434 



SCIENCE 



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



is in better accord with the chemical rela- 

 tionships of helium than is the model pro- 

 posed by Bohr. It leads to a value 25.59 

 volts for the ionizing potential in agreement 

 with experimental determinations while Bohr's 

 theory gives too high a value. In the model 

 which I proposed the two electrons move in 

 separate orbits in a plane containing the 

 nucleus. The electrons are always sym- 

 metrically located with respect to a second 

 plane which passes through the nucleus and 

 is perpendicular to the plane of the orbits. 

 Each electron thus oscillates back and forth 

 along an approximately semi-circular path. 



We may conceive of the hydrogen molecule 

 ■as having a similar structure except that 

 there are two nuclei. The electrons may 

 thus move in separate orbits in a plane which 

 is perpendiciilar to and bisects the line con- 

 necting the nuclei. The positions of the 

 <electrons at any time are symmetrical with 

 respect to another plane which passes through 

 both nuclei. Starting from two points on 

 ■opposite sides of the center of the molecule, 

 we may imagine the electrons to revolve 

 ■about the center in opposite directions. After 

 something less than a quarter revolution the 

 electrons come so close to one another that 

 the repulsive forces between them bring them 

 both to rest. These forces then cause them 

 ■to return back along the same paths to the 

 starting points. They then continue their 

 motion and complete another quarter of a 

 cycle before they again come to rest. Each 

 electron thus oscillates along a nearly semi- 

 'circular line. 



On the basis of the classical mechanics, by 

 a series of approximations, it is possible to 

 calculate the size and shape of the orbits and 

 the relative velocities of the electrons at any 

 point in their paths in terms of the distance 

 between the nuclei. If we let a be the dis- 

 tance from the center of the molecule to the 

 mid-point of the nearly semicurcular orbit of 

 the electron, then the distance between the 

 nuclei is 0.619 X a and the radius vector of 

 the electron at the ends of the orbit (where 

 the electron comes to rest) is 1.152 X «• The 

 ;angle through which the electrons move is 



71° 26' each side of the m.id'-point as measured 

 from the center of the molecule. The angu- 

 lar velocity of the electrons at the mid-points 

 of their paths is such that if they continued 

 to move with this velocity they would travel 

 through 106° 00' during the time that they 

 actually take to move tO' the end of the orbits 

 (i. e., through 71° 26'). The total energy 

 (TF) of the molecule (kinetic plus potential) 



is found to be 1.604 "" where W ^ is the 



a 

 corresponding energy for the hydrogen atom 

 according to Bohr's theory and a^ is the 

 radius of the electron orbit in the hydrogen 

 atom (0.530 XlO-s cm.). 



It should be possible by means of the 

 quantum theory to determine a, and fix the 

 absolute dimensions of this model. But, so 

 far as I know, the quantum theory has not 

 yet been formulated in such a way that it 

 can be applied with certainty to the type of 

 motion that we are here considering. The 

 quantum condition fpdq = nh is only valid 

 when the co-ordinates are chosen in a partic- 

 ular manner, and for a case like the one in 

 hand I have not been able to find any general 

 method for determining what system of co- 

 ordinates should be used. It may be, how- 

 ever, that others having greater familiarity 

 with the recent mathematical development of 

 the quantum theory will be able to determine 

 the value of a for the model under consider- 

 ation. 



I have therefore proceeded to calculate the 

 value of a from the known heat of dissociation 

 of molecular hydrogen into atoms, and then 

 to test this result by calculating other proper- 

 ties of hydi'ogen. Taking q the heat of dis- 

 sociation (at constant volume), as 84,000 

 calories per gram molecule we find that 

 TF/W = 2.270. Since q is proportional to 

 W — 2 W„ it takes a relatively large change in 

 q to have much effect on the value of W. 

 Thus an error of eight per cent, in deter- 

 mining the heat of dissociation (which is 

 greater than the probable error), would cause 

 only a one per cent, error in W and in a. 

 From the relation previously given, we thus 

 find a = 0.707(j„ = 0.375 X lO-^ cm. When the 



