(Activity courtesy of The Science House, North Carolina State University’s partnership to promote hands-on, inquiry based K-12 STEM education.)
Grade level: 5 -11
Time: 30 – 45 minutes
In this activity, students in grades 5 – 11 learn about radioactivity, the rate at which an isotope decays, and the concept of half-life. They will count and record the number of decayed “atoms” and graph the results.
After doing this activity, students will be able to:
- Understand the concept of half life
- Understand radioactive decay process
- Create and interpret half-life (exponential) graphs
- Understand the difference between a linear and exponential progression
National Science Education Standards [grades 5 -8]
- Energy is a property of many substances and is associated with heat, light, electricity, mechanical motion, sound, nuclei, and the nature of a chemical. Energy is transferred in many ways.
- In most chemical and nuclear reactions, energy is transferred into or out of a system. Heat, light, mechanical motion, or electricity might all be involved in such transfers.
- Electrical circuits provide a means of transferring electrical energy when heat, light, sound, and chemical changes are produced.
Common Core State Mathematics Standards
- Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. [Grade 6]
- Know and apply the properties of integer exponents to generate equivalent numerical expressions. [Grade 8]
- Distinguish between situations that can be modeled with linear functions and with exponential functions. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. [High school]
- Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). [High school.]
American Diploma Project Mathematics Benchmarks
A.A. 2b. Represent and interpret functions using graphs, tables, words, and symbols.
Some naturally occurring isotopes of elements are not stable. They slowly decompose by discarding part of the nucleus. The isotope is said to be radioactive. This nuclear decomposition is called nuclear decay. The length of time required for half of the isotope to decay is the substance’s half-life. Each radioactive isotope has its own particular half-life. However, when the amount of remaining isotope is plotted against time, the resulting curve for every radioisotope has the same general shape.
Each group needs:
- 50 pieces of plain M&M™ candy (with printing on one side)
- 1 resealable bag
- Graph paper
Prepare bags ahead of time or have students:
- Place 50 atoms of candium (pieces of candy) in a sealed bag.
- Gently shake for 10 seconds.
- Gently pour out candy and count the number of pieces with the print side up.
- Record the data: These atoms have “decayed.”
- Return only the pieces with the print side down to the bag and reseal it.
- Consume the “decayed atoms.”
- Gently shake the sealed bag for 10 seconds.
- Continue shaking, counting, and consuming until all the atoms have decayed.
- Graph the number of undecayed atoms vs. time.
Data and Observations
|Half-life||Total Time||# of Undecayed Atoms||# of Decayed Atoms|
- What is a half-life?
- In the experiment, what was the half-life of the element candium?
- At the end of two half-lives, what fraction of the atoms had not decayed?
- Describe the shape of the curve drawn in step 9.
- Repeat the experiment three more times, starting with 30 atoms, 80 atoms, and 100 atoms of candium. Compare the resulting graphs.
- Repeat the experiment using half-lives of 5 seconds, 20 seconds, and 1 minute. Compare the resulting graphs.
Answers to Extensions
- Half-life is the length of time required for one half of an isotope to decay.
- The half-life of candium in this activity was 10 seconds.
- At the end of two half-lives, 1/4 of the original sample remained and 3/4 of the sample had decayed into a new element.
- The graph is a decreasing logarithmic curve.
- The shape of the graphs will be almost the same.