On the atomic fields of helium and neon

Abstract

The methods of determining molecular fields, described in previous papers, are here applied with certain modifications to the cases of helium and neon. There is considerable observational material available in the case of helium, both as regards its isotherms and as regards its viscosity over a large range of temperature, but it has not as yet been used with any success to yield satisfactory information about its outer field. Keesom, who obtained a number of theoretical formulæ for the second virial coefficient of the equation of state, was unable to find any which would satisfactorily explain the temperature variation of this coefficient in the case of helium, as determined experimentally by Kamerlingh Onnes; in fact, the experimental coefficient showed at the higher temperatures a distinct maximum, and this property none of his theoretical formulæ possessed. The maximum property has, moreover, been confirmed by the later experimental work of Holborn and Otto. The formula, given in a recent paper, is, however, more successful in this direction, and the method of using it, there described, leads to the conclusion that the field of helium can well be represented by the superposition of repulsive and attractive fields, each according to an inverse power law. Furthermore, the values of the force constants are here determined. It has long been recognised that the temperature variation of the viscosity of helium cannot adequately be represented by the theoretical Sutherland formula, with the obvious inference that helium cannot be regarded (even roughly) as a rigid sphere with a superimposed attractive field. This is perhaps not surprising in view of the comparatively simple electronic structure of helium. Kamerlingh Onnes has shown that the variation can best be represented by the simple law, in which the viscosity varies as a power of the temperature. This formula, although first given as an empirical result, corresponds theoretically to a molecular model, in which the molecules are regarded as point centres of force repelling according to an inverse power law. The information available concerning the viscosity of helium is here used, for the first time, to determine the actual value of the repulsive force constant. It is further shown that the result is consistent with that found by the other (entirely independent) method, above described. The field thus determined is one of repulsion according to an inverse 14th power of the distance and a very weak attraction according to an inverse 5th power.