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Half-Life Simulation

Introduction: Connecting Your Learning
How can scientists measure the age of fossils or other objects using radioactivity? Why is it that radioactive chemicals, or radioisotopes, can be safely injected into a person for diagnostic purposes with no lingering effects? Why is there so much concern about where people discard radioactive wastes? These questions can all relate to radioactive half-lives, or the time required for a given radioactive sample to lose half of its radioactivity. Small quantities of natural radioactivity exist in the environment in part due to the constant bombardment from outer space of cosmic rays. This continually creates small amounts of radioactive carbon and other radioisotopes which are incorporated in carbon-containing compounds, such as carbon dioxide used in photosynthesis, which then becomes part of glucose, which can be eaten by an animal, and on through the food web. As long as living organisms are absorbing substances from their environment by breathing, drinking, or eating, they absorb this radioactivity, much of which becomes part of the organism’s body. Once dead, obviously no more is absorbed, so whatever was there will slowly, over time, undergo radioactive decay. Eventually, no radioactivity will remain. However, that can take many millions of years for some types of radioactivity. (Some radioisotopes, such as those used for medical diagnoses, decay quite rapidly — a matter of microseconds — so after a few minutes, virtually no radioactivity remains. Unfortunately, many radioactive wastes decay very slowly, making it difficult to find safe repositories that will contain them for, say, thousands of years. By comparing the ratio of radioisotopes to non-radioactive isotopes, the amount of time that has passed for a given sample can be calculated.
In this lab, you will simulate radioactive decay, make a half-life curve, and use it to make some predictions.
Resources and Assignments
Multimedia Resources None
Required Assignments Lab 14 Report
Materials (Lab Kit) None
Materials (Student supplied) • Approx. 200 Plain M&M®s
• Tray
• Graphing calculator
Focusing Your Learning
Lab Objectives
By the end of this lesson, you should be able to:
1. Investigate a half-life simulation.
2. Use radioactive dating to calculate the age of the simulation examples.
Procedures
1. Count out 200 M&M®s and place them with the “M” side up on the tray. The tray represents a rock sample and the candies with the marked side represent the entire radioactivity the sample contains initially.
2. Give the tray a shake so that many of the candies flip over. One shake represents the passage of 5,000 years.
3. Count and remove all of the M&M®s that flipped over to the unmarked side. These represent the radioactivity that underwent nuclear decay and transmutated into a different element.
4. Repeat Steps 2 and 3 until all the candies are gone. (If you give the tray a shake and none of the candies flip over, be sure to record the shake as the passage of 5,000 years but with zero transmutations.)
5. Normally, eating in the lab is not permissible; make sure that everything is clean and properly disposed of.
Assessing Your Learning
Discussion
1. Plot a line graph with the number of “radioactive” particles left (you must start with 200 at time = 0. Subtract the first amount that flipped over for the first 5,000 years. Then subtract the second amount from that number — not the 200 — at 10,000 years, etc.) versus time (on the horizontal axis). Be sure that it is properly labeled and titled.
2. Explain why your “radioactive decay” curve is not perfectly smooth; in other words, besides the fact that this is not really radioactive and you are shaking a tray instead of the passage of real time, why are real radioactive decay curves very predictable?
3. What do mathematicians call the shape of this curve?
4. If the half-life of your sample is 5,000 years, calculate the value for k, the rate constant. Be sure to show your calculations.
5. Assume that your “radioactivity” was C-14 (carbon-14, carbon with mass number 14) and that it undergoes beta decay. Write the balanced nuclear equation for this reaction.
6. Carbon dating can be used to get a measurement of the age of a carbon-containing sample. (Scientists actually use mass spectroscopy and measure ratios of isotopes, which is a bit more complicated than can be replicated here.) Using the curve you created in Step 1, determine the age of a sample with this amount of radioactivity left:
a. 75%
b. 50%
c. 25%
d. 0%
Lab Report
Make sure to complete a full lab report and submit it via email by the due date.
Submission
Important information: Please follow the procedure below in the completion of your assignments.
Compose your responses to the questions in a word processing program. Run spell check. Review your work to make sure that you have completely answered all questions.
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When you have finished, you will need to close the browser window to return to your course.
Select the following link to upload: Lab 14.

Title: Half-Life Simulation
Introduction

Objectives
 Investigate a half-life simulation.
 Use radioactive dating to calculate the age of the simulation examples.
Purpose:
(a) Materials
• Approx. 200 Plain M&M®s
• Tray
• Graphing calculator
(b)Procedures
1. Count out 200 M&M®s and place them with the “M” side up on the tray. The tray represents a rock sample and the candies with the marked side represent the entire radioactivity the sample contains initially.
2. Give the tray a shake so that many of the candies flip over. One shake represents the passage of 5,000 years.
3. Count and remove all of the M&M®s that flipped over to the unmarked side. These represent the radioactivity that underwent nuclear decay and transmutated into a different element.
4. Repeat Steps 2 and 3 until all the candies are gone. (If you give the tray a shake and none of the candies flip over, be sure to record the shake as the passage of 5,000 years but with zero transmutations.)
5. Normally, eating in the lab is not permissible; make sure that everything is clean and properly disposed of.
This the counting part from the first shake to the last shakes:
66
38
30
24
17
8
6
3
2
1

Discussion
1. Plot a line graph with the number of “radioactive” particles left (you must start with 200 at time = 0. Subtract the first amount that flipped over for the first 5,000 years. Then subtract the second amount from that number — not the 200 — at 10,000 years, etc.) versus time (on the horizontal axis). Be sure that it is properly labeled and titled.
2. Explain why your “radioactive decay” curve is not perfectly smooth; in other words, besides the fact that this is not really radioactive and you are shaking a tray instead of the passage of real time, why are real radioactive decay curves very predictable?
3. What do mathematicians call the shape of this curve?
4. If the half-life of your sample is 5,000 years, calculate the value for k, the rate constant. Be sure to show your calculations.
5. Assume that your “radioactivity” was C-14 (carbon-14, carbon with mass number 14) and that it undergoes beta decay. Write the balanced nuclear equation for this reaction.
6. Carbon dating can be used to get a measurement of the age of a carbon-containing sample. (Scientists actually use mass spectroscopy and measure ratios of isotopes, which is a bit more complicated than can be replicated here.) Using the curve you created in Step 1, determine the age of a sample with this amount of radioactivity left:
a. 75%
b. 50%
c. 25%
d. 0%

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