430 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 16 



= ^X 1.38 X 10 fi X 0.03 X 1.6 X 10~ 12 X ^ = 5.67 X lO" 11 

 47r 9o 



A _ /disintegrations^ / gamma rays \ /sec\ = ^ ^ Q ^ 



\ milhcune-sec / \disintegration/ \hr/ 



= 1.33 X 10 11 



(millicuries \ , . . . 0.1 n fiQ „ /7 , 

 j-, ) (decay factor) = ^7^ e -°- G93t/T 

 gm of tissue/ J 60,000 



= 1.67 X 10- 6 X e-°- 693 " r 



g = geometrical factor for cylinder (Sec. 16.7) = 200 



Thus, the dosage rate for the 1.38-mev gamma ray is 



dx = I Aug = 2.5 X 10" 3 X e -°- 69WT r per hr. 



Repeating the calculation above for the 2.76-mev component yields 



d 2 = 4.0 X 10- 3 X e -°-™ st/T r per hr. 



Finally the actual gamma-ray dosage rate at the center of the trunk for any 

 time t following injection of Na 24 is 



d = d x + d 2 = 6.5 X 10" 3 X e-°- 69SI/T r per hr. 



Neglecting the initial mixing period because it is short compared to the 

 half-time of Na 24 in tissue, the dosage rate immediately after injection is 

 just 6.5 X 10~ 3 r per hr, and after five days it is 2.4 X 10 -5 r per hr. It may 

 be noted that the dosage rate produced by the beta particles from Na 24 

 immediately after injection is 2.3 X 10~ 2 rep per hr. The change in dosage 

 rate with time is somewhat more complicated for the beta particles because 

 of the accumulation of sodium in bone. 



Calculations of the accumulated gamma-ray dose during any prescribed 

 interval of time presents no added difficulty in this simple case since elimina- 

 tion of sodium depends almost entirely on the decay half-life. Integrating 

 the expression for d above (see Sec. 16.6) the accumulated dose at any time 

 following injection of Na 24 is 



6 5 V 10~ 3 T 

 U ~ 0.693 " U e } 



At the end of the first day, for example, the gamma-ray dose received at the 

 center of the trunk is D — 9.4 X 10 -2 r, and at the end of the fifth day it 

 becomes D = 0.14 r. 



The precise significance of a dose calculation such as the example worked 

 out above should always be borne clearly in mind. In this instance the 

 meaning of the computed values is quite evident. The dose was calculated 

 for only one point in the body, the point at the center of the trunk where 



