Sec. 16.3] INTERNAL DOSIMETRY 417 



particle, after losing its kinetic energy to the absorbing medium, undergoes 

 annihilation, producing in the process two gamma rays, each of 0.511 mev 

 (m c 2 ). This amount of available energy sometimes cannot be disregarded, 

 and the positron-active isotope may then also be treated as a gamma-ray 

 emitter. 



The energy made available per gram of tissue per second by the decay of a 

 beta emitter is given by the product of the number of disintegrations per 

 second per microcurie, the concentration u of the isotope in microcuries per 

 gram of tissue, and the average energy E$ of the beta particles. 



E d = 3.7 X WuEf, ev/sec/gm 



Similarly, the total energy made available per gram of tissue in the interval 

 of time to / following administration of active material is 



E D = 3.7 X 10 4 £e T u dt = 3.7 X W'EpU ev/gm 



in which 3.7 X 10 4 £/ is the number of disintegrations that have occurred in 

 the tissue per gram of tissue during the interval. 



The quantities u and U depend on the rates of metabolic accumulation 

 and elimination as well as on the rate of radioactive decay. In general, 

 therefore, u and U are functions of time and are given in Sec. 16.6 for various 

 cases of biological interest. The simplest possible case may be noted as an 

 illustration. If u microcuries of isotope of long half-life remain fixed in an 

 organ, u is a constant equal to u . The quantity U for the interval of time 

 to / is then 



ii T 

 U ' 0.693 U e ' 



where T = decay half-life 



The average beta-particle energy Ep is not to be confused with maximum 

 energies given in tables of radioactive isotopes. The particles emitted by 

 any isotope vary continuously in energy from zero up to the maximum Em &x . 

 If the beta spectrum is simple and no conversion electrons are present, the 

 average energy in many instances is about E = £m ax /3. In general, however, 

 beta spectra are complex; each nucleus decays with emission of one of several 

 possible beta particles for which the maximum energies are different. Fur- 

 thermore, the presence of strongly converted gamma rays greatly influences 

 the average energy. Under either of these conditions reliable values of E$ 

 can be determined only from the observed energy distribution obtained with 

 the beta spectrograph. Values of E$ determined by this method for some of 

 the commonly used isotopes are given in Table 6. 



With the available energy calculated from the formulas above the dose 



