26 January 2007
Simulation Write-Up: Radioactive Decay
My simulation was a model of radioactive decay using pennies. I first saw a version of
this model being used by three teachers in physical science and chemistry classes at Charlotte
High School in Charlotte, MI. Credit is therefore due to T. Jones, C. Snyder and J. Crossman for
inspiration. However, as I can recall very little of the activity that was used, I have made my
own variation of the activity.
Radioactive decay is a process that occurs on an atomic level and cannot be directly
observed in an easy fashion in a school classroom. Radioactive nuclei are unstable and will
decay until they reach a stable isotope. In this activity, students model the decay of radioactive
nuclei by placing pennies in a cup then pouring the pennies on a flat surface. Any coins that land
head down are considered to be decayed.
In order to do this activity, each group of students will need a cup and a roll of pennies;
these are the nuclei. First, students will need to mark five nuclei on the tails side with a small
piece of tape and number the pennies one through five. Next, all nuclei are placed in the cup and
shaken then poured out on a flat surface. Any nuclei that are tails up have decayed. The
students should count the number of decayed nuclei and remove them to the side of the counting
area or another cup. All the undecayed nuclei are then returned to the cup to undergo another
round. This is repeated for as many rounds is needed to get all the nuclei to decay. For each
round, students should record the initial number of nuclei in the cup, the number of nuclei that
decay, and if any of the numbered nuclei decay. Students should repeat the exercise at least once
more to get enough data.
The data may be pooled and plotted or analyzed by the entire class. Depending on the
math level of the class, simply plotting the data and showing the trend of exponential decay by
making a best fit line may be the extent of data analysis. For classes with more math knowledge,
the students may be asked to calculate the rate of decay and the half-life of the nuclei using
exponential functions (usually found in the text). The class should also analyze the data to see if
there was any pattern in the order in which the numbered nuclei decayed. This is to illustrate
that you cannot predict when a specific nucleus will decay.
This simulation is beneficial because it shows the general trend of exponential decay and
gives a set of data which model the behavior of radioactive nuclei when they decay. It allows
students to see the exponential decay pattern associated with radioactive decay and calculate the
rate of decay and the half life. It also models the uncertainty of when a specific nucleus will
decay and the fact that all nuclei have the same odds of decaying in each round. Whether or not
a coin ends heads up or not is independent of any other coin. Finally, it also models the fact that
to find the rate of decay or half-life of a material, many nuclei are needed. It is highly unlikely
that the pattern of exponential decay will be seen in one run of the simulation. The pooled class
data is more likely to give the desired trend.
This simulation falls short with the dependence on the math skills of a student. Lower
level students could have a hard time with the math needed to analyze the data. Also, such a
huge set of data could present issues when trying to plot or calculate. I suggest using a program
such as Microsoft Excel to help deal with the data. Also, this simulation is more to see the
mathematical relationship involved in decay and does not explain the decay process. The teacher
would need to cover this in addition to doing the activity.