Constitution and Stability of Atom Nuclei. 335 



series. The relations are evident from the figure, and will 

 not be described on account of lack of space. It is evident 

 that at each corner of a square in fig. 7, where the P, N, 

 M, and n lines all meet, is a possible position for an isotope, 

 but that only a few of the corners are occupied by atomic 

 species of considerable abundance. The slight abundance 

 of atoms of isotopic number and of nuclear formula (p^)m 

 when M is an odd number is particularly noticeable. 



Theoretical Form for Fajan's Rule*. 



The relations presented in fig. 1 suggest a theoretical form 

 for Fajan's empirical rule. This may be given as follows : 

 If the net positiveness of different atomic species is kept 

 constant (by keeping M constant, or for isotopes) the 

 instability with reference to the emission of negative 

 electrons (beta particles) increases as the relative negativeness 

 (N/P) increases, while there is an increase of stability with 

 reference to the emission of positive or alpha particles. 

 The rule does not tell whether an alpha or a beta particle 

 will be emitted, since that evidently depends upon the 

 grouping of the particles in the nucleus, but merely relates 

 to the energy of an emission provided it takes place. 



hypothesis concerning the increase of n/p 

 with the Atomic Number. 



The writer has already presented an hypothesis concerning 

 the increase of N/P with the atomic number. It may be 

 assumed that the net positive charge on the nucleus is 

 accompanied by a resultant self repulsion, and that the 

 groups hold together against this repulsion through the 

 action of electrical couples. However, as the nucleus becomes 

 more positive this self repulsion increases, so that the value 

 of the relative negativeness (N/P = 1/2) which gives the 

 greatest stability to a light atom, is no longer sufficiently 

 large to overcome this repulsion. To overcome this the 

 atom adds on either negative electrons alone, or groups of 

 the formula p x e y in which y is more than 1/2 of x, so N/P is 

 increased above 1/2. The groups which are suggested by 

 the relations of the atomic species are {p B e 2 ) + , (/V->)°, (^) 6 j 

 and the group prominent in the radioactive series 0> 4 <' 4 )°, 

 which the writer has designated as the helio group. This 



* Kossel has suggested a less general theoretical form for this rule. 

 See J. Am. Chem. ISoc. xlii. p. 1971 (1920) for a discussion of the two 

 forms. 



