Dr. 0. Hahn on Radioactinium. 



Ill 



If Xj and X 2 respectively are the constants of change of 

 these substances, then 



XjPo = A^Qo- 



Let P -f Q represent the number of atoms of radioactinium 

 and actinium X present at any time t after the actinium is 

 removed. Then 



P = P, 



■\\t 



Q = 



Qo 



Ag — A/{ 



Q* 



t-Xi.e-**)- 



The activity I t at any time t is proportional to 



XjP + k . X 2 Q, 



where k is a constant. If I is the initial activity, 



P, *Q 

 I 7^P + k.\ a Q P o + Q 



I XxPo + Aj.^Qo l + k 



The rise-curve is complementary to this, and consequently 



Activity at any time t 

 Final activity 



1- 



|_ A 2 — A,! 



— \.e~ x 



■>] 



1 + * 



Pig. 3. 



»o 



50 



iW 







^' 



^'~'~ 



_ — — ~~~ 







i 



i— 







\, 





I 



J^ 















■'' 



















/ 





















,' v 2r^ 





















30 40 50 



7/AW /A' DAYS. 



100 



Taking the periods of radioactinium and actinium X as 

 19*5 days and 102 days respectively, the theoretical curve is 

 given in fig. 3, Curve I., the maximum activity being taken 

 as J 00. The value of k is assumed to be 3'5 — the same value 



* These equations are given in •' Kadioactivity,' vol. ii. p. 334. 

 Phil. Mag. S. 6. Vol. 13. No. 73. Jan. 1907. N 



