The Great M&M Experiment

Teaching about radioactive decay and geochronology has its challenges. I think it is important to include in introductory courses, and I’ve tried a variety of exercises and techniques to try to convey some of the more important aspects. My goals are simple really, I want the students to understand the basics of how the systems work and why they are reliable. My favorite exercise to help me teach about decay, is without a doubt, the Great M&M Experiment.

Let’s start by discussing some of the things that can confuse students, particularly the odd fact that on the scale of an individual atom, radioactive decay is unpredictable, but on the scale of billions of atoms, it behaves literally, like a finely tuned clock. This is actually a very familiar concept to them, they just might not realize it. It is the same concept, for example, that explains why Las Vegas exists, and why the house always wins. We typically bombard them with concepts like “half-life,” which are often intended to simplify things, but in my experience rarely do. Many students think that the concept of a half-life is goofy, and is something that has been imposed upon a decay system.

I’ve started taking a different approach, one that tries to explain the basic concept using something they all understand and then transitions to the complex systems geoscientists deal with.

I call it the Great M&M experiment, but you can also do it flipping coins or anything else. M&M’s are delicious, and only have an “M” printed on one side. So it you take a Dixie cup full of them and turn it over on a lab bench, about half of them will land with the “M” up, and about half will land with the “M” down. This isn’t news, but it turns out that if you have enough M&M’s, you can easily create a decay curve. Here’s how I do it.

1. Give everyone some number of M&M’s. With small classes I’ll do 30, with large classes maybe 10. With really large classes I use a variation that uses pennies, I’ll explain that later**.

2. Have them turn the cup over onto a desk or bench, making sure not to dump candy on the floor. I usually have them put down paper to they can eat things when they are done.

3. If an M&M lands with the “M” side up, we say it has decayed, and we remove it to a second Dixie cup.

4. Count the number of candies that didn’t decay and record that number.

5. Place the candies that didn’t decay back into the tossing cup, and repeat steps 2-4 until all of the candies have decayed.

6. Compile the numbers up front, counting the number, or percent, of the total candies left undecayed after each step. What you’ll end up with is something like this.

 

 

Results from a 2003 M&M experiment

These are the results from the largest experiment I ever ran, where 40 students each had 100 M&M’s. I show both the results for each step (average and standard deviation), and the “theoretical” relationship. When I used this many candies, I wasn’t surprised at how well it worked, however since this run I’ve started using fewer and fewer total candies. A total of 40 even works well, kind of amazing.

OK, so that is great. But what is important I think is to demonstrate where the exponential decay curve comes from. It isn’t magical or made up, but is the natural result in a system that is governed by probability. You can then discuss what these curves would look like if instead of a 50% chance of decay, you used dice, or something with 10 sides. Compare the M&M curve to these

Please forgive the terrible color scheme, I made this before I became the Excel ninja that I am today.

These are still exponential decay curves, they just take longer to “flatten out.” A six-sided die (yellow), where we say it decays when we roll 1 for example, takes a bit longer. Nerd dice with 12 or 20 sides would take even longer.

Half-life, and the decay constant, are really just ways of describing the shape of the curve, how quickly the number of parents declines. You can show how the amount of time (or flips) required to cut the number of M&M’s in half is constant, for example. A curve for ²³⁸U would look about the same, just instead of the number of rolls, we’d be looking at time, and it would take 4.5 billion years to lose half of them. In fact, you can think of ²³⁸U as a die with bajillions of sides. Something like this

So the terms we use are really just ways to describe the curves, and the curves are just the natural result of any process governed by probability. From this, transitioning to a decay and accumulation curve, and then to the parent to daughter ratio of a system (what we actually measure), isn’t that dramatic of a leap.

to

I’m not saying this is magic, and that everyone will get it immediately. I’ve just found that terms like “half-life” and “decay constant” are big stumbling blocks for students. Showing them the origin and meaning of those terms really isn’t difficult, and can be easily tied to ideas they already understand.

** In really large classes, I’ll hand out 1 penny to each student, and have them all stand up. They flip the coin, and if they flip heads they sit down. Sure I have to count the whole class, but that gets easier each flip, and with even 100 students, generates a great decay curve like clockwork.