THE STRUCTURE OF ATOMS 27 



mathematical relation to each other, namely, that they are 

 proportional to the squares of the successive integers i, 2, 

 3, and 4. This is to be looked upon as perhaps the most 

 fundamental fact underlying the periodic arrangement of 

 the elements. It is significant that in Bohr's theory these 

 same numbers, i, 4, 9, 16, etc., play a prominent part. 

 Thus the energies of the electron in the various "station- 

 ary states" are proportional to one, one-quarter, one-ninth, 

 one-sixteenth, etc., and the diameters of the various pos- 

 sible orbits in Bohr's theory are proportional to i, 4, 9, 

 16, etc. In Bohr's theory the various stationary states 

 correspond to different number of quanta (Planck's quan- 

 tum theory), the innermost orbit corresponding to one 

 quantum, the second orbit to two quanta, etc. We should 

 thus consider (Table I) that the electrons in the ist shell 

 are monoquantic, those in both layers of the 2nd shell are 

 diquantic, etc. It is interesting that Born and Lande from 

 quite other evidence have concluded that the outermost 

 electrons of the chlorine atom (2nd layer of the 2nd shell) 

 are diquantic instead of triquantic as was at first assumed. 



The foregoing theory of the arrangement of electrons 

 in atoms explains the general features of the entire peri- 

 odic system of the elements and is particularly successful 

 in accounting for the position and the properties of the 

 so-called 8th group and the rare earth elements. It also 

 serves to correlate the magnetic properties of the elements. 



Let us now consider the bearing of this theory of atomic 

 structure on the phenomena of chemical valence. The out- 

 standing feature of the theory is that there are certain 

 groups of electrons, such as the pair in the first shell and 

 the octet in the second, that have a remarkable stability. 

 Those atoms in which all the electrons form parts of such 

 stable groups (viz., the inert gases) will have no tendency 

 to change the arrangement of their electrons and will thus 

 not undergo chemical change. Suppose, however, we 

 bring together an atom of fluorine (N = 91 )* and an atom 



1 We will denote the atomic number of an element by N. 



