In this exercise, simulate radioactive decay by studying the outcome of coin tosses.

Procedure

Each coin toss that lands heads-up will represent an atom that does not decay, whereas a coin that lands tails-up will represent decay to the daughter atom. You will start with 50 coins representing a sample of 50 parent isotopes.

1. Calculate the predicted number of parent isotopes you will have after each half-life if you were to start with a sample containing 50 parent atoms. Record the predictions in Data Table 1.

Note: Remember the half-life is the time it takes for half of the parent isotope to decay to its daughter isotopes.

1. Gather 50 pennies and follow these instructions for Trial 1:
2. Toss each penny once and record the total number of pennies that land heads-up in Data Table 1. The heads-up pennies represent the remaining parent isotopes that did not decay. Move the tails-up pennies to the side; these represent the daughter isotopes that underwent decay.
3. Collect the pennies that landed heads-up and toss each penny once. Record the number of pennies that land heads-up in Data Table 1.
4. Repeat this process until all remaining coins land tails-up.

Note: Completely fill out the data table. Any remaining trials that were not conducted should be recorded as "0" in the data table. For example, if it only takes 6 trials to reach all tails-up coin tosses, record a "0" for trials 7 - 10.

1. Repeat step 2 two more times, and record the results for Trial 2 and 3 in Data Table 1. 
2. Graph the data in Data Table 1 of the half-lives for predicted number of parents and also actual parents in Trials 1, 2, and 3. Plot the number of parent isotopes on the dependent, vertical axis (y-axis) and plot the number of half-lives on the independent, horizontal axis (x-axis). Add an exponential trendline to the predicted number of parents.

Note: If you do not have access to graphing software, download and print the Graph Paper Template to create the graph and draw an estimated trendline.

1. Take a photo of the completed graph and upload the image into Graph 1.

Data Table 1: Predicted vs. Observed Simulated Parent Isotopes

Number of Half-livesPredicted       # of ParentsActual     # of Parents 

                                                                                                Trial1      Trial 2     Trial 3

0                                                            50                                50            50         50                                                    

1                                                             25                                 25            21          24                                    

2                                                            13                                  11              13          14                                                                                   

3                                                             6                                   6              6            6                                     

4                                                             3                                   4              2            2                                      

5                                                             2                                   2               1            1                                       

6                                                             1                                    1                0           0                                                            

7                                                             0                                   0               0            0                                                        

8                                                             0                                   0              0            0                                               

9                                                             0                                   0              0            0                                               

10                                                            0                                   0              0            0                                        

1. How did the predicted values compare to the actual values in Data Table 1 and Graph 1? Explain sources of variability in the outcomes of this experiment.

2. What would Graph 1 look like if only 5 pennies were used in this experiment? What if 10,000 pennies were used? Based on your responses, what might be inferred about the relationship of half-life and sample size?