Introduction

The discovery of radioactivity allowed scientists to develop new methods of determining Earth's age, with astonishing results. Our planet is far older than people had thought! Students can understand the mechanism of radioactive half-life and how it helps determine age by experimenting with pennies, dice, and sugar cubes to simulate the radioactive decay of different isotopes.

A radioactive isotope's nucleus is unstable and spontaneously decays, giving off radiation and changing into a different isotope. The rate at which nuclei decay is constant. Half-life describes the interval of time during which half of the original atoms decay.

Materials for each group:
• shoe box with lid
• 80 pennies, 80 dice, or 80 sugar cubes
• 80 paper clips
• graph paper
• marker

1. Give each group a shoe box and one set (80) of either pennies, dice, or sugar cubes. Explain that the pennies, dice, and sugar cubes represent atoms of different radioactive isotopes. The boxes symbolize rocks containing those isotopes. Each team's mission is to determine the half-life of their isotope. Make sure at least one group is assigned to each of the materials. Sugar cubes should all be marked on one surface with the marker.
2. Share with students the following steps for simulating decay of their isotope. (You may want to model the procedure once.) Have students create a chart similar to the one below.
   
   
   
   • Cover box and turn over twice.
   • Remove all radioactive atoms that have decayed. These are represented by pennies that show heads, sugar cubes with the marked side face up, or dice showing a 1 or 2. Record number on chart.
   • Replace "decayed atoms" with paper clips to represent stable daughter atoms which the radioactive atoms have changed into.
   • Record number of pennies, sugar cubes, or dice (the undecayed atoms) that remain.
   • Repeat the steps until all pennies, sugar cubes, or dice have been replaced with paper clips.
   
   
3. Have teams use their charts to find their isotope's half-life. A half-life is a measure of the average lifetime of a radioactive substance, and specifies the time it takes for one-half of the original atoms to decay. Here, time is represented by trials. How many trials does it take for half of the original 80 atoms to decay (be replaced by paper-clip daughter atoms)? After half (or 40) of the atoms are replaced, how many trials does it take for half of the remaining atoms to decay? Students should record these numbers and continue finding the number of trials it takes to remove half the atoms, until all have decayed.
   
   
4. Students should average the numbers of trials determined in step 3. Half-lives of actual isotopes are constant lengths of time. In this model, the number of trials per half-life might vary.
   
   
5. Determine a theoretical age for the shoe-box specimen: If each trial represents 1,000 years, what is the isotope's half-life in years?
   
   
6. Students can graph their data to illustrate their isotope's rate of decay. Plot the number of trials (years) on the horizontal axis and the number of undecayed atoms on the vertical axis. Compare and discuss graphs for different isotopes. How are the curves similar and different? What do the curves suggest about the rate of radioactive decay in general?
   
   

1. Groups can challenge each other to determine the "age" of a box containing their isotope, based on the half-life they established. First, each group should assign the number of years a trial represents (such as 1 trial equals 1,000 years) and choose an age for the "rock" the box represents.
   
   
2. Have students fill the box with the appropriate number of radioactive atoms and stable daughter atoms to represent the age of their rock.
   
   
3. Have groups exchange boxes and half-life information. Ask each team to calculate the age by comparing the ratio of the original radioactive atoms to daughter atoms.
   
   

For results for this activity, click here.
Earth and Life Sciences Program Contents

The Long View
Seeing and Believing
DNA "Fingerprinting"