92 Prof. J. W. Nicholson on Atomic Structure 



of Bohr's theory, the spectrum of helium as ordinarily mani- 

 fested cannot be obtained. Moreover, it was proved that none 

 of the possible steady states of the two electrons leads to a 

 formula approaching that of Rydberg. The most important 

 steady states give formulae like Balmer's which do not pre- 

 serve the Rydberg constant B. Tne reason for the latter 

 property is that Bohr's deduction of the universality of B in 

 all spectra depends on the assumption that steady states 

 exist in which one electron is at a great distance from the 

 others, whose joint effect, with that of the nucleus, is approxi- 

 mately equivalent to that of a hydrogen nucleus The paper 

 in the Philosophical Magazine shows that this is at least 

 impossible for three electrons in all, and therefore for lithium, 

 which, as a matter of experience, does retain the Bydberg 

 constant in its spectrum. The paper in the ' Monthly Notices ' 

 shows that it is equally impossible for helium. Stationary 

 states, derivable from the ordinary electrostatic forces, there- 

 fore are very limited, and if Bohr's theory is to proceed 

 further, some change must be made. 



When we consider the essentials of the theory, the limits 

 of possible change become apparent at once. The derivation 

 of the hydrogen formula requires that the angular momentum 



in the atom should be a multiple of ^ — when there is only 



one electron present. The same supposition is involved in 

 obtaining the Pickering series of lines, where again there is 

 only one electron concerned. This multiple property may, 

 however, change when there is more than one electron. 



The second necessity which is vital for the hydrogen 

 formula is that the law of attraction of an electron to the 

 nucleus is that of the inverse square. This can easily be 

 seen by trying the law r n . We do not get even the form 

 of Balmer's formula unless n=— 2. As Bohr's theory has 

 been shown to be quite unsuccessful when there is more than 

 one electron, we must combine the following hypotheses in 

 any attempt to develop it further: — 



(1) Nuclei attract bound electrons according to the inverse 

 square law. 



(2) Bound electrons do not repel each other according to 

 this law. 



(3) The angular momentum of an electron may cease to be 



Til 



^— , where t is an integer, if there are other electrons 



present. 

 As we shall see, (2) and (3) are not alternatives, but are 



