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LVIL Note on the Relation between the Life of Radioactive 

 Substances and the Range of the Rays emitted. By F. A. 



LlNDEMANN *. 



APART from the extraordinarily simple law which deter- 

 mines the chemical properties o£ each successive 

 radioactive element in terms of its predecessor and the type 

 of ray emitted, there are only two well-established quantita- 

 tive relations in radioactivity'. One, which holds absolutely, 

 is that all simple radioactive substances disintegrate according 

 to the formula 



X=X„<r-" s 



X being the quantity remaining after t seconds, if X was 

 the quantity present at time 0. The other relation, which 

 has not been tested so rigidly, connects the radioactive 

 constant \ in the above formula with the range R of the 

 a particle emitted by the equation log\ = A + B log R. In 

 the following paper it will be shown that both the above 

 relations may be derived from certain fairly simple assump- 

 tions. This theory leads to a definite physical meaning for 

 the constants A and B, which enables one to calculate 

 numerical values for certain atomic constants from them : 

 as will appear, these values harmonize well with other 

 measurements and theories. 



Though at present necessarily confined to substances 

 emitting ol rays, similar considerations may probably be 

 applied to ft ray products. 



The first assumption is that the nucleus of a radioactive 

 element, supposed to contain particles in movement, becomes 

 unstable when N independent particles all pass through 

 some unknown critical position within a short time r. This 

 view would appear quite plausible if Rutherford's atomic 

 model is accepted. 



The second assumption is that the above short time t is of 

 the order of the time taken by a strain to traverse the 

 nucleus. This hypothesis may perhaps be vindicated best 

 by an analogy. If a number of small impulses from one 

 side are applied to a pendulum, they will lead to the maxi- 

 mum amplitude of swing if they are all applied within the 

 time during which the pendulum is moving in one direction. 

 It is suggested that each particle passing through the critical 

 position gives rise to a strain in the nucleus and that the 

 atom breaks up when all these strains follow one another 



* Coniniiuricated by Sir Ernest Rutherford, F.R.S. 



