SUCCESSION OK ( ll\\.;i:s IN KADTOACTIVK BODIKS. -\h 



in thus of the right order of magnitude. The agin-nu-nt would be still closer if the 

 number of a particles were taken as 2 X 10", the number deduced from the heating 

 effect of radium, rather than 10 n . It is probable that the volume obtained by 

 RAMSAY and SODDY is a maximum estimate, on account of the difficulty of removing 

 traces of other gases. 



We may thus conclude with some confidence that about 2 x 10" particles are 

 expelled per second per gramme, and that the number of atoms per gramme breaking 

 up per second is 5 X 10 10 . 



Since 1 cub. centim. of hydrogen contains 3*6 X 10 19 molecules, it can readily be 

 deduced that 1 gramme of radium contains 1'8 X 10 81 atoms, taking the atomic 



weight of radium as 225. 



5 X 10' 



The fraction of radium breaking up is thus ,. , or 2'8 X 10" ' per second, 



1'8 X 10 



that is, 8 '8 X 10 ~ 4 per year. Thus in a gramme of radium almost one milligramme 

 breaks up per year. 



Now there is every reason to suppose that the amount of radium breaking up per 

 second is always proportional to the amount present, as in the case of all the active 

 products. If N is the number of atoms initially present, the number N/ at any 

 time t is given by N//N = e~ A ', where X is equal to the fraction of the radium dis- 

 integrating per second, i.e., for radium X = 2'8 X 10~ u (sec)" 1 = 8'8 X 10~ + (year)" 1 . 



The time taken for the radium to l>e half transformed will be about 800 years ; 

 while the urerage life of the radium is X~ l , or 1100 years approximately. 



Now, pure radium bromide has an activity nearly 2,000,000 times that of uranium, 

 measured by the a rays, and the activity of thorium, weight for weight, is about the 

 same as uranium. Taking, as a first approximation, that the activity is proportional 

 to the number of a particles expelled, it can readily be deduced that in thorium, where 

 there are four products which expel a rays, as in the case of radium, the average life 

 X-' is 1100 X 2 X 10 a , or 2 X 10" years. 



In uranium, where there is only evidence of one change emitting a rays, the 

 average life is only one quarter as long, i.e., 5 X 10 8 years. 



Since each radio-atom expels one a particle of atomic weight about that of 

 hydrogen or helium, the atoms of the intermediate products will not differ much in 

 weight from the parent atom. 



The approximate weight of each product present in a gramme of radium can be 

 readily deduced. Let N A , N B , N c be the number of atoms of the products A, B, C 

 present per gramme in radioactive equilibrium. Let X A , X B , Xc be the corresponding 

 constants of change. Then if q is the number of the parent atoms breaking up per 

 second, 



y = X A N A = X B N B = 

 Consider the case of the radium products where the value of ij is 5 X 10 10 per 



