398 



ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 15 



to the smaller of ki and k 2 . The expression above for x 2 is equally valid when 

 A is the precursor of only B and all the material that leaves A reappears, 

 usually as a different chemical form, in B. 



It is apparent from inspection of the formula above that when k x = k 2 

 it is no longer valid. In this special case it takes the indeterminate form 

 0/0 and must, therefore, be used in its limiting form when ki — > k 2 which is 



x 2 



kXMi 

 M 2 



tc 



-kt 



microcuries/gm 



e. Series of Three-phase Changes. However complex a system may be, 

 it is often possible to investigate a specific phase of it by introducing labeled 



TIME 

 Fig. 113. Uptake and elimination of tagged material in three phases. The curves indi- 

 cate the time variation of specific activity in each phase when the labeled material, intro- 

 duced at phase A, passes directly through all three phases. It is possible in certain 

 instances for the labeled material to leave also by other routes as indicated by the broken 

 lines. The areas under the curves will then be somewhat smaller, each by a different 

 factor, than if all the material were to pass from A to C. 



material directly into the phase or into the immediately preceding phase. 

 If it is necessary to go back two or more phases, the reactions, particularly 

 in biological systems, tend to become exceedingly complex. When, however, 

 a substance in phase A passes successively through a series of phases 



A-*B^>C-> ■ • • 



and only A can be tagged, the concentration of the tagged molecules in C 

 can be described by an expression similar to those above. After introducing 

 into A an amount of labeled substance to raise the specific activity to X 

 microcuries per gm, the material, possibly in different chemical forms, passes 

 from A to B, B to C, and from C it is eliminated or otherwise metabolized. 



