20 RADIOISOTOPES IN BIOLOGY AND AGRICULTURE 



tion of time. The fraction of A removed is (Ao - A)/Aq. Substituting 

 from Eq. (1-15), 



Fraction removed = -: = 1 — e"*^' (1-18) 



In addition to the illustrations below, these equations are widely appli- 

 cable and well known for such phenomena as absorption of light (Beer's 

 law), rate of growth of bacterial cultures under specific conditions, radio- 

 active decay (see below), and absorption of gamma rays (see Chap. 3). 



Simple Removal from One Phase. The data in Table 1-2, taken from 

 the graph in reference (47), may be used to illustrate the exponential 

 removal of injected labeled ferric /3-globulinate from plasma of man. The 



Table ]-2. Removal of Injected Labeled Ferric /3-globulinate from 



Plasma of Man 



[From graph in Louis B. Flexner, Dean B. Cowie, and Gilbert J. Vosburgh, Studies 

 on Capillary Permeability with Tracer Substances, in "Biological Applications of 

 Tracer Elements," Cold Spring Harbor Symposia Quant. Biol., 13 : 88-98 (1948).] 



semilog plot is illustrated in Fig. 1-2, and it is apparent that the removal 

 was exponential. From the data and graph it can be calculated that the 

 process was represented by the equation A = Aoe""""^-', that ty, was 

 ^7 96 min, and that 0.7 per cent of the ferric globulinate was lost per minute 

 from the plasma over the time interval during which the observations 

 were made. 



Radioactive Decay — Composite Curves. The spontaneous disintegra- 

 tion, or decay, of radioactive elements has been shown by statistical theory 

 and by experimental observation to be an exponential process. As such, 

 Eqs. (1-10) to (1-18) apply directly, and radioactive decay can be con- 

 sidered as exponential removal from a single phase. The symbols are 

 usually given the following terminology when used with decay rates: 



k = disintegration constant 

 ti,^ = half-life 



Since all atoms of a given radioisotope have the same decay probability, 

 which is independent of the age of any particular atom, the life of a given 



