﻿982 Prof. -H. A. Wilson on 



of decomposition of a radioactive substance depends on its 

 atomic temperature in much the same way that the velocity 

 of an ordinary chemical reaction depends on the ordinary 

 temperature. 



A somewhat similar rather loose analogy may be drawn 

 between the emission of negative electrons by hot bodies and 

 the emission of a rays. The higher the temperature the 

 greater the velocity of emission, and the greater the number 

 emitted in unit time. 



If we suppose that the work necessary to be done by an 

 « particle before it can escape from an atom is approximately 

 the same for all radioactive atoms, then in view of the above 

 considerations we might expect a formula of the type 



X = A<^e-Q/ 2 * (1) 



to be true. Here </> denotes the atomic temperature, Q the 

 energy in calories required for the escape of one gram 

 molecule of a particles, and A is a constant. The formula 

 suggested is of the well-known type which represents the 

 variation of the velocity of reactions and thermionic currents 

 with temperature. 



The mean kinetic energy of a molecule of a gas is equal 

 to fR#, where R is the gas constant for one molecule and 6 

 the absolute temperature. The range (d) of an a particle is 

 equal to fiv 3 , where /3 is a constant and v is its velocity. 

 Hence we have 



| R<£ = i m r = \ m IqY\ 



or 



Substituting this in (1) we obtain 



-»©>■ 



where B is a new constant. This equation gives 

 logX — £ log d = a + bd~%, 



where a = log B- J log/3 and b= — 3RQ/3&/2m. 



In the figure the values of logX — jlogd are plotted 

 against d~*; and it appears that a nearly linear relation 

 exists between these quantities in both series of radioactive 

 bodies. 



