Exercise on radiometric dating. The objective of the activity is to use both the head and tail sides of pennies to simulate the decay of a radioactive element. We will use our data to try and describe radioactive decay using a mathematical formula. This learning experience emphasizes mathematical techniques in science. Time Frame - About 1 hourMaterials
Advance Preparation/BackgroundRemind participants/students that when we write “2 to the 3rd power,” the number 2 is called the base and the number 3 is called the exponent. When a number is written with an exponent it is said to be in exponential form. For example, we may write the number 8 in exponential form as a power of 2.
ProcedureFor this exercise we will start with each of the 16 pennies heads up. Therefore, we will call our radioactive element “heads.” This element, “heads” will decay to the element called “tails.” The decay rate will be constant. Specifically, every 100 years one-half of the “heads” present will decay to “tails.” We refer to this amount of time for one-half of the original material present to decay as the half-life. The half-life of “heads” is 100 years. You will now complete several half-life simulations using the 16 pennies. Starting with all 16 pennies in a heads-up position, turn pennies over to tails to indicate decay of the element. Enter your observational data in the chart below as you go. You will make 4 entries on each of 4 half-life intervals. Start with the first line at the passage of 100 years, i.e., the total time passed = 100 years. Enter the total time passed, number of half-lives, number of heads and number of tails at this interval of the simulation. The second line of data should be at 2 half-lives. Again enter all 4 observations as you did for the first line. The third line of data should be at 300 years and the fourth line should be at 400 years. Complete the chart in similar fashion as outlined in the instructions above.
Extension of data to a mathematical formulaNow complete this second chart using data from the first chart and your knowledge of fractions and exponents. For example, the first line would be after 1 half-life, there is 1/2 of heads remaining and the denominator of the fraction is 2. Remember, when you write the fraction of heads remaining using exponent form, you will be writing a fraction and expressing the denominator in exponential form as a power of 2.
At the start of the exercise, the presenter/teacher will ask the following questions?
Formative Assessment - BPurpose: To demonstrate how using the half-lives of isotopes can use radiometric dating to find the age of a rock. The decay of radioactive isotopes is like a clock ticking away, keeping track of the time that has passed since the rock has formed. As time passes, the concentration of parent material in a rock decreases as the concentration of daughter product increases. A geologist can calculate the absolute age of the rock in a process called radiometric dating by measuring the amount of parent and daughter materials in a rock and by knowing the half-life of the parent material. Carbon-14 is a parent material, which decays to its daughter material, nitrogen-14. The half-life of an isotope is the time it takes for half of the atoms in the isotope to decay. The half-life of carbon-14 is 5730 years; therefore, it will take 5730 years for half of the carbon-14 atoms to decay to nitrogen-14. Only half of the atoms of carbon-14 remaining after the first 5430 years will decay during the second 5730 years. Therefore, after two half-lives, one-fourth of the original carbon-14 atoms still remains. Half of these carbon-14 atoms will decay during the next 5730 years; therefore after three half-lives, one-eighth of the original carbon-14 atoms still remains. Carbon-14 is useful for dating fossils up to 50,000 years old. Organisms take in carbon from the environment to build tissues. When the organism dies, some of the carbon-14 decays and escapes as nitrogen-14 gas. By measuring the amount of carbon-14 remaining, the age of the fossil can be determined. Follow the steps listed below to illustrate the radioactive decay of carbon-14; then answer the questions:
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