Equation for Production of Radionuclides

The amount of activity produced by irradiation of a target material with a charged particle beam can be quantitated by 

Equation (7.2) indicates that the quantity of radionuclides increases with time of irradiation, intensity, and energy of the particles (related to a) of the incident particle, and the amount of target material. The term (1-e A() is called the saturation factor, which approaches to unity when t is five to six half-fives of the radionuchde in question. At that time, the yield of the radionuchde is maximum, and its rates of production and decay become equal, indicating that there is no gain in activity by further irradiation. For irradiation for five to six half-lives of the daughter, Eq. (6.2) then becomes 

The values of I are measured by various techniques, the description of which is beyond the scope of this book, but they are available from the cyclotron operators. The values of a also have been determined for various nuclear reactions and are available in literature. The number of atoms N of the target is given by 

Note that 1 ampere (A) is equal to 1 Coulomb (C)/s, and 1C equals to 6.25 x 1018 protons, so in a cyclotron where protons or 11 are accelerated, the beam intensity is conventionally expressed in iA/cm2-h. The yield of the radionuclide is then expressed in MBq or mCi per pAh. 

Calculate the activity of 18F produced when 1 g of 70% enriched H2lsO is irradiated for 1 h with a proton beam of 30 pA/cm2 in a cyclotron. The half-life of18F is 110min and the cross section for the lsO (p, n) 18F reaction is 300 millibam (1 barn = 10 24 cm2). 

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