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### Summary

In this lab, students visualize the random nature of atomic decay (or first order chemical reactions). It helps them answer the inevitable question of what happens when a decaying material reaches a single particle of the species. It also helps them realize the important difference between macroscale and microscale phenomena.

### Grade Level

Middle School, High School

### NGSS Alignment

This lab will help prepare your students to meet the following scientific and engineering practices:

**Scientific and Engineering Practices:**- Developing and Using Models

### Objectives

By the end of this lesson, students should be able to:

- Explain the rate of nuclear decay using the half-life of a radioactive element.
- Perform half-life calculations.

### Chemistry Topics

This lesson supports students’ understanding of:

- Half-lives

### Time

**Teacher Preparation**: 10 minutes

**Lesson**: 20–30 minutes

### Materials

For each group:

- A bag of 20 pennies

### Safety

- Have students wash their hands after handling pennies.

### Teacher Notes

- This activity will be most effective if students have already been introduced to the concepts of radioactive isotopes and radioactive decay. You might use this activity to introduce half-life or after you have already discussed it in class.
- If you don’t have time to make bags of 20 pennies apiece, you could have a bunch of pennies and have students count out their own sample.
- Candy with a symbol could also be substituted for pennies (M&M’s for example).

### For the Student

### Lesson

### Background

Radioactive elements decay by several methods so their nuclei can give off energy to become more stable. The rate of this decay is called the half-life. The half-life is defined as the amount of time it takes for half of the atoms in a sample of an element to decay into another element. The half-life is not an exact measurement because it is impossible to tell exactly when each atom decays, so it’s what happens on average. This experiment will show you how decay really happens.

When you flip a penny, there is a 50% chance that it will turn up “heads,” and a 50% chance that it will turn up “tails.” If you assume a penny that lands tails side up results in nuclear decay, then one flip of all of the coins should be the equivalent of one half-life. This experiment will familiarize you with how nuclear decay really occurs, and it will help you become more familiar with half-life calculations.

### Problem

To mimic a radioactive isotope’s half-lives by flipping a coin.

### Materials

A bag of pennies

### Procedure

- Record the bag number. Count the number of pennies in the bag. You should have 20 pennies to work with.
- Shake and drop the pennies. Record how many pennies end up as heads. These are the atoms that did NOT decay and are still the original element. Set aside the pennies that fell tails side up because they represent the atoms that decayed into a different element.
- Flip the remaining coins.Again, record the number of pennies that landed heads side up and set aside the tails side up pennies.
- Repeat until you have zero pennies land on heads.
- Repeat steps 2–4 twice more to record a second and third trial of data.
- Calculate the average number of atoms remaining, rounded to the nearest whole number, after each flip.
- When you are finished, please make sure you still have all 20 pennies, put them back in the bag, and return it to your teacher.
- Wash your hands after you have turned in your pennies – money is covered in germs!

### Results

Bag #:___________ Number of pennies returned to bag:_____________

Number of times flipped | Trial 1: Atoms Remaining | Trial 2: Atoms Remaining | Trial 3: Atoms Remaining | Average # of Atoms Remaining |
---|---|---|---|---|

0 | ||||

1 | ||||

2 | ||||

3 | ||||

4 | ||||

5 | ||||

6 | ||||

7 | ||||

8 | ||||

9 | ||||

10 | ||||

11 | ||||

12 |

### Analysis

- How many half-lives
*should*it have taken to get to 0 atoms left? - How many flips did it actually take to get to 0 atoms in each of the trials?
- Trial 1:_____
- Trial 2:_____
- Trial 3:_____

- How many flips did it take on average?_____
- Each flip is equivalent to a half-life. Did your number of half-lives differed from what you expected in question #1? Why?
- Did your calculated average number of flips seem closer to or further from your original estimate (in #1) than your original trials?What do you think would happen to your average if you did more trials?
- How might your results differ if you used 200 pennies instead of 20? Do you think it would be closer or further from your original estimate (in #1), or the same as what you got with 20 pennies? Why?
- The actual length of a half-life of radioactive elements varies. Some elements have half-lives that are only fractions of a second, and others are thousands, millions, or even billions of years! Take two imaginary elements, X and Z. X has a half-life of 10 years, and Z has a half-life of 20 years. If you start with 100 atoms of each element:
- How many of each element are left after 20 years?
- How many of each element are left after 40 years?
- How many half-lives does it take for each element sample to decay entirely? How many years is this for each element?