Recoil of Radium 1) from Radium C. 



227 



definite ranges *, and if radium A is distributed uniformly 

 on the surface of a fiat plate, the radium B and therefore 

 the radium C subsequently formed will be uniformly dis- 

 tributed through a depth a equal to the range of the recoil- 

 stream from radium A in the plate. For, consider atoms of 

 radium Aon the surface of the plate at A (see figure). The 



radium B produced will be shot downwards into the plate 

 and distributed uniformly over the surface of a sphere of 

 radius a. The fraction confined within the surface of a 

 segment of the sphere of thickness Bx at a depth x below 



. hx 



the surface is — , since this is the ratio of the area of the 

 a 



segment to that of the hemisphere. Radium C is now pro- 

 duced in situ from the radium B, and if c is the range of the 

 recoil-stream from radium C, the fraction of atoms coming 

 from the segment considered which emerges from the plate 



£ t y 



can be seen to be — — ; for this represents the ratio of the 



area of the cap of the sphere of radius c outside the plate to 

 the total area of the sphere. Consequently, the probability 

 that an atom of radium B will be projected from the surface 

 of the plate to a depth x and then give rise to an atom of 



C — 1! OX 



radium D which escapes from the plate will be CT * . — . 

 r l 2c a 



The efficiency of the recoil, as usually defined, will have half 



this value, since half of the atoms of radium D must of 



necessity be projected away from the surface of the plate. 



* Wertenstein, Theses presentees a la Faculte des Sciences, Paris, 

 1913. 



Q2 



