Half Life Model

David N. Steer (steer@uakron.edu)and Kyle Gray (krg10@uakron.edu), University of Akron
This material is based upon work supported by the National Science Foundation under Grant No. GEO-0506518.


While working in groups to facilitate peer tutoring, students manipulate a hands-on, physical model to better comprehend the nature of half life. Students use the model to simulate the decay of radionuclides. The resulting data are graphed and used to calculate ages in several hypothetical scenarios.

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Learning Goals

Students will understand
  • The definition of a half life.
  • That the number of decaying atoms changes with each half life but the percentage of decaying atoms remains constant.
  • The random nature of radioactive decay.
  • How to use half-life data to calculate the age of a given material.
  • The age limits of using various radioisotopes.

Context for Use

This model works well with groups of two to four students. The time required to complete this activity may be longer than desired for a large, undergraduate lecture class, but is well suited for an undergraduate laboratory class or secondary science class.

Description and Teaching Materials

Each student model consists of the following materials:
Half Life Model
  • 50 small washers (per group)
  • Gold spray paint
  • One small ziplock bag
  • One plastic "shoebox" container with a lid
  • One red pencil
  • One blue pencil
  • Student handout

During a lecture, have the student groups place the washers into the box silver side up. (The silver side represents the parent and the gold side represents the daughter product.) Students record the number of silver washers (50 parent isotopes) in the box. After closing the lid, students shake the box five times, open the box and count the number of silver washers. After recording the number of silver washers in the box as well as the cumulative number of gold washers, the students remove the gold washers, replace the lid, and shake the box again. This process is repeated until zero silver washers in the box.

Students use the data collected and the colored pencils to graph the number of silver and gold washers for each trial and label each curve as the parent or daughter. They also answer an assessment question (See handout (Microsoft Word 40kB Aug19 08)).

After debriefing the exercise, draw a graph using the average number from each trial. This curve will be very close to the theoretical value. (After our first semester of using this model, we used data from a previous class to calculate the average values for each trial.) Explain how any one group might have results that are different from the theoretical value, but when the data from the entire class are averaged together, the results match the expected values. This can lead into a discussion on the randomness of radioactive decay.

Teaching Notes and Tips

Some groups may experience the following problems:
  • They might shake their boxes an insufficient number of times. Encourage them to shake the boxes the same number for each trial.
  • Near the end, some groups may become frustrated when their final washer refuses to land gold side up. Encourage them that this is normal and to keep repeating the process until they succeed.
  • Some groups may loose a large percentage of washers in one trial. Explain to them that this is a normal consequence of the random nature of such events.


Several different assessment techniques can be used depending on time and the needs of your class.
  • If you have a personal response system, you can ask ConcepTest questions that focus on the definition or use of half life. (See References and Resources for sample ConcepTest questions)
  • By walking around the class, the instructor can observe how well the groups comprehend the underlying concepts and ask individual students to explain their conceptual understanding
  • Students could complete a worksheet containing questions about using half life
  • Students could write a 'minute paper' explaining half life or how to use half life to calculate the age of a rock

References and Resources

Worksheet (Microsoft Word 40kB Aug19 08) used with this model
Archived ConcepTest questions used with this model: Other Half-Life Activities: