The activity of a radionuclide produced by irradiation of a target mater-
ial with charged particles in a cyclotron or with neutrons in a nuclear reactor
is given by
A=INs(1 −e−lt) (5.1)where
A=activity in disintegrations per second of the radionuclide produced
I =intensity or flux of the irradiating particles [number of particles/
(cm^2 · sec)]
N=number of target atoms
s=formation cross section (probability) of the radionuclide (cm^2 ); it is
given in units of “barn,” which is equal to 10−^24 cm^2
l =decay constant given by 0.693/t1/2(sec−^1 )
t =duration of irradiation (sec)
Equation (5.1) indicates that the amount of radioactivity produced
depends on the intensity and energy (related to the cross-section s) of
the incident particles, the amount of the target material, the half-life of the
radionuclide produced, and the duration of irradiation. The term (1 −e−lt)
is called the saturation factorand approaches unity when tis approximately
5 to 6 half-lives of the radionuclide in question. At that time, the yield of
the product nuclide becomes maximum, and its rates of production and
decay become equal. For a period of irradiation of 5 to 6 half-lives, Eq. (5.1)
becomes
A=INs (5.2)A graphic representation of Eqs. (5.1) and (5.2) is given in Figure 5.2.
The intensity of the irradiating particles is measured by various physical
techniques, the description of which is beyond the scope of this book;
however, the values are available from the operator of the cyclotron or the
reactor. The formation cross sections of various nuclides are determined by
experimental methods using Eq. (5.1), and they have been compiled and
published by many investigators. The number of atoms Nof the target is
calculated from the weight Wof the material irradiated, the atomic weight
Awand natural abundance Kof the target isotope, and Avogadro’s number
(6.02 × 1023 ) as follows:
(5.3)
After irradiation, isotopes of different elements may be produced
and therefore should be separated by the appropriate chemical methods.
These radionuclides are identified and quantitated by detecting their
radiations and measuring their half-lives by the use of the NaI(Tl) or
N
WK
Aw=
×
××602 10.^23
50 5. Production of Radionuclides