Materials

M&M'sÔ

SkittlesÔ

Paper Plate

Styrofoam cup

Introduction

In this exercise, we will see a simple model of radioactive decay where M&M'sÔ and later SkittlesÔ will represent the "radioactive" substance.

Procedure

Part 1 – Simple Decay and Half life

1. Count out 20-30 M&M'sÔ and verify that each one has an M on one side. Record the number of M&M'sÔ. Record the initial number of M&M'sÔ as the number remaining for step 0.

2. Shake the M&M'sÔ in the cup and toss them onto a paper plate. Remove the M&M'sÔ that have the M showing and count the number remaining. Record in the row labeled step 1 the number of M&M'sÔ remaining and the total number removed.

3. Repeat the trials until all the M&M'sÔ are gone. Note that you may need more or less than number of steps provided in the table. You may eat the M&M'sÔ if you so desire.

Step	Number Remaining	Total Number removed
0		0
1
2
3
4
5
6
7
8

Part 2

In this part, we will investigate what happens to a nucleus when it decays. The simple answer is that it turns into products. Repeat part 1, except when you remove an M&M'sÔ replace it with a skittle. Record both the number of M&M'sÔ and the number of SkittlesÔ for each step.

Part 3

Often when a nucleus decays, one or more of the products are also radioactive. Repeat part 2 only this time, replace an M&M'sÔ with a yellow, orange, or red skittle. Toss all of the candies and replace any orange, red or yellow SkittlesÔ with the S up with a green or purple one. Record the trial number, the number of M&M'sÔ the total number of orange, yellow, or red SkittlesÔ and the number of green or purple skittles. (You should have four columns of data.)

Data Analysis and Questions

Part 1

Use LoggerPro 3.1 to graph the number of M&M'sÔ vs. step.

Q1) What kind of graph do you see?

Q2) The half life is defined as the time the remaining number of isotopes decays to half the amount. Note the half life does not refer only to the initial amount. Approximately what fraction of M&M'sÔ were left after the first step?

Q3) By approximately what factor was the number of M&M'sÔ reduced from the first step to the second?

Q4) By approximately what factor was the number of M&M'sÔ reduced from the second step to the third?

Q5) In terms of number of steps, what is the "half life" of the M&M'sÔ ?

Q6) In each half life, half of the remaining amount is reduced. From the initial amount, approximately what fraction will remain after 3 steps?

Q7) An exponential decay is described by the equation N(t) = N₀e^-kt, where N(t) represents the amount of substance remaining at time t, N₀ represents the initial amount and k is a constant known as the decay constant

Part 2

On the same axis, graph both the number of M&M'sÔ and the number of SkittlesÔ versus step number.

Q1) What relationship is there between the number of skittles and the number of M&M'sÔ at each step?

Q2) What conservation law is approximately shown by this relationship?

Part 3

On the same axis, graph the number of M&M'sÔ, the number of yellow, red, or orange skittlesÔ, and the number of green or purple SkittlesÔ.

Q1) What relationship is there between the number of M&M'sÔ and the total number of SkittlesÔ?

Q2) What conservation law is approximately shown by this relationship?

Q3) Why does the number of red, yellow, or orange skittles behave differently than the other two curves?