22 



RADIOISOTOPES IN BIOLOGY AND AGRICULTURE 



procedure, which is vaHd for other systems of exponential removal besides 

 decay, is illustrated in Table 1-3 and Fig. 1-3. Column 2 gives the 

 observed counts per minute of a mixture as a function of time, and these 

 are plotted on a log scale to give the composite curve in Fig. 1-3. It is 

 noted that at the longer time intervals a straight line is obtained which 

 represents the exponential removal of the long-lived component. The 

 extrapolation of this line intercepts the ordinate at 2000, which represents 

 the counts per minute due to this component at zero time. From this 

 line B are taken the values that are shown in column 3. The values in 



Table 1-3. Analysis of Composite Decay Curve (Two Components) 



column 3 are subtracted from those in column 2 and are plotted to give the 

 curve for component A. The intercept gives the value of 1000 counts/- 

 min, which represents the relative amount of A present at zero time. 

 The respective slopes give values of 0.0484 and 0.00795 for the disintegra- 

 tion constants, from which the half-lives are calculated as 14.3 and 87 

 days. This particular curve can be expressed as counts per minute at time 

 t - lOOOe-o"^^'*' + 2000e-'"'«^-'^'. It may be helpful in consideration of the 

 following systems to note the physical meani?ig of the numerical constants in 

 this equation. 



Multicomponent systems may be treated in the same way, but the 

 analysis becomes less precise as the number of components increases, 

 especially if the rate constants k are close together. Frequently the 

 method of least squares must be applied to the raw data for accuracy. 

 Often the existence of several components cannot be detected from the 

 data even by careful statistical analysis. The behavior of several com- 

 ponents is thus said to be lumped into that of only one component. 



