100 ISOTOPE METHODS 



an average of d disintegrations, then the zero class of the Poisson dis- 

 tribution lets us write the fraction of atoms in which there has been no 

 decay as 



N_ -d 

 No" 6 ■ 



Since the number of disintegrations increases steadily with time, it may 

 be written as 



d = \t. 



Thus the final expression for the survivors of radioactive decay is 



_N_ -u 

 No" 6 ' 



In a time equal to 1/X, the surviving fraction is e _1 , or 37%. For purely 

 historical reasons, 1/X is not used directly as the index of the average 

 lifetime of these atoms, but rather the index is taken as the time to 

 reach 50% survival. From the Poisson formula, this value may be shown 

 to be related to X by the expression 



0.693 

 T= -A-' 



where r is the time for half of the atoms to disintegrate; it is r, the 

 half-life, which is listed in the table above. 



The units in which radioactivity are measured are, basically, the 

 number of disintegrations per second, chosen because it is proportional 

 to the number of radioactive atoms present. Physicists chose for the 

 unit of activity that of one gram of radium: 3.7 X 10 10 disintegrations 

 per second; this unit is called a curie. For biological purposes, this unit 

 is between 1000 and 1,000,000 times too high to be practical, and you 

 will find reference to millicuries and microcuries. 



In any given experiment, the total number of disintegrations per 

 second need not be the most important aspect, however, for one can have 

 the same number with different total amounts of the chemical species. 

 For example, the fraction of all carbon atoms which is radioactive could 

 vary from 100% downward (if pure isotope were being used). The frac- 

 tion of atoms which is radioactive is ordinarily expressed in terms of the 

 specific activity of the substance, i.e., disintegrations per second per 

 gram, although in biological studies it is more usual to express it in terms 

 of disintegrations per minute per microgram of substance. 



There are difficulties involved in the detection of disintegrations, and 

 the number registered by the counting apparatus is generally consider- 



