628 ADOLF F. VOIGT 



differences in sample thicknesses do not have to be large to have a 

 noticeable effect on the counting rate. For example, a thickness of 

 about 3 mg. per square centimeter would cut the observed C^^ 

 activity by half (see end of Sect. D4). Only half of those /3 rays 

 originating from the bottom of a source of this thickness would reach 

 the top and the net observed activit}^ would be cut by 20-30%. 



As the weight of inactive carrier present with a given amount of 

 a radioactive substance is increased, the measured activity may 

 increase slightlj^ at first, then decrease fairly rapidly, and then more 

 slowly (see Fig. 10). The original increase is due to scattering, in 

 this case scattering of the radiation into the counter by the additional 

 carrier atoms. The decrease that follows can be approximated by a 

 mathematically derived equation assuming a logarithmic absorption 

 of the radiation. Since ^ rays only approximately obey such an 

 equation and particularly since this equation considers only the 

 absorption and neglects the scattering, the correction curve obtained 

 in this way is not completely satisfactory. The ecjuation so developed 

 is: 



in which ijl, the absorption coefficient, is ecjual to 0.693/rfi/2 (see 

 Sect. Bl). .4n in this equation is the activity in the absence of 

 carrier, while A is that activity in the presence of cai rier having a 

 thickness (/. This thickness can be expressed in millhneters, milli- 

 grams per square centimeter, or other unit provided fx is expressed 

 in the same units. A simpler correction that may be appUed as an 

 approximation is to consider that all the radiation comes from a layer 

 midway between the top and bottom of the sample and then to apply 

 a correction based on the thickness to which this corresponds. Thus, 

 if the thickness of the sample is equivalent to 2 di/^, the ratio A/Aa cal- 

 culated on the latter hypothesis would be 0.5. while from the j^i-evious 

 expression one would obtain A/Aq = 0.54. 



However, since this expression does not lake into consideration 

 the scattering it is bettei- not to rely upon it but to determine the cor- 

 rection curve experimentally for the particular activity, carrier sub- 

 stance, and geometry involved. Such a curve as Figure 10 can 

 readily be obtained by taking equal aliqu(jts of a solution containing 

 the activity, adding varying known amoiuits of carrier in solution, 

 precipitating, drying, mounting, and counting in the manner chosen 

 as standard for the experiments. The observed activity is then 



