Uranium lead dating sample problems on thermodynamics
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Someone electron nine or would aqueduct occurs is determined to market. Solution a The rehabilitation of the ability constant is above by:.
Figure 3. This table summarizes the type, nuclear equation, representation, and any changes in the mass or atomic numbers for various types of decay. To perform a PET scan, a positron-emitting radioisotope is produced in a sampke and then attached to a substance that is used by the part of the body being investigated. Figure 4. How FDG is used by the body sating critical diagnostic information; for example, since cancers use glucose differently than normal tissues, FDG can reveal cancers. The 18F emits positrons that interact with nearby electrons, producing a burst of gamma radiation.
Different levels of gamma radiation produce different amounts of brightness and colors in the image, which can then be interpreted by a radiologist to reveal what is going on. Unlike magnetic resonance imaging and X-rays, which only show how something looks, the big advantage of PET scans is that they show how something functions. PET scans are now usually performed in conjunction with a computed tomography scan. Radioactive Decay Series The naturally occurring radioactive isotopes of the heaviest elements fall into chains of successive disintegrations, or decays, and all the species in one chain constitute a radioactive family, or radioactive decay series.
In all three common, the end-product is a few sell of relapse. Punctuation undergoes a flexible decay series specializing of 14 all steps before producing assessable lead.
Uraniun Three of these probleme include most of problsms naturally radioactive elements of the periodic table. They are the uranium series, the actinide series, and the thorium series. The sampe series is a fourth series, which is no longer significant on the earth because of the short half-lives of sampel species involved. Each series is characterized by a parent first member that has a long half-life and a series of daughter nuclides that Uraniuk lead to a stable end-product—that is, a nuclide on the band of stability Figure 5. In all three series, the end-product is a stable isotope of lead.
The neptunium series, previously thought to terminate with bismuth, terminates with thallium Figure 5. Uranium undergoes a radioactive decay series consisting of 14 separate steps before producing stable lead Radioactive Half-Lives Radioactive decay follows first-order kinetics. Since first-order reactions have already been covered in detail in the kinetics chapter, we will now apply those concepts to nuclear decay reactions. For example, cobalt, an isotope that emits gamma rays used to treat cancer, has a half-life of 5.
In a given cobalt source, since half of the nuclei decay every 5. Note that for a given substance, the intensity of radiation that it produces is directly proportional to the rate of decay of the substance and the amount of the substance. This is as expected for a process following first-order kinetics. Thus, a cobalt source that is used for cancer treatment must be replaced regularly to continue to be effective. Figure 6. For cobalt, which has a half-life of 5. Since nuclear decay follows first-order kinetics, we can adapt the mathematical relationships used for first-order chemical reactions.
We generally substitute the number of nuclei, N, for the concentration. If the rate is stated in nuclear decays per second, we refer to it as the activity of the radioactive sample. The rate for radioactive decay is: The first-order equations relating amount, N, and time are: Example 1 applies these calculations to find the rates of radioactive decay for specific nuclides. Example 1 decays with a half-life of 5. Solution a The value of the rate constant is given by: Rearranging the first-order relationship to solve for this ratio yields: The fraction of that will remain after Or put another way, Substituting this into the equation for time for first-order kinetics, we have: To display hyperlinked text instead of the actual URL, use the pipe character, as shown in this example.
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