108 BELL SYSTEM TECHNICAL JOURNAL 



rests all the present hope of achie\'ing numerically valid theories in 

 this division of atomic physics. 



One agreement between this theory and certain data may be demon- 

 strated without making any specific approximation. The farther 

 away the valence-electron remains from the kernel, the more nearly 

 identical with the field of a hydrogen nucleus is the field in which it 

 revolves, the more nearly should it behave like the electron of a hydro- 

 gen atom. Consider for instance, in a hydrogen atom, the orbit which 

 yields the Stationary State for which n the total quantum-number and 

 k the azimuthal quantum-number are both equal to 5. This orbit 

 is a circle of which the radius is 10"'^ cm.; far larger than the radius of 

 any inert-gas atom, presumably a fortiori far larger than the kernel 

 of any alkali-metal atom. Were the valence-electron of such an 

 atom to describe this circle, it would pass everywhere in a field very 

 nearly like that of a hydrogen nucleus, and should very nearly con- 

 form to the quantum conditions for this field. It follows that an 

 orbit drawn in the actual field, obeying the quantum-conditions 

 w = 5 and k=b, would be very nearly such a circle with very nearly 

 the same energy-value. The inference is drawm that for high values 

 of n and k, the Stationary States of an alkali-metal atom should be 

 very nearly identical with those of hydrogen. These orbits which lie 

 far out from the kernel of the alkali metal atom, or from the nucleus 

 of the hydrogen atom, have small energy-values. It may therefore 

 be said that if we tabulate the Stationary States of the two atoms in 

 order of decreasing energy-value, then the farther along the two 

 tabulations we go, the more nearly should the tw'o systems of Station- 

 ary States coincide. 



This is found to be true, under a limitation. The limitation is an 

 important aid in interpreting the arrangement of the Stationary States. 

 It will be recalled from the First Part of this article that the Station- 

 ary States of the sodium atom are arranged in several sequences (there 

 illustrated as columns in Fig. 7) known as the 5-sequence and the p- 

 sequence and the (^-sequence and the /-sequence and others; and to 

 these sequences successive values 1,2,3,4 ... of a symbol k were ap- 

 pended. One basis for this classification is that when it is made, the 

 occurrence or non-occurrence of transitions between any pair of 

 Stationary States, under normal conditions, can be determined by 

 applying the "selection-rule" that only such transitions occur as 

 involve a change of one unit in k. Now there are two reasons for 

 supposing that the only transitions which can occur are those in 

 which the Azimuthal Quantum-number of the valence-electron changes 

 by one unit. Unfortunately it is not possible to introduce these two 



