Radioactive Decay Model Using M&M’s
Name: ____________________
Background Information: Certain chemical elements have more than one type of atom. Different atoms of the same element are called isotopes. Isotopes of the same element have the same number of protons and electrons, but a different number of neutrons. Carbon has three main isotopes. They are carbon-12, carbon-13 and carbon-14. Carbon-14 is radioactive and it is this radioactivity which is used to measure age. Radioactive atoms decay into stable atoms by a simple mathematical process. Half of the available atoms will change in a given period of time, known as the half-life. For instance, if 1000 atoms in the year 2000 had a half-life of ten years, then in 2010 there would be 500 left. In 2020, there would be 250 left, and in 2030 there would be 125 left. By counting how many carbon-14 atoms in any object with carbon in it, we can work out how old the object is - or how long ago it died. So we only have to know two things, the half-life of carbon-14 and how many carbon-14 atoms the object had before it died. The half-life of carbon-14 is 5,730 years. However knowing how many carbon-14 atoms something had before it died can only be guessed at. The assumption is that the proportion of carbon-14 in any living organism is constant. It can be deduced then that today's readings would be the same as those many years ago. When a particular fossil was alive, it had the same amount of carbon-14 as the same living organism today. The fact that carbon-14 has a half-life of 5,730 years helps archaeologists date artifacts. Dates derived from carbon samples can be carried back to about 50,000 years. Potassium or uranium isotopes which have much longer half-lives, are used to date very ancient geological events that have to be measured in millions or billions of years. Complete these questions BEFORE you do the activity: 1. How does Carbon-12 differ from Carbon-13 or Carbon-14? 2. What is radioactive decay? 3. What is a half-life? 4. Explain how we can determine the age of a once-living thing by measuring the ratio of Carbon-14 to Carbon-12. Activity Directions: You are going to be simulating the radioactive decay of an unstable isotope. Any atom of that isotope has a 50% chance of decaying over the course one half-life (the duration of which is a constant for any given isotope; i.e. about 5700 years 14 235 for C, about 700,000,000 years for U). For this model, let’s assume that an M&M represents an atom. If the side showing the letter “m” is up, the candy represents an undecayed atom of a radioactive isotope. If the blank side is up, it represents a decayed atom (it has become another element). A half-life is a single trial (steps 2-5 below). Procedure: 1) Count out 100 plain M&M’s that have one side showing the letter “m” and the other blank. Set all 100 sample M&M’s face up and graph the result as trial 0. This represents atoms of a radioactive isotope in a volcanic rock when it first formed, or living thing at the time of death. 2) Put the 100 sample M&M’s into a cup and shake it. Please don’t let them escape. 3) Pour the contents of the cup out onto a white sheet of paper. Count the number of “undecayed” (face up) M&M’s and put those and only those) back into the cup. 4) Record the number of “undecayed” (face down) M&M’s on your group’s column of the table and graph it. The “decayed” M&M’s can be eaten at this point. You have completed a single run. 5) Shake the cup again. 6) Repeat until you have run out of “undecayed” M&M’s or when you have finished 10 runs. 7) Put your group’s data on the table on the whiteboard. Record the data from the other groups and calculate the average for each run. 8) Graph the following data, using a different color for each line: your group’s # of atoms for each run, the class average and the probable (predicted) values. 9) Do the questions on the back of this handout.
Class Data Table: Put your data on the whiteboard in the front of the classroom. You will add data from at least 6 other groups at the end of class. Run Group 1 0 1 2 3 4 5 6 7 8 9 10
Group 2
Group 3
Group 4
Group 5
Group 6
100
100
100
100
100
100
Class Total
Class Average
Probable Value 100 50 25 12.5 6.25 3.125 1.56 0.78 0.39 0.19 0.098
M & M data # of Parent-isotope Atoms Left (M-up candies)
100
80
60
40
20
0 0
1
2
3
4
5
6
7
8
9
10
# of Half-lives (Trials)
Reflection Questions: 5. Why didn’t each group get the same results? 6. What do the probable values represent? 7. Is there anything improbable about the probable values, whether as applied to M&M’s or to atoms? 8. Which line, the class average or your group’s results, most resembles those of the probable values? Why? 9. For how many half-lives do real or simulated atoms behave like probabilistic values? What are the implications for radiocarbon-dating and uranium-dating? 10. Why can’t we use Carbon-14 dating to find the age of dinosaur bones and rocks? What type of radioactive isotopes could we use to find their age?
