58 APPLIED RADIOACTIVITY 



changes are the most important links in this chain of reactions. We 

 depend upon the characteristic gamma radiations at this stage of the 

 degenerating process to furnish the necessary effective, deeply pene- 

 trating radiations used in gamma-radiation therapy. 



The schematic disintegration diagram indicates that radium C may 

 undergo disintegration in either of two ways. By the emission of an 

 alpha particle it degenerates to RaC", or by the emission of a beta parti- 

 cle and a gamma ray it changes to radium C. As the alpha-ray process 

 of degeneration occurs in only 0.04 per cent of the atoms present, for all 

 practical purposes this transformation product is negligible. The other 

 99.96 per cent of the radium C atoms participating undergo a high-speed 

 beta-particle ejection with its accompanying gamma radiation. The 

 resulting product is radium C, of atomic weight 214. Radium C in 

 turn degenerates with the emission of an alpha particle to radium D. 

 By successive steps radium D degenerates into radium G, a stable isotope 

 of lead of atomic weight 206, which is the end of the uranium-radium 

 chain. 



Decay Constant 



In the process of disintegration of a radioactive element, we are in 

 reality observing only the statistical nature of the disintegration of a 

 large group of atoms, in which, on the average, the number of atoms 

 that are disintegrating each second is a constant fraction of those present 

 at any given moment. 



For instance, if we isolate 10,000 atoms which possess the property 

 of disintegration at the rate of 2 per cent per second, then during the 

 first second we would lose 200 atoms, leaving 9800. During the second 

 second we would lose 2 per cent of 9800 or 196, leaving 9604. In the 

 next second we again lose 2 per cent of these, etc. 



We are here dealing with the exponential law of depreciation. Thus, 

 if we let N be the number of atoms which survive after a time t, and No 

 the number originally present at time zero, then the above exponential 

 law of depreciation of number is expressed thus : 



.— xt 



N = N e 



where X is the constant indicating the rate of disintegration of the atoms. 



The radioactive decay constant X is defined as that proportion of active 

 matter which undergoes change each second. The larger the value of this 

 constant, the greater will be the activity of disintegration. 



The magnitude of the decay constant of each of the therapeutically 

 valuable radioactive atoms is shown in Table II— 1. 



