Radiometric Dating Name_______________________ Lab Objective: To use graphical information and rates of decay to calculate the age of Earth materials. Introduction: Determining the age of geologic material is determined by examining the relative numbers of various isotopes in a rock. Recall that the number of protons determines what element an atom is, and the number of neutrons determines the isotope. Radioactive decay is the spontaneous decay of an unstable (radioactive) parent isotope into a more stable daughter product. We use the term half-life to describe the time it takes for one-half of the unstable parent element to transform into a stable daughter element. The radioactive dating of a mineral is based on the ratio between parent and daughters left within the sample. As the number of parent isotopes deceases, the number of daughter isotopes increases by the same amount, so the sum remains constant. The graph below shows the relationship between parent and daughter isotopes over time. Radiometric Decay Graph Radiometric dating has been carried out since 1905 when it was invented by Ernest Rutherford as a method for determining the age of the Earth. In the century since then, the techniques have been greatly improved and expanded. Dating can now be performed on samples as small as a nanogram using a mass spectrometer. Absolute dating methods can provide a narrow age range for the formation of a geologic feature, such as a lava flow. Determination of the numerical age usually depends on obtaining a rock sample and separating out a particular mineral, element, or compound (such as salt, or lead), then performing spectroscopy to obtain the data needed to calculate the age. The method for extracting the mineral depends on the mineral. For example, to extract Argon, the sample is baked in a special oven to force the gas out, thereby allowing scientists to capture the gas as the rock is heated. Heating may affect mineral formation and can even reset the “geologic clock” in many instances. Meaning, a lava flow can be easily dated to the point of solidification, but a metamorphic rock may only tell you the date associated with metamorphosis, and minerals in sedimentary rocks may not tell you when the rock was created, but only indicate when those sediments cooled from magma long ago. Essentially, some methods are only appropriate for certain situations. It is also important to understand that errors associated with each method can exist, and scientists needed to understand the limitations of each method. Many errors are associated with having to measure such small amounts of residual elements, but with future technologies, these errors can be reduced. Some dating methods were only accurate to within 30 million years, but today we are seeing errors margins decrease to about 2 million years. Half-life Table of Common There are a variety of different Elements elements that can be used Radioactive Parent Stable Daughter Half-life to assess the age of a particular material. Rubidium-87 Strontium-87 49 billion years Rubidium-Strontium dating methods have been Uranium-238 Lead-206 4.5 billion years used to date igneous rocks and lunar material. Potassium-40 Argon-40 1.3 billion years Potassium-Argon dating methods can be used on Uranium-235 Lead-207 704 million years materials high in potassium (like micas and feldspars). Uranium-Lead dating is often performed on the mineral Zircon. Zircon is resistant to physical weathering and is very chemically inert. Zircon also forms multiple crystal layers during metamorphic events, recording an isotopic age of the event. One of zircon’s great advantages is that any sample provides two “clocks”, one based on uranium235's decay to lead-207 and one based on uranium-238's decay to lead-206 providing a built-in crosscheck that allows accurate determination of the age of the sample. Precision is enhanced if measurements are taken on multiple samples from different locations of the rock body, and if multiple dating methods are used. This way, we can reduce error and become more confident in our ability to date geologic events. Methods: Use the radioactive decay graph and the half-life table provided to answer the questions that follow. You will need a ruler and a calculator to help you with this activity. **Hint: The number of half-lives multiplied by the length of the half-life equals the age of the sample. You must show all of your work to receive full credit! Examples are provided. Results: 1. If you have 25% parent and 75% daughter, and the half-life is 500 years, what is the age of your rock? Step 1: Use the Radiometric Decay Graph. Step 2: Multiply. 25% parent material = 2 half-lives 75% daughter material = 2 half-lives 2 half-lives multiplied by 500yrs = 1000 years old 2. If you have 80% parent and the half-life is 500 years, what is the age of your rock? 3. If you have 750 atoms of Strontium-87 and 250 atoms of Rubidium-87, what is the age of your rock? Step 1: Calculate the ratio of parent and daughter material. 750 atoms + 250 atoms = 1000 atoms in total 750/1000 = 75% daughter material 250/1000 = 25% parent material Step 2: Use the Radiometric Decay Graph. 75% daughter material = 2 half- lives 25% parent material = 2 half-lives Step 3: Multiply. 2 half-lives multiplied by 49 billion years* = 98 billion years old *These numbers are provided in the Half-life table on page 2. 4. If you have 1320 atoms of Uranium-238 and 1320 atoms of Lead-206, what is the age of your rock? 5. If you have 3752 atoms of Potassium-40 and 6259 atoms of Argon-40, what is the age of your rock? 6. If you have 61,946 atoms of Uranium-235 and 190,266 atoms of Lead-207, what is the age of your rock? (Be careful which half-life you use.) 7. If you have 95,031 atoms of Rubidium-87 and 45,058 atoms of Strontium-87, what is the age of your rock? 8. EXTRA CREDIT: (1pt) If a rock is 3 billion years old and contains 700 atoms of Argon-40, how many atoms of Potassium-40 does the rock contain?
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