# M&M Model for Radioactive Decay

## Summary

A tasty in-class demonstration of radioactive decay using two colors of M&M's. Illustrates the quantitative concepts of probability and exponential decay. This activity is appropriate for small classes (<40 students).

Used this activity? Share your experiences and modifications

## Learning Goals

• to illustrate the exponential nature of radioactive decay
• to demonstrate the concept of half-life
• to illustrate probability and how abundance of radioctive elements actually determines rate of decay.

## Context for Use

This is a fun and tasty way to illustrate radioactive decay and the important mathematical concepts that go along with decay. It is best used in-class or in a lab after the concepts of half-life and decay have been introduced. Depending on how many times it gets passed around the class, this can take 15-30 minutes. Required equipment includes: a known quantity of two colors of M&M's or other colored candy (50 of each is probably enough) plus extra of the "radiogenic" isotope, a jar and some graph paper.

This particular activity works best for small classes. Several alternate ideas for large classes or small group work are linked in References and Resources near the bottom of this page.

## Description and Teaching Materials

With a small class, pass around a jar of M&M's with a known quantity of two colors (e.g., red and green holiday M&M's) in it. Have each student reach in (blindly) and take an M&M. If the M&M is red (radioactive), it has decayed, keep it out of the jar and replace it with a green (radiogenic) candy; if it is green, it goes back into the jar. As the jar gets passed around the room, the number of red M&M's gets smaller and the green get more abundant. Therefore, it gets harder and harder to pick a red one. This simulates radioactive decay well and helps students to understand why the number of decaying isotopes gets smaller as the number of radioactive isotopes gets smaller.

You can graph this "experiment" if you know how many of each color you started with and how many red M&M's have been removed. After a certain number of "decays", stop and count how many reds are left. Continue through another sequence of "picks" and plot reds again. Repeat this procedure a few more times. See if the students can figure out how long a "half-life" is for this problem based on the graph you generated.

## Teaching Notes and Tips

This is a relatively easy and fun demonstration for a smaller class. So that you (and the students) can keep count of the number of "decayed" M&M's, tell the students not to eat the decayed atoms right away. When the experiment is finished they may eat their radioactive atoms. Make sure that others who haven't picked radioactive atoms get some of the radiogenic isotopes to eat.

There are several variations of this experiment: One is to start with all radioactive elements -- simulating something like a zircon (which excludes the radiogenic Pb) and show them how that works. This is a simpler system and may be easier for them to comprehend. Using some "initial radiogenic isotopes" can be useful, though. It is a good introduction to using isotopes as tracers (e.g., initial Sr ratio). Make sure that the students understand that if a mineral that includes the radiogenic isotope is used, the initial number of radiogenic isotopes must be calculated in order to calculate age.

The References and Resources section of this page has other adaptations of this to include individual or small group activities with M&M's.

## Assessment

Mostly, this exercise needs a quick check of whether the concepts of half-life, probability, dependence on quantity and exponential functions were understood. There are several ways that this can be done:
• If you have a student response system, a quick quiz with questions that cover these four concepts is an easy way to determine the students' understanding.
• Having students work through a short problem (in groups or on their own) that applies these concepts in a geologic context -- a problem where they have to read a graph or calculate how many isotopes are left after x half-lives -- can also provide a quick check.
• A short written quiz might also be a way to assess comprehension.
• One of the best ways that i can think of to test comprehension with this exercise is to have the students figure out the "half-life" of this system (i.e., How many "picks" constitutes a half-life?). If they understand the concepts, they should be able to figure this out.

## References and Resources

Science NetLinks has a very nice lesson plan for a similar activity entitled Radioactive Decay: A Sweet Simulation of a Half-Life

Science House has a template for Radioactive Decay of Candium

Teachers Experiencing Antarctica and the Arctic has an activity entitled The Dating Game that actually has the students apply what they are learning to a real problem.