SAO 



NATURE 



[Seitlmli;k i, 192, 



The Hydrogen Molecule. 

 By Prof. H. Stanley Allen. 



MODICLS for the representation and elucidation of 

 physical phenomena ha\e played an important 

 part in the advancement of science. Mathematicians, 

 who employ the method known as " the ignoration 

 of co-orclinates," may be satisfied with either a kinetic 

 or a static model for an atom or a molecule, but the 

 physicist and especially the chemist will, as a rule, 

 prefer a static model. Sir J. J. Thomson ' has done 

 much to bridge the gap between chemistry and 

 physics by making a serious attempt to show how, 

 on the electronic theory of matter, atoms may be 

 linked together to form the stable system which 

 constitutes a molecule. To avoid the difficulties 

 inherent in the view that the electrons are in orbital 

 motion, he is led to postulate a more complicated 

 law of force than that of the inverse square of the 

 distance. For example, he considers the result of 

 assuming a repulsion varying inversely as the cube 

 of the distance superposed on the ordinary electro- 

 static attraction between a positive charge and an 

 electron. Such a law of force may be adjusted to 



unit, that is, the one hundred millionth part of a 

 centimetre. The distance between the centres of the 

 spheres is 0-531 A.U., with an error of perh -"^ '••>•• or 

 two units in the third significant figure. N al 



meaning is to be attached to the size of i... ,...;.:' s 

 themselves. 



In a paper publbhed by the Physical Society ' 

 London* the writer has pointed out that a force 

 of exactly the type required in Langmuir's theory 

 is provided by the quantum mechanism described 

 by Prof. E. T. Whittaker.* Thus a static atom may 

 be obtained by transferring the motion of the cl' 

 in Bohr's atom to the rotation of a " magnetic v. 

 in the quantum mechanism. The question then 

 suggested itself whether it might not be possible to 

 obtain a static model of the hydrogen molecule by 

 endowing the nucleus or the electron with a magnetic 

 wheel. After considering various possible cases of 

 this kind which gave models not differing greatly in 

 scale from what might be expected on experimental 

 grounds, it appeared that the simplest ana probably 



(a) Hydrogen atom. 



(b) Hydrogen molecule 

 (Hohr). 



{c) Hydrogen molecule 

 (static model). 



(</) Charged hydrogen molecule. 



Fig. I. — Models representing the hydrogen atom and molecule. Black balls represent the positive nuclei and white balU the electrons ; 



scale above the models = i A.U. (coooooooi cm.). 



meet the requirements of the quantum theory. Dr. 

 Irving Langmuir* has shown that a model of a static 

 hydrogen atom may be obtained possessing many of 

 the properties of the Bohr atom with its circling 

 electrons, if it be assumed that, in addition to the 

 Coulomb force between charged particles, there exists 

 a " quantum force " given by 



^-\{-\\ 



acting between an electron (mass m, charge e) and 

 a nucleus. In this formula n is an integer, and h is 

 Planck's constant. When the electrostatic attraction, 

 e^lr*, between electron and nucleus is balanced by the 

 repulsion due to the " quantum force," the stationary 

 electron is in stable equilibrium at a distance from 

 the nucleus r =a-, where 



me' 



fnh\ * 



which is the radius of a circular orbit in Bohr's theory 

 of the hydrogen atom. When w=i, we obtain the 

 normal hydrogen atom represented in Fig. i (a), in 

 which the black ball stands for the positive nucleus, 

 or " proton," the white ball for the negative electron. 

 The scale above the model represents one Angstrom 



' PhU. Mag., vol. 41, p. 510, 1921. 

 * Phys. Rev., vol. i8, p. 104, 1921. 



NO. 2809, VOL. I 12] 



the most accurate results were obtained by postulating 

 the existence of a " quantum force " of the kind 

 introduced by Langmuir, but exerting repulsion or 

 attraction according to the sign of the electrical 

 charges between which the force acts. It will, then, 

 be assumed that in addition to the electrostatic 

 force, e*/r*, between elementar\- charges, there exists 

 a " quantum force " 



F=e*.-x, 



which is repulsive for unlike charges, but attractive for 

 like charges. 



Before considering the configurations obtained on 

 this basis, it will be well to recall the model of the 

 hydrogen molecule devised by Prof. Bohr. This is 

 represented in its most stable form in Fig. i (6) on 

 the same scale as was employed for the hydrogen 

 atom. The two electrons (white balls^ spin round in 

 a circular orbit in a plane bisecting at right angles 

 the line joming the hydrogen nuclei. The elections, 

 which are always at opposite ends of a diameter of 

 the circle, have each an amount of angular momentum, 

 nhl2ir, determined b}' Nicholson's quantum condition. 

 It is easy to show that an electron must be at the 

 vertex of an equilateral triangle having as its base the 



* Proc. Phys. Soc., vol. 34, p. 198, 1922. 



* Proc. Roy. Soc. Edin., vol. 42, p. 129, 1922. 



