A Penny for Your Neutron: a Model of Half-Life

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A Penny for Your Neutron: A Model of Half-life

GSE - S2 (9-11) –6: Students demonstrate an understanding of physical, chemical, and nuclear changes by …  6d: explaining the concept of half-life and using the half-life principal to predict the approximate age of a material.  6c: explaining and/or modeling how the nuclear make-up of atoms governs alpha and beta emissions creating changes in the nucleus of an atom results in the formation of new elements.

Problem: How can you make a model of beta decay? Materials (per group)  100 pennies  Paper or plastic cup  Graph paper Procedure 1. Work in groups of three. Designate one classmate to be the coordinator, one to be the “Geiger counter,” and one to be the recorder. 2. Place 100 pennies into a paper or plastic cup. The pennies will represent carbon-14 nuclei. 3. Have the coordinator shake the cup of pennies and carefully empty them onto the table. Have the counter separate the pennies that are heads up from those that are tails up. The heads represent carbon- 14 nuclei that have decayed and the tails represent unchanged carbon-14 nuclei. This step represents one half-life. Have the recorder record the number of carbon-14 nuclei remaining after one half-life (tails) in the data table below (“Our Experiment” column). 4. Return the unchanged carbon-14 (tails) to the cup. Repeat step 3 five more times. 5. Have the coordinator put your data up on the board so the class average can be calculated for each half- life. When this is complete, copy the data into your table. 6. Complete the “Actual” column in the data table using the correct way to show decay of a radioisotope. Observations Your Experiment Class Average Actual Half- Remaining carbon-14 Half- Remaining carbon-14 Half- Remaining carbon-14 lives nuclei lives nuclei lives nuclei 0 100 0 100 0 100 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6

Analysis 1. Draw a graph of the number of “Remaining C-14 nuclei (y-axis) vs. “half-life” (x-axis) for each column (Our Experiment, Class Average & Actual.) There should be three lines on the same graph. Use a different color for each line and make a Key to go with each color. The graph should also have a proper title and each axis should be labeled. Each group member creates their own graph. 2. Does this model of beta decay correctly represent the rate of decay of a radioactive element? (How does “Your Experiment” data line compare with the “Actual” data line on the graph?)

3. Which data, yours or the class’s, is more accurate in showing how beta decay works? Does this make sense? Why or why not?

4. Do you think that after more half-lives you would eventually have no carbon-14 atoms remaining? Why or why not?

5. Why do scientists use carbon-14 to date fossils?

6. C-14 has a half-life of 5730 years. Suppose a piece of wood contains 84mg of C-14. After 3 half-lives, how much C-14 would it still contain? How many years would this be?

7. A body of what is thought to be a man who died in the ice age is found in Canada. During that time period, most living organisms contained 240 mg of C-14, but when the man was found, his bones contained only 15 mg of C-14. How old is this bone? C-14 has a half-life of 5730 years. 8. What was the original size of a sample of carbon-14 that has been decaying for 34,380 years and it currently weighs 75 grams? C-14 has a half-life of 5730 years.