588 Prof. Rutherford and Mr. Soddy 



is brought out most clearly by a comparison of the respective 

 energy relations of radioactive and chemical change. It is 

 possible to calculate the order of the quantity of energy 

 radiated from a given quantity of radio-element during its 

 complete change, by several independent methods, the con- 

 clusions of which agree very well among themselves. The 

 most direct way is from the energy of the particle projected, 

 and the total number of atoms. For each atom cannot produce 

 less than one " ray " for each change it undergoes, and we 

 therefore arrive in this manner at a minimum estimate of the 

 total energy radiated. On the other hand, one atom of a 

 radio-element, if completely resolved into projected particles, 

 could not produce more than about 200 such particles at 

 most, assuming that the mass of the products is equal to 

 tbe mass of the atom. This consideration enables us to set a 

 maximum limit to the estimate. The a. rays represent so 

 large a proportion of the total energy of radiation that they 

 alone need be considered. 



Let m = mass of the projected particle, 



v = the velocity, 



e = charge. 



Now for the a ray of radium 



v = 2'b 10 9 , 



— =6 10 3 . 

 m 



The kinetic energy of each particle 



hnv 2 = 7c — v^e = 5 10 14 <? . 



1 2 e 



J. J. Thomson has shown that 



e=6 10- 10 E.S. Units = 2 lO" 20 Electromagnetic Units. 



Therefore the kinetic energy of each projected particle 

 = 10 -5 erg. Taking 10 20 as the probable number of atoms 

 in one gram of radium, the total energy of the rays from the 

 latter =10 15 ergs =2*4 10 7 gram-calories, on the assumption 

 that each atom projects one ray. Five successive stages in the 

 disintegration are known, and each stage corresponds to the 

 projection of at least one ray. It may therefore be stated that 

 the total energy of radiation during the disintegration of one 

 gram of radium cannot be less than 10 s gram-calories, and 

 may be between 10 9 and 10 10 gram-calories. The energy 

 radiated does not necessarily involve the whole of the energy 

 of disintegration and may be only a small part of it. 10 8 

 gram-calories per gram may therefore be safely accepted as 



