Hydrogen Nuclei from Swift a Particles. 89 & 



direction of the incident u ray is approximately proportional 

 to p sec 0, where p is the probability that an atom will recoil 

 at an angle 6 from a single a particle. 



Combining the assumption that the whole energy of the 

 recoil atom is dissipated in the production of ions with the 

 experimental fact that the velocity of a recoil atom is propor- 

 tional to the cube root of its remaining range, it is easy to 

 show that the ordinates of the total ionization curves are 

 given by 



\ = f ^KRf (cos 3 6 - cos 8 0> 2/3 sec 6 F (6) d6, 



'Jo 



where F(#) is the number of atoms recoiling at an angle 

 less than 6 from a single a particle as it passes through 

 1 cm. of hydrogen gas at N.T.P., <fi is the angle at which 

 an atom is shot that just reaches the range at which 

 J q is measured, 6 is any angle less than $, R 3 is the 

 maximum range of the recoil atoms, and K is a constant 

 involving the dimensions of the apparatus and the ionizing 

 power of a recoil atom. Beside the assumption that the- 

 whole energy of a recoil atom is dissipated in producing 

 ions, the conservations of energy and momentum are assumed 

 to hold during the collision. 



A solution could not be found for the above integral, 

 so F(0) was assumed to have the form A<9 + B<9 2 + C# 3 + D6> 4 , 

 and the values of the constants were calculated by evaluating 

 the integral by a Simpson's Rule method for four different 

 values of cf> and equating it to the appropriate value of 1^ 

 taken from curves J and K. The equations obtained were 

 as follows : — 



Radium C. 



<P = 10° -03X10" 2 = 1950[A+3-4x2B + 17x3C+86x4D], 



(p = 20° -87X10- 2 = 1950[A + 35-9x2B + 323x3C + 5080x4D], 



<P = 25° -85x10 2 = 1950[A+74-5x2B+1040x3C + 16660x4D] > 



= 35° 2-48X10"" 2 = 1950[A+215'8x2B+4322x3C+97850x4D], 



Thorium C. 



<p = 10° -115xl0- 2 = 2240[A+34x2B+17x3O+86x4D] > 



^=20° -88 xlCT 2 = 2240[A-f35-9x2B+323x3C+5080x4D] > 



<p= 25° 1'725X10- 2 = 2240[A+74'5x2B+1040x3O+16660x4D], 



^ = 35° 4-49 xl0r2 = 2210[A+215-8x2B+4322x3O+97350x4D]i 



