Learning Objectives This Exemplar will teach the following concept from the ACS Examinations Institute General Chemistry ACCM: I. Matter consists of atoms that have internal structures that dictate their chemical and physical behavior. F. Atoms maintain their identity, except in nuclear reactions. 1. Atoms change identity in nuclear reactions; it is possible to write nuclear equations that follow these changes. 3. Measurements of radioactivity can be used to identify which unstable isotopes are present in a sample and in what quantity. a. Radioactive half-lives are unique and may be used to identify what isotopes are present. b. Radioactivity may occur via alpha, beta, gamma, or other decay events and the type of radioactivity observed is often an important component of identifying the decaying isotope. Coronary Artery Disease and Technetium-99m Coronary Artery Disease (CAD), the most common form of heart disease, is caused by a buildup of cholesterol deposits within the coronary arteries. Annually, CAD accounts for about 610,000 deaths in the United States, about one in every four deaths, making it the leading cause of death in the US. Most of the time, patients are unaware they have CAD until they have a heart attack (Brown et. al., 2020). Advances in medical technology have made it easier to diagnose CAD, using a form of imaging known as Myocardial Perfusion Imaging. Myocardial Perfusion Imaging uses SPECT (single photon emission computed tomography) to demonstrate how well blood is able to flow through the heart muscle (Maddahi et. al., 1990). SPECT requires the usage of a highly radioactive element, Technetium-99m, to work properly. Technetium-99m is a silver-gray metal that can be found naturally in Earth’s crust but is manmade for most usages. Compared to Technetium-99, Technetium-99m has a much lower half-life: approximately 6 hours (National Center for Biotechnology Information, 2022). The following exercises will demonstrate why Technetium-99m is ideal for nuclear medicine diagnostics. Generated Images of Blood Flow using Myocardial Perfusion Imaging (Burrell and MacDonald, 2006) Beta Decay in Context Technetium-99m is first formed through the beta decay of Molybdenum-99, an isotope of Molybdenum-98 which was bombarded by neutrons. Since Technetium-99m has such a short half-life, it is not financially advisable to transport large amounts of Technetium-99m to hospitals, since most will have decayed by the time it arrives. Instead, Molybdenum-99 is transported (Freeman, 2019). In beta decay , a neutron will effectively become a proton , which is modeled by the release of a beta particle , appearing in a nuclear decay equation as an electron. As a neutron changes into a proton, the resulting nucleus will have the same atomic mass number and a one-point increase in atomic number. The release of a beta particle helps the radioactive nucleus gain stability . Any form of radioactive decay releases a large amount of energy, associated with instability (Zumdahl and Decoste, 2017). Let’s break down the beta decay of Molybdenum-99: Example \(\#1\) What is the energy released in the beta decay of Molybdenum-99 in J/atom? The mass of Technetium-99m is 98.906250 amu (atomic mass units) and the mass of Technetium-99m is Molybdenum-99 is 98.907707 amu . Solution Step 1: Set up an equation for the beta decay of Molybdenum-99 to Technetium-99m \begin{equation} { }_{42}^{99} \mathrm{~Mo} \rightarrow{ }_{-1}^0 \mathrm{e}+{ }_{43}^{99m} \mathrm{Tc} \nonumber\ \end{equation} Step 2: Calculating the mass defect observed between products and reactants \[\Delta m = mass of products - mass of reactants \nonumber\] \[\Delta m = 98.906250 amu - 98.907707 amu \nonumber\] \[\Delta m = -.001457 amu \nonumber\] Although a beta particle is emitted, its mass is regarded as negligible. Step 3: Einstein's equation \[E = mc^2 \nonumber\] In this case, E is energy in joules, m is the mass defect (which must be converted to kilograms), and c is the speed of light. c = 2.998 x 10 8 m/s. \[E = (-.001457 amu)(\frac{1.66*10^{-27} kg/atom}{1 amu})(2.998*10^8 m/s)^2 \nonumber\] Remember: 1 amu is equal to 1.66 x 10 -27 kg. In order to use Einstein's equation, we must convert atomic mass units from the first part of the problem to kilograms. Answer 2.174 x 10 -13 J/atom Gamma Emission Technetium-99m similarly goes through nuclear decay, specifically, gamma emission . In decaying, Technetium-99m releases a gamma photon instead of a beta particle. The gamma photon associated with the decay of Technetium-99m has an energy of 140 keV . Technetium-99, the product of Technetium-99m decay, eventually undergoes beta decay to become Ruthenium-99 (Gottschalk, 1966). Unlike beta decay, gamma emission increases stability by solely releasing energy, not with any associated particle. The decay process is shown below, where γ represents the emitted gamma photon. \begin{equation} { }_{43}^{99m} \mathrm{~Tc} \rightarrow{ }_{0}^0 \mathrm{\gamma}+{ }_{43}^{99} \mathrm{Tc} \nonumber\ \end{equation} Technetium-99m is injected into a patient’s bloodstream intravenously. During a cardiac stress test, which utilizes Myocardial Perfusion Imaging while a patient is exercising, gamma cameras will be used to detect Technetium-99m absorption into the heart muscle. Healthy heart muscle will absorb Technetium-99m, which will then begin to decay and emit gamma photons with an energy of 140 keV, cameras are rotated around the patient’s torso while they are performing the cardiac stress test (Johns Hopkins Medicine, 2021). Three Other Types of Radioactive Decay 1. Alpha Decay : alpha decay occurs in heavier radioactive nuclei, and effectively produces a helium atom in the process. This results in the atomic mass of the radioactive nuclei decreasing by four and the atomic number decreasing by two; basically, the emission of 2 neutrons and 2 protons (Zumdahl and Decoste, 2017). \begin{equation} { }_{92}^{238} \mathrm{~U} \rightarrow{ }_{2}^4 \mathrm{He}+{ }_{90}^{234} \mathrm{Th} \nonumber\ \end{equation} 2. Positron Production : positron production effectively involves a proton turning into a neutron, the opposite of beta decay! Rather than modeling an electron being released, a positron is released, the antiparticle of an electron. Because a proton is turned into a neutron, the atomic number (proton number) will decrease by one, but the mass will stay the same (Zumdahl and Decoste, 2017). \begin{equation} { }_{11}^{22} \mathrm{~Na} \rightarrow{ }_{1}^0 \mathrm{e}+{ }_{10}^{22} \mathrm{Ne} \nonumber\ \end{equation} 3. Electron Capture : in electron capture, an electron within the inner orbital of the atomic nucleus is “captured” by the nucleus. The resulting nucleus will display a one-point decrease in atomic number. In this case, the electron would be modeled on the reactant side of the equation, rather than the product (Zumdahl and Decoste, 2017). \begin{equation} { }_{80}^{201} \mathrm{~Na}+{ }_{-1}^0 \mathrm{e} \rightarrow{ }_{0}^0 \mathrm{\gamma}+{ }_{79}^{201} \mathrm{Au} \nonumber\ \end{equation} The Half-Life of Radioactive Materials The true medical efficiency of Technetium-99m lies in its half-life, six hours (National Center for Biotechnology Information, 2022). Because Technetium-99m’s half-life is comparatively short, patient exposure to radioactivity is minimized. Let’s look at the half-life in the following example problem: Example \(\#2\) A sample of Technetium-99m has an activity of 15.0 millicuries (mCi). If the half-life of Technetium-99m is 6.0 hours, how long before the activity is 4.7 mCi? Assume the decay of Technetium-99m is a first-order reaction. Note A millicurie is a specific unit of activity for radioactive elements and is regarded as 3.7 x 10 10 decays per second. This problem will work just the same as if we were dealing with concentrations! Step 1: Modeling a first-order reaction. First-Order Reaction Equation: A = A 0 e -kt A = final activity (4.7 mCi in this case) A 0 = initial activity (15.0 mCi) k = rate constant t = time A first-order reaction always has a half-life of t 1/2 = .693/k. Knowing this, we can rewrite the equation above, since we do not know the rate constant. Step 2: Rewriting the Equation A = A 0 e -(.693/t 1/2 )*t Here, we've simply substituted k in terms of the half-life, which we do know. Step 3: Plugging in known values and solving. 4.7 mCi = (15.0 mCi)e -.693t/6 hrs \[ln(\frac{4.7 mCi}{15.0 mCi}) = \frac{-.693t}{6.0 hrs} \nonumber\] -1.16049 = -.1155t t = 10.05 hours Solution It will take 10.05 hours before the activity is 4.7 mCi with an initial activity of 15.0 mCi. Check out the “Further Reading” section for more on how to derive the equation for first-order reactions. As shown in the above example, it takes a fairly little amount of time for the radioactivity of Technetium-99m to sufficiently decrease. In fact, in 24 hours, 93.7% of all the Technetium-99m injected has already decayed, minimizing overall patient exposure to radioactivity (Wikipedia, 2022). References 1. Brown, J.; Gerhardt T. Kwon; E. Risk Factors for Coronary Artery Disease. PubMed, 2020 , 1-68. National Library of Medicine. https://www.ncbi.nlm.nih.gov/books/NBK554410/ (accessed 28 Oct. 2022). 2. Burrell, S.; MacDonald, A. Artifacts and Pitfalls in Myocardial Perfusion Imaging. JNMT , 2006 , 34 (4), 193-211. https://tech.snmjournals.org/content/34/4/193.short (accessed 28 Oct. 2022). 3. Freeman, T. Battle of the elements: Technetium-99m diagnoses disease then decays away. 2019. https://physicsworld.com/a/battle-of-the-elements-technetium-99m-diagnoses-disease-then-decays-away/ (accessed 28 Oct. 2022). 4. Gottschalk, A. Radioisotope Scintiphotography with Technetium 99m and the Gamma Scintillation Camera. AJR Am. J. Roentgenology . 1966 , 97 (4), 860-868. DOI: 10.2214/ajr.97.4.860 5. Maddahi, J.; Kiat, H.; Van Train, K. F.; Prigent, F.; Friedman, J.; Garcia, E. V.; Alazraki, N.; DePuey, E. G.; Nichols, K.; Berman, D. S. Myocardial perfusion imaging with technetium-99m sestamibi SPECT in the evaluation of coronary artery disease. Am. J. Card. 1990 , 66 (13), 55–62. DOI: 10.1016/0002-9149(90)90613-6 6. Myocardial Perfusion Scan, Stress. Johns Hopkins Medicine. 2021. https://www.hopkinsmedicine.org/health/treatment-tests-and-therapies/myocardial-perfusion-scan-stress (accessed 28 Oct. 2022). 7. National Center for Biotechnology Information. Molybdenum-99. https://pubchem.ncbi.nlm.nih.gov/compound/Molybdenum-99 (accessed 28 Oct. 2022). 8. National Center for Biotechnology Information. Technetium Tc-99m. https://pubchem.ncbi.nlm.nih.gov/compound/Technetium-Tc-99m (accessed 28 Oct. 2022). 9. Wikipedia. Technetium-99m. https://en.wikipedia.org/wiki/Technetium-99m (accessed 28 Oct. 2022) 10. Zumdahl, S. S.; Decoste, D. J. Chemical Principles 8th Edition. Boston, Ma: Cengage Learning, 2017. Further Reading 1. LibreTexts Chemistry. First-Order Reactions. 2021. https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Kinetics/02%3A_Reaction_Rates/2.03%3A_First-Order_Reactions (accessed 2022-10-28)