Spectra of the Elements, and Structure of the Atom. 543 



radioactive, giving a particles with a smaller velocity of 

 ejection than usual, some place may have to be found for 

 unstable elements of lower atomic weight. In any case, 

 van den Broek's hypothesis involves, in its present form, 

 the supposition that the atomic numbers of lithium, beryl- 

 lium, and boron are three, four, and five respectively, and in 

 this paper we shall find that, on Bohr's theory of the consti- 

 tution of atoms more complex than helium at least, this 

 cannot be reconciled with theoretical considerations. If we 

 are to retain Bohr's theory of such complex atoms, that 

 theory must give up van den Broek's hypothesis in its present 

 form, and substitute a modified hypothesis. This portion of 

 Bohr's theory, however, is admittedly of a more tentative 

 form, and is only precise for the two simplest elements, 

 hydrogen and helium, which do not come within the scope 

 of this paper. The need for modification of van den Broek's 

 hypothesis, pointed out in the paper, therefore does not bear 

 upon Bohr's spectral theory in any way, or even to a great 

 extent on his theoretical reason for the existence of Bydberg's 

 universal constant in all spectra. 



It must be pointed out that the necessity for the abandon- 

 ment of van den Broek's hypothesis in its present form, and 

 the substitution of a similar form which allows the atomic 

 number to be different from the position in the Periodic 

 Table, is solely determined by the portions of Bohr's theory 

 which are not related to the hypothesis, for example, the 

 specification of the equal and constant angular momenta of 

 all electrons in the atom, and the mode of determination of 

 the probable valency of an element, based on the supposition 

 that the readiness of an atom to take up an electron and 

 form a new charged configuration may be determined from 

 a consideration of the total energies which should be applied 

 to the configurations in order to scatter their component 

 parts to an infinite distance from each other. It may be 

 that either of these procedures is incorrect. As regards the 

 first, for example, the only definite cases worked out by 

 Bohr, in so far as spectra are concerned, are those of 

 hydrogen and helium with only one electron. In these cases, 

 it is essential to suppose that the angular momentum of the 

 electron is hj2ir, where h is Planck's constant; but in the 

 presence of other electrons, this relation to h may be modified 

 and come to depend on the number of electrons. 



There are indications that this modification is necessary. 

 For example, if the angular momentum of each electron 

 in the neutral helium atom is A/27T, we cannot obtain the 

 ordinary helium spectrum, as a future paper will show. 

 Moreover, in systems with a simple nucleus, this modification 



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