Name:
Date:
Class:

### Background

You have been learning about radioactive decay of atoms and about half-life. In this simulation you will cut a piece of paper on a regular schedule to have a hands-on model for the math of half-life. In the boxes below you will see the formulas wewill be using with all variables identified.

``` R  = (1/2)n
```
R is the fraction of the material that remains after some amount of time has passed. | n is the number of half-lives that have passed.
``` ttotal = nt1/2
```
ttotal is the total time | n is the number of half-lives that have passed | t1/2 is the length of the half-life

### Materials

• a piece of notebook or computer paper
• scissors
• pen or pencil
• calculator

### Procedure

Read the directions completely before beginning. You will be cutting a piece of paper in half once every 30 seconds for 4 ½ minutes.

1. You have a radioactive piece of paper. It represents a large number of atoms that are radioactive and which decay at a specific rate. To simulate this decay cut the piece of paper in half. Set aside one half. This half has already decayed and the atoms in that half are no longer radioactive. Mark the decayed half with a numeral one. In your data table note that it took 30 seconds to reach the point where one half of your atoms have decayed.
2. After 30 more seconds cut the remaining piece of paper in half. Mark one of the new pieces with a numeral two and set it with the piece marked with a one. Now one quarter of the original atoms remain radioactive and three quarters are stable.
3. Wait 30 seconds and then cut your remaining piece in half again. Mark one piece with a numeral three and set it with the other marked pieces.
4. Repeat this process until you have cut the paper in half a total of nine times. Then proceed to answer the questions below.

### Questions

1. Fill in the following table based on the paper (sample of atoms) you cut up.
 Number on Piece (n) Fraction of Original Atoms (R) Percent of Original Atoms (R) Total Time up to Cutting this Piece (ttotal)
2. In this simulation, what does the whole sheet of paper represent?
3. What do the pieces you set aside and marked with numbers represent?
4. What do the pieces you haven’t cut yet represent?
5. How much paper remained un-cut after 1.5 minutes?
6. How much paper remained un-cut after 4 minutes?
7. Will there ever be a time when the paper is too small to cut anymore? What does this fact represent in terms of radioactive atoms?
8. What is the half-life, in seconds, for the paper-cutting in this simulation?
9. What is the relationship between the number on the piece of paper and how many half-lives have passed?
10. Write a short summary of how this simulation worked to communicate how radioactive decay works and how it can be described by half-life. Use the terms “fraction remaining”, “half-life”, “number of half-lives”, and “total time” in your description. Be specific and use numbers when possible.
11. What fraction of the paper would remain after 5.5 minutes?
12. If an isotope has a half-life of 20 minutes then how long will it take to decay to 12.5% of the original amount?
13. If an isotope has a half-life of 20 minutes then how long will it take to decay to 6.25% of the original amount?
14. If an isotope has a half-life of 10 minutes then how long will it take to decay to 3.125% of the original amount?
Before beginning the activity, introduce students to the idea of decay rates by defining the key terms and showing them the way the number of atoms that are still radioactive changes over time using a simulation such as the Radioactive Dating Game simulation from PhET. This activity can be done to prepare students for the activity which provides an introduction to half-life.
Last updated: Jan 02, 2019        Home