CHAPTER 15 

 THEORY OF TRACER METHODS 



15.1. Introduction. The multitude and diversity of applications to which 

 tracers have been put make a detailed description of tracer methods imprac- 

 ticable in the present volume. The discussion here will be confined, there- 

 fore, to some of the principles of tracer methods which have found the most 

 frequent use. On the other hand, an exhaustive treatment of the possible 

 mathematical descriptions of biological, chemical, and physical systems in 

 which tracers could be utilized would in any case perhaps not be warranted 

 since it would present nothing essentially new. A tagging agent is assumed 

 to be chemically and physically indistinguishable to the system and hence 

 will follow, in most instances, processes already described in great detail in 

 standard references on physics, chemistry, and especially thermodynamics. 



Labeling agents are most commonly radioactive isotopes and rare stable 

 isotopes, but they include, as well, substances such as dyes. It is required 

 only that the tracer be chemically and physically exactly equivalent to the 

 substance it represents or displaces and that it in no appreciable way affect 

 the system differently from its normal counterpart. Although distinguish- 

 able to the observer, the labeled substance cannot be discriminated by the 

 system so that tagged and untagged molecules enter each process with equal 

 probability. In certain instances this condition is not altogether satisfied. 

 Thus, in dynamic systems in which H 2 or H 3 is introduced as a tracer for 

 hydrogen, or C 13 or C 14 for C 12 , it is known that some discrimination occurs 

 because of the large mass differences in the isotopes. Particularly in tracer 

 experiments with hydrogen isotopes it is necessary to give special attention 

 to possible differential diffusion and reaction rates. Such isotope effects 

 are less pronounced with carbon and are probably entirely negligible for 

 isotopic tracers of greater mass. Very often the tracer must be present in 

 minute quantities to satisfy the condition of indistinguishability. This is 

 especially important with radioactive tracers. A high radiation density 

 produced by excessive amounts of a radioactive tracer may have a profound 

 effect on the character and dynamics of the system into which it is intro- 

 duced. In order to guard against the influence of excessive radiation it is 

 sometimes desirable to estimate, if possible, the maximum doses to be 

 expected in various parts of the system for a given quantity of radioactive 

 tracer. A third possibility of disturbing the system is encountered when 



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