Half-life Gizmo Answer Key

Name: Douglas Doyle Date: 06-09-2022 Student Exploration: Half-life Directions: Follow the instructions to go through the simulation. Respond to the questions and prompts in the orange boxes. Vocabulary: daughter atom, decay, Geiger counter, half-life, isotope, neutron, radiation, radioactive, radiometric dating Prior Knowledge Questions (Do these BEFORE using the Gizmo.) 1. Have you ever made microwave popcorn? If so, what do you hear while the popcorn is in the microwave? Wiring then popping 2. If you turn the microwave on for two minutes, is the rate of popping always the same, or does it change? Explain. Still the same, although depending on the microwave and popcorn, perhaps for a shorter period of time Gizmo Warm-up Like an unpopped kernel in the microwave, a radioactive atom can change at any time. Radioactive atoms change by emitting radiation in the form of tiny particles and/or energy. This process, called decay, causes the radioactive atom to change into a stable daughter atom. The Half-life Gizmo allows you to observe and measure the decay of a radioactive substance. Be sure the sound is turned on and click Play ( ). 1. What do you see and hear? Random popping both audortial and visual Note: The clicking sound you hear comes from a Geiger counter, an instrument that detects the particles and energy emitted by decaying radioactive atoms. 2. What remains at the end of the decay process? Daughter atoms 3. Is the rate of decay fastest at the beginning, middle, or end of the process? begining Get the Gizmo ready: Activity A: Decay curves ● Click Reset ( ). Be sure that User chooses half-life and Random decay are selected. ● Check that the Half-life is 20 seconds and the Number of atoms is 128. Question: How do we measure the rate of radioactive decay? 1. Observe: Select the BAR CHART on the right side of the Gizmo and click Play. 1. What happens to the numbers of radioactive and daughter atoms as the simulation proceeds? radiation Daughter particles 2. Do the numbers of radioactive and daughter atoms change at the same rate throughout the simulation? Explain. No, it becomes less. ✏️ 2. Experiment: Click Reset, and select the GRAPH tab. Run a simulation with the Half-life set to 5 seconds and another simulation with the Half-life set to 35 seconds. Sketch each resulting decay curve graph in the spaces below. 3. Interpret: How does the Half-life setting affect how quickly the simulated substance decays? Shorter half life faster decay 4. Collect data: Click Reset. Change the Half-life to 10 seconds and click Play. Select the TABLE tab and record the number of radioactive atoms at each given time below. 0 s: 128 10 s: 55 20 s: 28 30 s: 11 40 s: 6 50 s: 3 5. Analyze: What pattern, if any, do you see in your data? I hardly notice any differences save the general decline. 6. Revise and repeat: Use your data from #4 above to fill in the first line of the data table below. Then repeat the experiment four more times. Calculate the average number of radioactive atoms for each time. Trial 0s 10 s 20 s 30 s 40 s 50 s 1 128 55 28 11 6 3 2 128 71 33 17 11 7 3 128 58 27 16 4 3 4 128 64 32 17 9 5 5 128 60 31 12 5 2 Averages: 128 62 30 15 7 4 7. Analyze: A half-life is defined as the amount of time it takes for half of the radioactive particles to decay. For the simulated substance, every 10 seconds represents one half-life. How does your data demonstrate the definition of a half-life? On average, it is half of the previous one. 8. Revise and repeat: Click Reset. Real radioactive samples will contain billions of radioactive atoms. To model the decay of a large sample, change from Random decay to Theoretical decay on the SIMULATION pane. Click Play and record the numbers of radioactive atoms: 0 s: 128 10 s: 64 20 s: 32 30 s: How does this data demonstrate the meaning of half-life? Every life is exactly half of the previous one. 16 40 s: 8 50 s: 4 Activity B: Get the Gizmo ready: Measuring half-life ● Click Reset. ● Select Isotope A from the left drop-down menu. ● Check that Theoretical decay is selected. Introduction: Different isotopes of the same element have the same number of protons but different numbers of neutrons in the nucleus. Some isotopes are radioactive. Question: How do we find the half-life of a radioactive isotope? 1. Observe: Select the GRAPH tab, and click Play. Based on the graph, what is your estimate of the half-life of isotope A? 15 2. Measure: Turn on the Half-life probe. Use the probe to measure how long it takes for exactly one-half of the original radioactive atoms to decay. What is the exact half-life of isotope A? 31 3. Collect data: In the first row of the table below, write how many seconds represent one half-life, two half-lives, and so forth. On the next row, predict the number of radioactive atoms that will be present at each time. Then use the probe to find the actual values. Half-life 0 Time (seconds) 1 2 3 4 5 31 62 94 125 155 Predicted # radioactive atoms 128 64 32 16 8 4 Actual # radioactive atoms 128 64 32 16 8 4 4. Calculate: Calculate the percentage of radioactive atoms that are left after each half-life. Half-life 0 1 2 3 4 5 Percentage radioactive atoms 100 50 25 12.5 6.25 3.125 5. Apply: Suppose you found a material in which 12.5% of the original radioactive atoms were present. If the half-life is 47 years, how old is the material? around 200 years of age 6. Apply: Use the Gizmo to find the half-life of Isotope B. What is it? 17 7. Extend your thinking: The slow decay of radioactive materials can be used to find the age of rocks, fossils, and archaeological artifacts. In a process called radiometric dating, scientists measure the proportions of radioactive atoms and daughter atoms in an object to determine its age. Carbon-14 is a useful isotope because it is found in wood, ash, bone, and any other organic materials. You can use the Half-life Gizmo to model the decay of Carbon-14, which has a half-life of approximately 6,000 years (actual value is 5,730 years). In the Gizmo, select User chooses half-life and Theoretical decay. Set the Half-life to 6 seconds (to represent 6,000 years) and the Number of atoms to 100. Use the Gizmo to estimate the age of each of the objects below. For these questions, each second in the Gizmo represents 1,000 years. Description Age (years) Egyptian papyrus with 63% of its original carbon-14 atoms 4000 Aboriginal charcoal with 22% of its original carbon-14 atoms. 13000 Mayan headdress with 79% of its original carbon-14 atoms 2000 Neanderthal skull with 3% of its original carbon-14 atoms 30500