88 



I SOT OP I C TRACERS AND NUCLEAR RADIATIONS 



[Chap. 4 



air cannot be calculated with accuracy by a simple expression because of the 

 involved dependence on the stopping power of different atoms. Neverthe- 

 less, when the range in air is known, a rough estimate of the range of alpha 

 particles in substances other than air can be calculated from Geiger's formula 

 in the energy interval for which it is valid. 



R = 3.2 X 10- 



RoVa 



cm 



where R„ = range in air in cm 

 p — density of absorber 

 A = average atomic weight of absorber 

 Proton ranges have not been investigated so exhaustively as those of alpha 

 particles but can be computed from the range formula with somewhat 

 greater accuracy at lower energies because of the smaller straggling; the 

 minimum velocity conditions for protons holds for energies as low as ~ 0.2 

 mev. However, if the alpha-particle range in a substance is known, the 

 range of a proton with the same initial velocity can be obtained from the 

 relation 



M a \Z p / 



Rv = rr 



+ const 



cm 



Table 11. Ranges of RaC Alpha Particles in Various Substances [16] 



where M p , z p , M u , z a = mass and charge of proton and alpha particle, 



respectively 

 The constant is included to adjust the range at very low energies since the 

 straggling of alpha particles is greater than that of protons. Blackett and 

 Lees [23] have evaluated the constants and give the range relation as 



R p = 1.007222a - 0.20 



cm 



In a similar way deuteron ranges can be obtained from the ranges of alpha 

 particles with the same initial velocity from the relation 



