center, is 0.4250 a^ or 0.225 X 10-« cm. 

 The energy of the ion is then 1.522 W^. 

 Since this is larger than that for the hydro- 

 gen atom, this ion will be stable. The differ- 

 ence between this energy and that for the 

 hydrogen molecule (i. e., 0.748 F„) corre- 

 sponds to the enei'gy required for ionization. 

 Expressed in volts this is 10.15 volts, which is 

 in fair agreement with the experimental 

 values (11 to 11.5 volts). 



In the second method of applying the 

 quantum theory I have used the relation 

 fydq = h where I have taken q to be the dis- 

 tance measured from the center along the 

 rectilinear path, and p is the momentum in 

 the direction of this path. As far as I know 

 there is no good reason for choosing this 

 particular coordinate system except that it 

 seems to be the simplest. These assumptions 

 lead to the value 6 = 5261 a^ = 0.279 X 10-^ 

 cm. The energy is then 1.229 W^, which 

 again corresponds to a stable hydrogen ion 

 but the ionizing potential is 14.1 volts. 



The evidence in favor for these models is 

 far from conclusive but in view of the fact 

 that Bohr's models for the hydrogen molecule 

 and ion can not be correct it seems important 



