Question 12.9.Q1: Used in some 80 % of all nuclear medicine imaging tests, tec......
Used in some 80 % of all nuclear medicine imaging tests, technetium99m (Tc-99m) is the most widely used radionuclide for imaging in nuclear medicine. Its parent nucleus is molybdenum-99 (Mo-99) which decays into Tc-99m through β^− decay with a half-life of 2.75 days (66 hours).
Technetium-99m is an isomeric (metastable) radionuclide emitting 140 keV gamma rays with a physical half-life of 6.01 hours. It provides sufficiently high-energy γ rays for clinical imaging and has a half-life long enough for investigation of metabolic processes, yet short enough so as not to deliver an excessive total body dose to the patient.
The relatively short 6-hour half-life of Tc-99m makes the logistics of source production, delivery, and storage problematic.
A method to circumvent the transportation and delivery problem was developed in 1950s at the Brookhaven National Laboratory in Upton, NY, whereby a supplier, rather than shipping the Tc-99m radionuclide, ships the longer-lived parent radionuclide Mo-99 in a device referred to as radionuclide generator and Tc-99m is extracted from the generator when it is actually needed.
Two techniques, both based on nuclear reactor technology, are used for producing the parent radionuclide Mo-99 used in Tc-99m generators for onsite generation of the Tc-99m radionuclide. One technique is based on neutron activation of stable nuclide Mo-98 to produce the daughter radionuclide Mo99 through the neutron capture reaction { }_{42}^{98} \mathrm{Mo}(\mathrm{n}, \gamma){ }_{42}^{99} \mathrm{Mo}. The second, more common, technique uses fission of enriched uranium-235 to produce Mo-99 as one of the many fission fragments in the U-235 target bombarded with thermal neutrons.
(a) Describe the targets used in production of Mo-99 with:
(1) Neutron activation of Mo-98 technique.
(2) Fission of uranium-235 technique.
(b) Discuss post-production processing of targets in the two Mo-99 production techniques.
(c) Find the appropriate model for describing the growth of the Mo-99 radionuclide when either Mo-98 or U-235 target is bombarded with thermal neutrons in a nuclear reactor.
Calculate the maximum achievable specific activities of Mo-99 produced from pure natural molybdenum target and pure natural uranium target in a nuclear reactor with a fluence rate \dot{\varphi}=5 \times 10^{13} \mathrm{~cm}^{-2} \cdot \mathrm{s}^{-1}. Most of the appropriate data can be found in Appendix A; however, the additional information provided in Table 12.32 may be useful.
(d) Express the specific activity a_{Mo-99}(t) against time t for the two Mo99 production techniques of target activation in a nuclear reactor. For pure natural molybdenum target as well as for natural uranium target calculate and plot at least 10 points ranging in specific activity a_{Mo-99}(t) from 0 to 0.98 \left(a_{Mo-99}\right)_{max}.
Table 12.32 Some atomic and nuclear properties of molybdenum-98 and uranium-235 that may be of use in answering questions related to the production of molybdenum-99 for use in molybdenum–technetium radionuclide generators
\begin{array}{lll} \hline \text { Parent P nuclide } & \begin{array}{l} \text { Molybdenum-98 } \\ (\text { Mo-98) } \end{array} & \begin{array}{l} \text { Uranium-235 } \\ (\mathrm{U}-235) \end{array} \\ \hline \text { Natural abundance } w_{\mathrm{P}}(\%) & 24.13 & 0.72 \\ \hline \text { Cross section } \sigma_{\mathrm{P}}(\mathrm{b}) & 0.13 \text { (neutron activation) } & 587 \text { (nuclear fission) } \\ \hline \text { Daughter D radionuclide } & \text { Mo-99 } & \text { Mo-99 } \\ \hline \text { Branching ratio } f_{\text {Mo-99 }}(\%) & 100 & 6.1 \\ \hline \end{array}
(a) Both techniques currently used in production of Mo-99 radionuclide rely on thermal neutron irradiation of appropriate targets in a nuclear reactor; however, each technique is based on its own specific physical process and uses its own specific target: (1) neutron activation technique uses thermal neutron capture in Mo-98 parent nuclide to produce Mo-99 daughter radionuclide and (2) nuclear fission technique uses nuclear fission of uranium-235 radionuclide and extracts Mo-99 from the family of fission fragments produced in the U-235 target.
(1) Neutron activation of Mo-98 into Mo-99 (neutron activation target) The most common target for neutron activation of Mo-98 into Mo-99 is molybdenum trioxide \left(MoO_3\right) without any Mo-98 enrichment. Molybdenum has 7 natural stable isotopes with Mo-98 (abundance 24.13 %) the most abundant natural molybdenum isotope. Enrichment of Mo-98 in molybdenum target can produce up to a 4-fold increase in specific activity of the molybdenum target; however, in comparison with the enrichment process, irradiation with neutrons of larger targets is more economical.
In addition to Mo-98 two other natural isotopes in molybdenum target also get activated: Mo-92 into Mo-93 and Mo-100 into Mo-101. However, both Mo-93 and Mo-101 have relatively short half-lives (6.9 h and 14.6 min, respectively) in comparison with Mo-99 half-life of 66 h, so that the two radioisotopes do not contribute appreciably to the radioactivity of the molybdenum neutron activation product. On the other hand, chemical impurities in molybdenum targets should be removed prior to neutron activation to maximize the radionuclidic purity of the Mo-99 product for use in nuclear medicine imaging.
(2) Fission of uranium-235 for Mo-99 production (nuclear fission target) Currently, most of the Mo-99 radionuclide used in Mo/Tc radionuclide generators is produced by bombarding a U-235 target with thermal neutron causing a nuclear fission reaction which results in U-235 fission. About 6.1 % of fission reactions produce Mo-99 nuclei either through direct fission or through subsequent decay of nuclear fission fragments. Targets used in production of Mo-99 are usually made of highly enriched uranium (HEU) to maximize the yield of Mo-99. The abundance of U-235 in natural uranium is 0.7 % compared to 99.3 % for U-238 and an HEU target contains U-235 in excess of 90 %, making the transportation and use of these targets problematic because of the possibility of use of these targets for military purposes. Targets come in the form of fuel plates containing an aluminum-uranium alloy or in the form of uranium oxide thin films coated inside a stainless steel tube.
(b) Post–irradiation processing in production of Mo-99.
(1) Neutron activation of Mo-98 into Mo-99 Target processing in which chemical impurities are removed to minimize the production of undesirable radionuclides is mainly done prior to target bombardment with neutrons. After bombardment the radionuclidic purity of the Mo-99 target product is verified by measuring activities of radionuclides other than Mo-99 and its daughter Tc-99m to ensure that they are at maximum acceptable levels or below.
(2) Fission of uranium-235 in Mo-99 production (fission targets) Processing of fission targets post irradiation allows production of high purity and high specific activity of Mo-99 radionuclide. Processing must be carried out rapidly after irradiation to minimize the loss of Mo-99 to natural radioactive decay.
The processing is carried out in hot cells where chemicals are added to dissolve the target. For targets containing aluminum, alkaline dissolution is used in a sodium hydroxide solution (NaOH) whereas acidic dissolution is used for uranium oxide based targets.
(c) Maximum attainable specific activity \left(a_{Mo-99}\right)_{max} for the two targets: (1) Mo98 target undergoing thermal neutron activation into Mo-99 and (2) U-235 target undergoing neutron fission producing Mo-99 as one of the fission fragments.
To calculate the maximum attainable specific activity \left(a_{Mo-99}\right)_{max} for the two targets (Mo-98 and U-235) we need to determine which of the available mathematical models for nuclear activation best describes the growth of the Mo-99 activity in the target. As shown in Prob. 251, three nuclear activation models are available in general: saturation model, depletion model, and depletion–activation model. Since the choice of which model to use depends largely on the activation factor m = σ_P\dot{φ}/λ_D for the given nuclear target (note: for m < 10^{−3} the simple saturation model of nuclear activation can be used for describing the growth of the daughter activity), we first determine m for the two target nuclides.
(1) For the Mo-98 target, the neutron activation cross section of the parent nucleus Mo-98 is \sigma_{\mathrm{Mo}-98}=0.13 \mathrm{~b}\left(1 \mathrm{~b}=1 \text { barn }=10^{-24} \mathrm{~cm}^2\right) and when the molybdenum target is placed in a neutron fluence rate \dot{\varphi}=5 \times 10^{13} \mathrm{~cm}^2 \cdot \mathrm{s}^{-1} the activation factor m is given as follows
(2) For the uranium target, only 6.1 % of all fission processes of the parent nuclei U-235 produce Mo-99. The production of Mo-99 in this case is governed by the an effective cross section \left(σ_{U-235}\right)_{eff} that is the product of the general fission cross section of the parent U-235 nuclide and the yield f_{Mo-99} = 0.061 of the daughter Mo-99 nuclide. The effective activation cross section \left(σ_{U-235}\right)_{eff} is thus as follows
\left(\sigma_{\mathrm{U}-235}\right)_{\mathrm{eff}}=f_{\mathrm{Mo}-99} \sigma_{\mathrm{U}-235}=0.061 \times(587 \mathrm{~b})=35.8 \mathrm{~b} . (12.294)
For U-235 target placed in a neutron fluence rate \dot{\varphi}=5 \times 10^{13} \mathrm{~cm}^2 \cdot \mathrm{s}^{-1} the activation factor m is
We conclude from (12.293) and (12.295) that the simple saturation model may be used to describe the growth of Mo-99 activity for both activation processes, since m < 0.001 for both processes. The general expression for the daughter activity \mathcal{A}_D(t) is, according to the saturation model of nuclear activation, given as follows (T.12.23)
\mathcal{A}_{\mathrm{D}}(t)=\mathcal{A}_{\mathrm{sat}}\left[1-e^{-\lambda_{\mathrm{D}} t}\right]=\sigma_{\mathrm{P}} \dot{\varphi} N_{\mathrm{P}}(0)\left[1-e^{-\lambda_{\mathrm{D}} t}\right] (12.296)
where \mathcal{A}_{sat} is the saturation activity, N_P(0) is the initial number of parent P nuclei, λ_D is the decay constant of daughter D, and σ_P is the cross section for thermal neutron interaction with the parent P atom, be it neutron activation of a molybdenum (Mo-98) target or nuclear fission of an uranium (U-235) target.
Using (12.296) we now write the specific activity of the Mo-99 daughter radionuclide as
where m_P stands for the mass of the parent nuclide and N_A is the Avogadro number. We use the ≈ sign in (12.297) because we are determining the specific activity of Mo-99 that is not carrier-free, rather, it is mixed together with all natural isotopes of either molybdenum in a molybdenum target or uranium in a uranium target. In (12.297) we then use for A_P the atomic weights for natural molybdenum \left(A_{Mo} = 95.962\ g/mol\right) and natural uranium \left(A_U = 238.0289\ g/mol\right), respectively, but we also account for the fraction by weight w_P of the particular parent isotope and for the branching ratio, as shown in the calculation of the maximum specific activity \left(a_{Mo-99}\right)_{max} below.
The maximum specific activities of the Mo-99 radionuclide are from (12.297) given as follows:
(1) For a pure natural molybdenum target
where w_{Mo-98} accounts for the fraction by weight of the Mo-98 isotope in natural molybdenum (24.13 %) from which the Mo-99 radionuclide is produced through neutron activation in nuclear reactor.
(2) For a natural uranium target
where w_{U-235} accounts for the fraction by weight of U-235 in natural uranium (0.72 %) from which the Mo-99 radionuclide is produced through the fission reaction of thermal neutrons on uranium target. The effective cross section \left(σ_{U-235}\right)_{eff} is defined in (12.294).
Comparing (12.299) and (12.298) we note that the maximum attainable specific activity of Mo-99 from a natural uranium target is about 3.3 times larger than that from a natural molybdenum target. Significantly higher specific activities through fission are achievable when instead of natural uranium target a highly enriched uranium target with f_{U-235} > 0.95 is used providing a two orders of magnitude increase in specific activity. Moreover, the chemical separation of Mo-99 from all other fission products in the U-235 fission target also increases the specific activity of the Mo-99 activation product. Therefore, for practical reasons most of the Mo-99 radionuclide produced in nuclear reactors for use in radionuclide generators around the world is produced through enriched uranium targets. The main drawbacks of this approach are the security concerns related to manufacturing, transportation, and use of highly enriched (nuclear weapons grade) uranium as well as the associated production of radioactive nuclear waste.
(d) Combining (12.297) and (12.298) or (12.299) we express the growth of specific activity a_{Mo-99}(t) as:
(1) For a pure natural molybdenum target
(2) For a pure natural uranium target
According to (12.300) and (12.301) the maximum specific activity \left(a_{Mo-99}\right)_{max} is attained at time t = ∞ in the two types of target. However, we can find a reasonable activation time frame by determining at what time t is the specific activity equal to say 98 % of \left(a_{Mo-99}\right)_{max}. Solving
for t_{0.98} we get t_{0.98} = 505 h. We thus choose a time scale from 0 to 600 hours and use (12.300) and (12.301) to calculate the growth of Mo-99 specific activity a_{Mo-99}(t) in steps of 50 hours from 0 to 550 hours. The results of the calculation are shown in Table 12.33 and plotted in Fig. 12.16 for pure molybdenum and pure uranium targets.
Table 12.33 Specific activity a_{Mo-99}(t) against activation time t calculated for natural molybdenum target from (12.300) and for natural uranium target from (12.301) for activation times between 0 and 600 h in steps of 50 h
\begin{array}{lllllllll} \hline \text { (1) } & \text { Activation time (h) } & 0 & 50 & 100 & 150 & 200 & 250 & 300 \\ \text { (2) } & \text { Molybdenum target } & 0.0 & 0.110 & 0.176 & 0.214 & 0.237 & 0.250 & 0.258 \\ \text { (3) } & \text { Uranium target } & 0.0 & 0.368 & 0.585 & 0.714 & 0.790 & 0.835 & 0.861 \\ \hline \hline \text { (1) } & \text { Activation time (h) } & 350 & 400 & 450 & 500 & 550 & 600 & \infty \\ \text { (2) } & \text { Molybdenum target } & 0.263 & 0.266 & 0.268 & 0.269 & 0.269 & 0.270 & 0.270 \\ \text { (3) } & \text { Uranium target } & 0.877 & 0.887 & 0.892 & 0.895 & 0.897 & 0.898 & 0.9 \\ \hline \end{array}
