SOME CONTEMPORARY ADVANCES IN I'lIYSICS—X 105 



guished from the others, by the circumstance that every one of them 

 involves the absence of an electron from the atom; consequently they 

 may be described as Stationary States of an atom-residue. There is 

 reason to believe that each distinct State involves the absence of a 

 particular one, or of one out of a particular group, of the electrons 

 bound to the nucleus during the earlier stages of the imagined building 

 of the atom by successive "binding" of electrons. The speculations 

 about X-ray spectra consist largely in attempts to correlate the 

 individual States with absences of particular electrons. 



O. The Helium Atom 



The problem of the nucleus with two electrons, the "dilemma of the 

 helium atom" as van Vleck calls it, is one of the most tantalizing in 

 contemporary physics. One feels confident a priori that the same 

 quantum conditions as suffice so beautifully to constrain the one- 

 electron atom to yield the hydrogen spectrum should also suffice, 

 when applied to the orbits of two electrons, to yield the spectrum of 

 neutral helium. Yet the various pairs of orbits conforming to these 

 quantum conditions, which have already been traced, have been 

 shown (with vast expenditure of intellectual labor by some of the 

 ablest mathematical physicists of our time) to entail energy-values 

 for the Stationary States which are hopelessly incorrect. 



For instance, one might assume that when the helium atom is in 

 its Normal State, the two electrons are revolving in a common circular 

 orbit about the nucleus, being at each instant located at opposite 

 ends of a diameter; and that this permitted orbit is determined by 

 the condition that the angular momentum of each electron, or per- 

 haps that of both together, is h/2ir. This seems an obvious general- 

 ization of the Quantum Conditions for hydrogen; but it yields a 

 false energy- value for the Normal State; and there is nothing more 

 to be said. Kemble and van Vleck demonstrated that no arrange- 

 ment in which the two electrons are symmetrically placed relatively 

 to a line through the nucleus entails the proper energy-value for 

 the normal state. This still leaves open the possibility that the two 

 electrons are unsymmetrically placed — a possibility which to some 

 people seems repellent enough to be excluded. Born and Heisen- 

 berg calculated the energy-values corresponding to pairs of orbits, 

 one of which lies far beyond the other at all points, and both of which 

 are concordant with the Quantum Conditions. These ought to 

 have agreed with the energy-values of the Stationary States which 

 are remote from the normal state and near the state of the ionized 



