# Half-Life Simulation

Introduction: Connecting Your Learning
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
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.
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
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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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