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Using Dice to Explore Radioactive Decay (9 Favorites)

ACTIVITY in Half Lives, Radioactive Isotopes. Last updated May 10, 2019.


Summary

In this activity, students will use dice to simulate the radioactive “decay” of samples of two different elements with two different half-lives. At the end of the simulation, all the groups will pool their data (by round) and then the class results will be graphed. The graphs will be analyzed to illustrate the process of radioactive decay and to determine the half-life of each element in the fictitious time units of “rounds”.

Grade Level

High School

NGSS Alignment

This activity will help prepare your students to meet the performance expectations in the following standards:

  • HS-PS1-8: Develop models to illustrate the changes in the composition of the nucleus of the atom and the energy released during the processes of fission, fusion, and radioactive decay.
  • Scientific and Engineering Practices:
    • Developing and Using Models
    • Analyzing and Interpreting Data

Objectives

By the end of this activity, students should be able to

  • Define the term “half-life”.
  • Understand that different radioactive atoms decay at different rates.
  • Understand that radioactive atoms decay into other atoms.
  • Describe the non-linear nature of a graph of radioactive decay.
  • Use a decay graph to determine the half-life of an element.

Chemistry Topics

This activity supports students’ understanding of

  • Radioactive isotopes
  • Radioactive decay
  • Half-lives

Time

Teacher Preparation: 5-10 minutes

Lesson: 80 minutes

Materials (per group)

  • One 6-sided die
  • Two recording charts (template provided)
  • One green pencil or pen
  • One red pencil or pen
  • Materials to create hand-drawn graphs (graphing paper etc.) or access to computer graphing program (NOTE: each student will be generating two graphs)

Safety

  • No specific safety precautions need to be observed for this activity.

Teacher Notes

  • Supplemental files included from download are:
    • Template for group color-coded data recording
    • Sample class data set including completed color-coded recording sheets, and samples of each type of graphs
    • Answer key for the post-activity analysis questions
  • Prior to this activity, students should have been exposed to the concept of radioactivity and radioactive decay.
  • Prior to starting the activity the teacher should remind students that while in this simulation the radioactive “atoms” decay directly into non-radioactive “atoms”, often this is not the case with real atoms. They often decay into radioactive atoms, which in turn can undergo further decay.
  • Prior to starting the activity, the teacher should review how to use the color-coded recording chart to keep track of which “atoms” remain radioactive and which have “decayed” and are non-radioactive for each round. Particular emphasis should be made to remind students that once an atom “decays” and is recorded as red, it should be skipped for all subsequent dice-rolling rounds. (See sample data record sheet)
  • For the first element sample, an atom will “decay” to a non-radioactive element if a 6 is rolled. As noted above, a color-coded chart will be used to keep track of which atoms decay into non-radioactive elements (red) and which stay radioactive (green). Atoms that do not decay on the first “round” will be tested again during a second “round” and the process will be repeated for eight rounds. For the second element, everything will be kept the same, but an atom will “decay” each round if either a 5 or a 6 is rolled.
  • Groups should be between 2-4 students and can be determined depending on what is appropriate for the size of the class and the space available. However, it is important that the total number of “atoms” tested by the class be 100 or more. Since each group tests 20 “atoms” of each element, there should be a minimum of five groups.
  • Class data will be captured in a class spreadsheet and students will use class data in their graphs. The class spreadsheet can be generated on a whiteboard/blackboard/smart board or as a shared electronic document (Google sheet, Excel etc.) depending on the preferences of the teacher.
  • After rolling the dice and filling out a color-coded recording chart for the “atoms” of each element, students will generate two graphs: one is a stacked bar graph for the number of radioactive and non-radioactive atoms present vs. rounds completed and the other is a line graph of the number of radioactive atoms of each element remaining vs. time (in rounds). Students should have familiarity with generating these types of graphs or the teacher will need to review this prior to the graphing portion of the activity. The graphs may be generated by hand or using a computer depending on the preferences of the teacher. Sample graphs are included as supplemental files.
  • The student portion for this activity is estimated at 80 minutes; however that can be reduced if the graphing portion is completed outside of class.
  • For lower level classes, it may be beneficial to have the total number of “atoms” of each element tested by the class be 100 so it is easier for students to identify when half of the “atoms” have “decayed”. (See sample graphs)

For the Student

Lesson

Background

Radioactive materials have a host of important uses in our lives including how we diagnose and treat various diseases, how we generate electricity and even how we monitor the presence of fire in our homes. The purpose of this activity is to model the radioactive decay of unstable, radioactive atoms.

Pre-lab Questions

Research two specific uses of radioactivity and describe each use below. Your description should include the specific radioactive atom or atoms involved as well as and details about how the radioactive decay is utilized to accomplish each task.

Use #1:

Use #2:

Objective

We are going use dice to model radioactive decay. The questions we are examining during this simulation include:

  • What happens to radioactive atoms when they decay?
  • How do scientists describe the rate of radioactive decay?

Procedure

  1. You will need a data recording sheet, die, one green pencil and one red colored pencil.
  2. Your group’s task is to simulate radioactive decay of 20 imaginary “atoms” of element #1 by following the steps listed below:
    Round One:
    1. You will roll the die twenty times (once for each atom)
    2. If you roll a “6” that atom has decayed into a non-radioactive atom* and you will color the box on the data recording sheet for that atom red.
    3. If you roll anything else, that atom has not decayed and you will color the box on the data recording sheet for that atom green.

Round Two thru Eight:
REPEAT steps 2 a, b, c FOR ONLY THOSE ATOMS THAT WERE GREEN IN PRECEEDING ROUND (still radioactive)

  1. Next you will repeat the process (steps 2 a, b, c) for 20 atoms of element #2 using a second (new) data recording sheet. This time you will mark the box for the atom red if you roll EITHER a “5” or a “6”.
  2. Enter your group’s data in the appropriate place in the shared class data table.

*NOTE: In our simulation for the sake of simplicity, once an atom decays, it is no longer radioactive. In reality, radioactive elements will often decay into other radioactive elements, which can undergo further decay.

Analysis

Part I: Graphing Our Data

  1. Each student should make stacked column graph of the class data illustrating the number of “radioactive” atoms remaining (still green) and the number of “decayed” atoms (turned red) for element #1 at the end of each round.

The graph should have the following characteristics:

  • X-axis: Independent variable: Rounds
  • Y-axis: Dependent variable: Number of atoms (“radioactive” or “decayed”)
  • Be sure to include a key, descriptive title, & label your axes
  1. Each student will also make a line graph of the class data for the number of “radioactive” atoms (still green) at the end of each round for BOTH element #1 and element #2.

Your graph should have the following characteristics:

  • X-axis: Independent variable: time (rounds)
  • Y-axis: Dependent variable: # of “radioactive” atoms remaining (still green)
  • Both data sets plotted on one graph
  • Each data set with points connected in a smooth curve
  • Be sure to include a key, descriptive title, & labeled axes

Part II: Analyzing Our Graphs

  1. Melanie thinks that when radioactive isotopes “decay” it means the atom disappears into nothing releasing radioactivity. Melanie’s idea is not completely correct. Explain using specific data we collected today to support your response.
  2. Scientists often measure the rate of decay of radioactive elements in terms of “half-life” or the amount of time required for half of a radioactive sample to decay. Using your line graph, determine the half-life for each element in today’s simulation.
    NOTE: Your unit of time will be “rounds”.
    1. Half-life of element #1:
    2. Half-life of element #2:
  3. After one half-life, ½ of the sample has decayed so ½ is still radioactive. After a second half-life, ½ of the remaining material (½ of the original) has decayed leaving ¼ of the original (½ of ½) still radioactive. At the end of three half-lives, what fraction of a radioactive isotope would you expect to still be “radioactive” (1/2, 1/4, 1/8, etc.)? What about five half-lives?
    1. Based on the class data half-life you calculated above, how many rounds would it take until 1/8 of the original element #1 sample was still radioactive? HINT: how many half-lives must have occurred?
    2. Based on the class data half-life you calculated above, how many rounds would it take until 1/8 of the original element #2 sample was still radioactive? HINT: how many half-lives must have occurred?
  4. Consider the following statement:
    The longer the half-life, the faster the rate of radioactive decay.
    1. Is this statement true or false?
    2. Explain using specific data we collected today to support your choice
  5. Consider the following statement:
    The rate of radioactive decay is always the same, constant value for all radioactive isotopes no matter what element they are.
    1. Is this statement true or false?
    2. Explain using specific data we collected today to support your choice.

Conclusion

Based on what you learned today, answer the following questions:

  • What happens to radioactive atoms when they decay? (Be specific, but be careful not to overgeneralize)
  • How do scientists describe the rate of radioactive decay? Is it linear?