### Purpose

To demonstrate that the rates of decay of unstable nuclei can be measured, that the exact time that a certain nucleus will decay cannot be predicted, and that it takes a very large number of nuclei to find the rate of decay.

### Context

This is the second lesson in a three-lesson series about isotopes, radioactive decay, and the nucleus. The first lesson, Isotopes of Pennies, introduces the idea of isotopes. The final lesson, Frosty the Snowman Meets His Demise: An Analogy to Carbon Dating, is based on gathering evidence in the present and extrapolating it to the past.

To do this lesson and understand half-life and rates of radioactive decay, students should understand ratios and the multiplication of fractions, and be somewhat comfortable with probability. Games with manipulative or computer simulations should help them in getting the idea of how a constant proportional rate of decay is consistent with declining measures that only gradually approach zero. The mathematics of inferring backwards from measurements to age is not appropriate for most students. They need only know that such calculations are possible. (*Benchmarks for Science Literacy*, p. 79.)

In this lesson, students will be asked to simulate radioactive decay by pouring small candies, such as plain M&M's® or Skittles®, from a cup and counting which candies fall with their manufacturer's mark down or up. The exercise they will go through of predicting and successively counting the number of remaining "mark-side up" candies should help them understand that rates of decay of unstable nuclei can be measured; that the exact time that a certain nucleus will decay cannot be predicted; and that it takes a very large number of nuclei to find the rate of decay.

This lesson can be done in two, 45-minute class periods. It may be combined with the Frosty the Snowman Meets His Demise: An Analogy to Carbon Dating, which can be done while students are flipping their candies. In your planning, be sure to include time at the end of the lesson for students to post their data and share the class data.

### Planning Ahead

Before the lesson, you will have to weigh out about 80 candies for each group of students. If you count ten and weigh them, then multiply by 8, you will know how many grams of candy to weigh out for each group.

### Motivation

To help students understand the history of radioactivity, have them go to Radioactivity: Historical Figures, on the Access Excellence Classic Collection site, to read about the contributions of Wilhelm Roentgen, Antoine Becquerel, Marie and Pierre Curie, and Ernest Rutherford.

As students read about these scientists, ask them to think about the following questions:

- What important discovery was made by Wilhelm Roentgen?
- What material did Antoine Becquerel work with in his own investigations of X rays?
- What did Becquerel discover through his experiments?
- What two elements were discovered by Marie and Pierre Curie?
- Why is Ernest Rutherford considered the father of nuclear physics? List Rutherford's major achievements.

Students can supplement this site with a visit to Isotopes Project. Have them go directly to the Nuclear Structure Systematics Home Page. Once to that page, students should then go to the Isotope Discovery History, a graph of the number of known isotopes versus the date, and to the Chart of Aristotle and Plato (found at the bottom of the page), which the site planners cleverly call "the first chart" of isotopes.

### Development

Tell students: *"Today we will simulate radioactive decay to understand what we mean by half-life. Radioactive decay, also known as radioactivity, is the spontaneous emission of radiation from the unstable nucleus of an atom." *

Ask students:

- In your own words, what do we mean by nuclear decay?
- What do you think is emitted during radioactive decay?

Have students go to the Isotopes Project website to look for more information about radioactive decay. Have students look at the Glossary of Nuclear Science Terms for alpha and beta decay. Ask students to explain the terms in their own words.

Tell students: *"Radioactive decay is a random process, like flipping a coin or other object that has its sides marked differently." *

Ask students:

- What is the chance of getting heads on any flip?
- What do we mean by random?

After students have discussed these questions, tell them:

*"We measure our rate of speed in a car in miles per hour. This method of measuring a rate won't work for radioactive decay. We know that radioactive substances disintegrate at a known rate, however. We call this rate the isotope's half-life. It is the length of time required for the disintegration of one-half of a given number of nuclei of a radioactive element. Let's begin with a small number. Suppose we have 100 nuclei of a radioactive isotope. After one half-life, half of the nuclei will have disintegrated, leaving 50 nuclei." *

Ask students:

- How many nuclei will be left after the second half-life?
- How many would you predict will be left after the third half-life?

Have students write their answers to these questions in their science journals. At the end of the lab, give them the opportunity to revisit these questions and change or justify their answers.

Procedure:

Give each student a copy of the laboratory procedure called Radioactive Decay: A Sweet Simulation of Half-life. You may group them in any size, but working in pairs is optimal for this exercise. Weigh out 80 candies for each group into cups before students arrive, as described in the Planning Ahead section above. Students should complete the Analysis section of the lab sheet, which will be used as part of their assessment.

Advise students to read through the simulation first so that they understand what they should do.

After students have completed the activity, discuss the answers to the analysis questions with the whole class. Also, return to the questions you asked in the introduction to the lesson and allow students to revise their answers. If they haven't changed their answers, ask them to explain why.

### Assessment

In addition to using answers to students' analysis questions and their graphs for assessment, consider having them respond to the following in their science journals or as a homework assignment:

Strontium is chemically similar to calcium. If you lived in a city where there had been a nuclear accident, you and your family might be exposed to strontium-90, which is the principal health hazard in radioactive fallout because it can easily get into the water supply or milk and then be ingested by people. Write about how the strontium-90 might accumulate in your body (teeth and bones) and how it might affect you. Include your ideas about how its half-life of 28.8 years would be important. Suggest ways that government agencies, such as your state's department of health, might test for strontium-90. Where in your environment might scientists look for large concentrations of strontium?

### Extensions

The IAEA News Center is the public information and news service of the International Atomic Energy Agency on the Internet. Links to all IAEA online services can be found here. Visit this site for more information about strontium-90 and about the nuclear accident in Chernobyl in 1986 and its aftermath.

The Photograhic Periodic Table of the Elements can be used to find all the known isotopes of all the elements, their decay modes, and half-lives.