Description:With the Half-Life Laboratory, students gain a better understanding of radioactive dating and half-lives. Students are able to visualize and model what is meant by the half-life of a reaction. By extension, this experiment is a useful analogy to radioactive decay and carbon dating. Students use M&M’s (or pennies and puzzle pieces) to demonstrate the idea of radioactive decay. This experiment is best used by student working in pairs.

**Grade Level:**

5-12 grade

**Disciplinary Core Ideas (DCI)**

3-5ETS1-2, MS-ESS1-4, HS-ESS1-6

**Time for Teacher Preparation**

40-60 minutes – To gather materials

**Activity Time:**

40-60 minutes (1 Class Period)

**Materials:**

- Bag of: M&M’s ®, pennies or, puzzle pieces
- Paper – 8.5˝ x 11˝
- Graph Paper
- Zip-Lock Bags
- Pen, Marker, or Pencil
- Student Data Collection Sheets

**Safety**

- Students should not eat M&M’s®, Pennies, or Puzzle Pieces

**Science and Engineering Practices**

- Ask questions and define problems
- Use models
- Analyze and interpret data
- Use mathematics and computational thinking
- Construct explanations
- Argue from evidence
- Obtain, evaluate and communicate information

**Cross Cutting Concepts**

- Patterns
- Cause and Effect
- Scale, Proportion, and Quantity
- Systems and System Models
- Energy and Matter: Flows, Cycles, and Conservation

**Objectives**

Students try to model radioactive decay by using the scientific thought process of creating a hypothesis, then testing it through inference. It is a great introduction to the scientific process of deducing, forming scientific theories, and communicating with

peers. It is also useful in the mathematics classroom by the process of graphing the data.

Students should begin to see the pattern that each time they “take a half-life,” about half of the surrogate radioactive material becomes stable. Students then should be able to see the connection between the M&M’s and Puzzle Pieces and radioactive elements in archaeological samples. Seeing this connection will help students to understand how scientists can determine the age of a sample by looking at the amount of radioactive material in the sample.

- To define the terms half-life and radioactive decay
- To model the rate of radioactive decay
- To create line graphs from collected data
- To compare data
- To understand how radioactive decay is used to date archaeological artifacts

**Background**

** Half-Life**If two nuclei have different masses, but the same atomic number, those nuclei are considered to be isotopes. Isotopes have the same chemical properties, but different physical properties. An example of isotopes is carbon, which has three main isotopes, carbon-12, carbon-13 and carbon-14. All three isotopes have the same atomic number of 6, but have different numbers of neutrons. Carbon-14 has 2 more neutrons than carbon-12 and 1 more than carbon-13, both of which are stable. Carbon-14 is radioactive and undergoes radioactive decay.

Radioactive materials contain some nuclei that are stable and other nuclei that are unstable. Not all of the atoms of a radioactive isotope (radioisotope) decay at the same time. Rather, the atoms decay at a rate that is characteristic to the isotope. The rate of decay is a fixed rate called a half-life.

The half-life of a radioactive isotope refers to the amount of time required for half of a quantity of a radioactive isotope to decay. Carbon-14 has a half-life of 5730 years, which means that if you take one gram of carbon-14, half of it will decay in 5730 years. Different isotopes have different half-lives.

The ratio of the amounts of carbon-12 to carbon-14 in a human is the same as in every other living thing. After death, the carbon-14 decays and is not replaced. The carbon-14 decays, with its half-life of 5,730 years, while the amount of carbon-12 remains constant in the sample. By looking at the ratio of carbon-12 to carbon-14 in the sample and comparing it to the ratio in a living organism, it is possible to determine the age of a formerly living thing. Radiocarbon dates do not tell archaeologists exactly how old an artifact is, but they can date the sample within a few hundred years of the age.

**M&M’s® (or Pennies or Puzzle Pieces)**

- Give each student 10 M&M’s® candies of any color and a zip lock bag. All of M&M’s® candies are considered radioactive.
- Have the student put the M&M’s® into the zip lock bag and shake the bag. Have the students spill out the candies onto a flat surface.
- Instruct the students to pick up ONLY the candies with the “m” showing – these are still radioactive. The students should count the “m” candies as they return them to the bag.
- Have the students record the number of candies they returned to the bag under the next Trial.
- The students should move the candies that are blank on the top to the side – these have now decayed to a stable state.
- The students should repeat steps 2 through 5 until all the candies have decayed or until they have completed Trial 7.
- Set up a place on the board where all students or groups can record their data.
- The students will record the results for 9 other groups in their data tables and total all the Trials for the 100 candies

**NGSS Guided Inquiry**

Explain about radiation and half-lives of isotopes. Tell students to design their own experiment, using paper, M&M’s®, Pennies, other 2 sided material or Licorice as a radioactive material undergoing decay to discover the nature of the half-life of that material.

You might suggest that the students experiment with their graphing results to see if trends begin to form.

**M&M’s® (or pennies or puzzle pieces)**

- Put 10 M&M’s® candies of any color into a zip lock bag. Each group is starting with 10 M&M’s® candies, which is recorded as Trial 0 in the data table. All of the M&M’s® candies are considered to be radioactive at the beginning.
- Shake the bag and spill out the candies onto a flat surface.
- Pick up ONLY the candies with the “m” showing – these are still radioactive. Count the “m” candies as you return them to the bag.
- Record the number of candies you returned to the bag under the next Trial.
- Move the candies that are blank on the top to the side – these have now decayed to a stable state.
- Repeat steps 2 through 5 until all the candies have decayed or until you have completed Trial 7.
- Record the results for 9 other groups and total all the Trials for the 100 candies.

**Data Collection**

Student Data Collection Sheets

**Post Discussion/Effective Teaching Strategies**

Questions provided on the Student Data Collection Sheets

**Questions**

*M&M’s® (or Pennies or Puzzle Pieces)*

- Define the term half-life.
- What does it mean when we say an atom has “decayed”?
- Do the number of atoms you start with affect the outcome? Explain.
- Did each group get the same results?
- Did any group still have candies remaining after Trial 7?
- Why do the totals for the 10 groups better show what happens during half-life rather than any other group’s results?
- What happens to the total number of candies with each trial (half-life)?
- Plot the total results on a graph with number of candies on the vertical axis and trial number on the horizontal axis. Is the result a straight or a curved line? What does the line indicate about the nature of decay of radionuclides?
- How do scientists use radioactive decay to date fossils and artifacts?

**Assessment Ideas**

- Question the student about how this experiment is similar to Carbon Dating.

**Differentiated Learning/Enrichment**

- Have the students calculate the age of objects when given the half-life, original amount, and current amount of that material.

**Enrichment Question**

- The population of the earth is doubling every 40 years. If the population of the earth is now 7 billion people, how many people will be here when you are 95 years old?