172 Dr. 0. Halm on Radioactinium . 



the preparation o£ radioactinium at any time t is propor- 

 tional to 



where k is a constant, which may he defined as the ratio of 

 the ionization resulting from the disintegration of an atom of 

 actinium X through the stages emanation and actinium B 

 to that resulting from the disintegration of an atom of 

 radioactinium. 



If I is the activity of the radioactinium immediately after 

 preparation, 



i t = yp+ft.XgQ 



I X x . n 



— e ~ Xif + — — ^— (<?-V — ^-V). 

 A^ — Xo 



This equation expresses the variation of activity of radio- 

 actinium, measured by the a rays. 



It now remains to form an idea of the magnitude of the 

 constant k. If each of the a ray products of actinium emitted 

 a particles which produced exactly the same ionization in the 

 surrounding gas, the value of k should be 3. This is obviously 

 the case, since the ionization due to the emanation and 

 actinium B is included with actinium X. The ionization, 

 however, is not the same for all the actinium products, for I 

 have shown that the ranges of ionization of the products radio- 

 actinium, actinium X, emanation, and actinium B are 4*8, 

 6*55, 5*8, and 5*50 cms. respectively. With a thin film of 

 radioactive matter, the ionization due to each a particle 

 escaping into the air should be approximately proportional to 

 the range in air. 



This relation has been shown by Boltwood * io hold closely 



for radium preparations. Consequently, if the measurements 



are made with a very thin film of radioactinium and under 



such conditions that the a particles are completely absorbed 



between the plates of the testing vessel, the value of k should 



, 6*55 4- 5*8 + 5*50 „ . , £0 



be -r-a =6u2, instead ot o. 



If, however, a comparatively thick layer of radioactinium 

 is employed, the value of k should be still greater. This 

 follows from the fact that the « particles of greatest range in 

 air not only produce more ionization in the gas but, in 

 addition, more escape into the gas, since they can reach the 

 surface from a greater depth of radioactive matter than the 

 u particles of smaller range. 



* Boltwood, Ainer. Jourii. Sci. June 190G. 



