Sec. 7.9] RADIOACTIVITY 169 



any later time is given by 



I 1 — I 2 



The activity of the daughter increases to a maximum and then decays after a 

 sufficiently long time at a rate corresponding to the longer of the two half- 

 lives. The ratio of daughter to parent substance in transient equilibrium is 



N 2 = T T \ N 



I 2 — I 1 



This mode of radioactive decay is shown in Fig. 49. The area under all 

 curves must be equal since the same number of atoms is involved in the 

 complete decay of parent and daughters. 



7.8. Decay of nth Component in a Radioactive Chain. If a given initial 

 quantity N of radioisotope decays into a series of radioactive daughter 

 substances, the quantity of the «th successive daughter substance after a 

 time / is given by [1] 



where 



N = N (aie-°- 692t/T i + a 2 e~°- 69Zt/T ^ + • • • + a n e-°- 6m/T ») 



T n-l 



<L\ = 



(7\ - T 2 )(T 1 - T z ) ■ ■ ■ (2\ - T n ) 



a 2 = 



a n 



(T 2 - T X )(T 2 - T 3 ) ■ ■ • (T 2 - T n ) 



r Tn—\ 



(T n - T,){T n - T 2 ) ■ • • (T n - Tn-J 



Ti, T 2 , . . . T n — half-lives of parent and successive daughter substances 

 7.9. Radioactivity Units, a. Curie. 1 curie = 0.66 mm 3 of radon at 0°C, 

 760 mm Hg. 



Definition: A curie is the quantity of radon in radioactive equilibrium with 

 1 gm of radium. 



The evaluation of the curie depends on the determination of the absolute 

 disintegration rate of radium since, from its definition, the curie is that 

 quantity of radon which disintegrates at the same rate as radium. Measure- 

 ments of the decay rate have in the past differed in magnitude by as much as 

 10 per cent, and in order to establish some standard an arbitrary value of 

 3.70 X 10 10 disintegrations per second per gram of radium was recommended 

 by the International Radium Standard Commission until agreement can be 

 reached on the third significant figure. Initially, the curie applied only to 

 radon in equilibrium with radium; however, its extension to the other decay 



