168 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 7 



uranium, the number of atoms of the product radioisotope after a time t is 



N = N {\ - e 



-0.6931/T 



) 



where N = saturation activity; the activity at which the rate of production 



of the isotope equals rate of its decay. This is equivalent to the 



rate of formation divided by X 



7.6. Radioactive Substance Produced by Parent of Long Half -life. When 



a radioactive daughter substance is produced for which the half-life To is 



short compared with that of the radioactive parent, i.e., T\ )>> T->, and 



assuming that only the parent substance is present initially, the quantity of 



the daughter substance after time t is 



N 2 = N ^(l - e 

 1 1 



-0.693*/ T2 



) 



where N = initial quantity of parent substance 



After many half-lives of the daughter, the parent and daughter are in secular 

 equilibrium and the decay of the latter is governed now by the decay of the 

 parent. The quantity of the daughter is then proportional to the ratio of 

 the half-lives of the two substances: 



N 2 = N ^ 

 1 1 



7.7. Parent and Daughter Substances of Comparable Half -lives. When 

 the half-lives of parent and daughter are of the same order of magnitude and 

 only the parent is present initially, the activity of the daughter substance at 



10 



ii 



12 



234 56789 

 HALF -LIVES OF PARENT 

 Fig. 49. Growth and decay of a series of daughter substances in a radioactive chain 

 A-+B—>C-+D->. Only the substance A is present initially. 



