610 BELL SYSTEM TECHNICAL JOURNAL 



in a primitive state, and indeed not advanced enough (in my estima- 

 tion) to be considered fully proved by its own successes. Quantum 

 mechanics has, however, many other buttresses, quite sufficiently 

 many to allow us to take it for granted ; and in this particular field it 

 has the prestige of prophetic powers. Until the experiments of Cock- 

 croft and Walton, no one had ever effected transmutation except with 

 alpha-particles of charge 2e and energy K amounting to several 

 millions of electron-volts. Now Cockcroft and Walton say that they 

 were encouraged to build the elaborate apparatus necessary for trying 

 it with protons of energy much less than one million electron-volts, 

 by Gamow's inference that particles of charge -\- e should have a 

 very much greater chance of penetrating through a potential-hill and 

 into a nucleus, than particles of equal kinetic energy and only twice 

 the charge — the inference from the fact that ne occurs in the exponent 

 of the exponential function appearing in equation (23) and others 

 like it. Moreover, the phenomenon of resonance was predicted by 

 Gurney (and mentioned by Fowler and Wilson, who, however, appar- 

 ently did not believe that it could ever be observed) before it was 

 discovered in the experiments of Pose. 



The merits of the crater model with the quantum-mechanical theory 

 have, however, not yet been fully presented, for I have left to the last 

 their application to radioactivity. 



One of the principal features of radioactivity — both the "induced" 

 variety described in the early part of this article, and the "standard" 

 variety known these thirty-five years — is the exponential decline or 

 decay of the intensity, hence of the quantity of any radioactive 

 substance, as time goes on. This signifies that the average future 

 duration, reckoned from any instant of time, of all the atoms surviving 

 unchanged at that instant, is the same whichever instant be chosen — 

 or, that the probability that an atom, not yet transformed at instant 

 /o, shall undergo its transformation within (say) a second of time 

 beginning at /o, has the same value however long the atom may have 

 existed up to this arbitrarily-chosen-moment /q. 



All this is commonly expressed by saying that radioactive trans- 

 formations obey the laws of chance. I quote (not for the first time) 

 a passage from Poincar^, which illustrates how this had to be inter- 

 preted before the advent of quantum mechanics; I take the liberty 

 of writing "nucleus" where he wrote "atom": 



". . . If we reflect on the form of the exponential law, we see 

 that it is a statistical law; we recognize the imprint of chance. In this 

 case of radioactivity, the influence of chance is not due to haphazard 

 encounters between atoms or other haphazard external agencies. The 



