﻿686 Dr. G. H. Henderson on the Decrease of 



It should be pointed out that since o appears as well in the 

 exponential integrals, the value of x is not very sensitive to 

 changes in b. 



Values of the range given by the formula have been 

 calculated for various velocities of the a. particle, and the 

 results are shown in the second column of Table I. The 

 evaluation of E/(— Y) has been carried out by interpolation 

 from the tables given by Jahnke and Emde "*. In column 

 three are ^iven the experimental results of Marsden and 

 Taylor f. Column four shows the ranges as calculated by 

 Bohr J. The Table refers to RaO in air at 15° C. 







Table I. 





v/v. 



Calc. 



Experimental. 



Calc. Bohr 



•9 



1-87 



1-90 



1-89 



•8 



3-43 



3-34 



3-35 



•7 



4-50 



4-48 



4-48 



•6 



5*23 



5-32 



5-35 



•5 



5-67 



5-97 



5-97 



From the table it will be seen that the calculated values 

 agree well with experiment. Both series of calculations fail 

 for low velocities of the a particles. Bohr's theory holds 

 down to values of V/V equal to about *5 ; the present 

 theory has not quite the same range of applicability, failing 

 below values of V/V of about "6. 



One or two points of interest should be noticed here. 

 First, we shall see what is the actual size of the radius 

 of action of the a, particle called for. Taking an a 

 particle moving with the initial velocity of radium C 

 (1*92 x 10 9 cm. /sec.) and a resonance potential of 10 volts, 

 when numerical values are substituted in (1), we obtain 



i ? 2 + a 2 =7'85xl0- 18 , a 2 = l-89xl0- 20 , 

 and hence 



j p 2 = 7-83xlO" 18 , 



Thus, p = 2*80x 10" 9 cm. is the distance from the electron 

 within which an u particle must come in order to transfer 

 to it energy corresponding to 10 volts. This distance is of 

 the order of one-tenth of the diameter of an atom. 



Secondly, there will be a velocity below which the u particle 

 will be unable to ionize, however close the collision. As the 

 velocity of the a particle decreases the value of jp increases 



* Jahnke u. Emde, Firoktionentafeln, p. 19. 



I Marsden and Taylor, Proc. Roy. Soc. A. 88, p. 443 (1913). 



% Bohr, Phil. Mag. xxx. p. 597 (1915). 



