and its Products of Transformation 

 period of polonium as 138 days ; 

 10-5 



837 



1000 



x3-4xl0 10 =3-57xlO'' 



since Rutherford * has shown that 3*4 x 10 10 atoms of radium 

 and its products break up per second. Substituting these 

 values, A 2 = ri9xlO -9 (sec. -1 ). This gives for the half 

 period of radium D 18'5 years. Using this approximate 

 value of \ 2 the correct value can at once be deduced from 

 the more accurate formula, viz. 



x 4 S 



N 



:\,(l-02e-^-l-09^- A ^). 



Substituting the approximate value of X 2 m e ~ x ' zt we find 



1-02 e~^ ='9863. Remembering that N= ^ =-172 x 10 15 



we get X 2 =1'24 x 10~ 9 . This corresponds to a period of 

 transformation of 17*7 years. 



A number of experiments have been made with different 

 tubes containing different quantities of emanation which had 

 been allowed to stand for different lengths of time. The 

 results are collected in the following table : — 



Number 



of 



tube. 



Amount of 



radium 

 emanation. 



Time 



before 



testing 



in days. 



Total number 



of particles 



expelled per 



second. 



X 2 . 



Half-trnns- 



formatiou 



period in 



years. 



1 



I0'5 mgrm. 



320 



1-63 xlO 5 



l-24xl0~ 9 



177 



2 



2(V2 



119 



2-36 xlO 5 



1-33X10" 9 



16-4 



3 



251 



118 



2-25 xlO* 



136xl0~ 9 



161 



4 



94 



126 



0867 XlO 5 



1-31x10" 9 



16 3 



5 



70 



129 



0677 X 105 



1-37 XlO" 9 



15 9 



Taking the mean of these determinations we find 



A 2 = l'33xl0- 9 (sec." 1 ), 



and the half period =1G"5 years, with a probable accuracy 

 of + *5 v^ars. 



* Loc. cit. 



