30 : 2/ Tracer Techniques 559 



to the number of radioactive atoms present. Expressed analytically, 

 this is 



£- -A* (1) 



where N is the number of atoms present, t is time, and A is a constant 

 characteristic of the particular isotope. Equation 1 can be integrated to 



N = N Q e- kt (2) 



where N is the number present at zero time. Equation 2 may be solved 

 for the time r in which N decreases by a factor of two ; namely 



ln 2 rv\ 



r = — (3) 



The time t is called the half-life. During each half-life, the number of 

 atoms of the isotope decreases by a factor of two. The half-life r, rather 

 than A, is customarily used to describe an isotope. 



In order that an isotope be useful for tracer studies, r must be in a 

 reasonable range. If r is too short, that is, of the order of seconds, the 

 isotope decays before one can do most tracer experiments. However, if 

 r is too long, then the number of disintegrations per second becomes 

 prohibitively low for the detection of usual tracer concentrations. The 

 isotope C 14 with a half-life of 5,700 years is close to the too-long limit. 



The activity of a sample of radioactive material is usually described by 

 the number of disintegrations per second. The number occurring in 

 1 gm of radium, 3.7 x 10 10 per second, is called a curie. One thousandth 

 of this, that is, a millicurie, is a more useful unit for biological tracer 

 studies. The number of atoms per millicurie is related to the half-life. 

 If there is 1 millicurie present 



d 4 = 3.7 x 10' = JSl N 



dt t 



Or, solving for N 



N — — : — - x 3.7 x 10 7 atoms 

 ln 2 



This number can readily be converted to gram atoms, or grams, using 

 Avogadro's number and the atomic weight. 



The radioactive isotopes are assayed by detecting their characteristic 

 radiations. These, in the case of artificial radioactive isotopes, usually 

 consist of a /3 ray and, in addition, sometimes a y ray. In the case of 

 orbital electron capture, 1 only a photon is emitted. The energy of the 



1 Orbital electron capture means that one of the electrons combines with the 

 nucleus to decrease the atomic number by one. 



