# Radioactive Decay and Popping Popcorn -- Understanding the Rate Law

This material is replicated on a number of sites
as part of the
SERC Pedagogic Service Project

#### Summary

In this Spreadsheets Across the Curriculum activity, students explore the exponential decay of radioactive parents through the analogy with popping popcorn. They build a spreadsheet to calculate the number of unpopped kernels of popcorn as a function of time starting with the probability that a given kernel will pop during a 10-sec interval. The module introduces the mathematics of the exponential function as a modeling function in both analytical and numerical contexts.

## Learning Goals

Students will:

- Consider a familiar occurrence of exponential decay in a quantitative way.
- Gain experience in forward modeling of an exponential decay phenomenon.
- Consider the relationship between the decay constant and the probability that a particular parent atom of a radioactive isotope will convert to its radiogenic daughter atom
- Gain experience in fitting a trendline to a column of data.

## Context for Use

This activity was designed for an upper-division math-in-geology course for geology majors but can easily be used in an introductory undergraduate geoscience class, as well as a high school pre-calculus class.

## Description and Teaching Materials

SSAC2005.QE514.CES1.1-student (PowerPoint 706kB Feb16 07)

The module is a PowerPoint presentation with embedded spreadsheets. If the embedded spreadsheets are not visible, save the PowerPoint file to disk and open it from there.

This PowerPoint file is the student version of the module. An instructor version is available by request. The instructor version includes the completed spreadsheet. Send your request to Len Vacher (vacher@usf.edu) by filling out and submitting the Instructor Module Request Form.

## Teaching Notes and Tips

The module is intended as a stand-alone resource. It can be used as a lab exercise or handwork assignment, or as the basis of an interactive classroom activity.

## Assessment

The last slide is an end-of-module assignment that can be used to examine student understanding and learning gains.

The instructor's version also includes a pretest that can be used to evaluate the effectiveness of the module.

## References and Resources

Teaching Quantitative Skills in the Geosciences
Foundations of Scientific Knowledge -- Radioactive Decay