Modeling the Half-Life of an Isotope

Isotopes are atoms of the same element with different atomic masses. These different masses are a result of having different numbers of neutrons in their nuclei. Isotopes can be stable or unstable (radioactive). Radioactive isotopes have unstable nuclei that break down in a process called radioactive decay. During this process, the radioactive isotope is transformed into another, usually more stable, element. The amount of time it takes half the atoms of a radioactive isotope in a particular sample to change into another element is its half-life. A half-life can be a fraction of a second for one isotope or more than a billion years for another isotope, but it is always the same for any particular isotope.

Strategy

You will make a model that illustrates the half-life of an imaginary isotope.
You will graph and interpret data of the isotope's half-life.

Materials

100 pennies
plastic container with lid
timer or clock with second hand
colored pencils

Procedure

Place 100 pennies, each head-side up, into the container. Each penny represents an atom of an unstable isotope.
Place the lid securely on the container. Holding the container level, shake it vigorously for 20 seconds.
Set the container on the table and remove the lid. Remove only pennies that are now in a tails-up position.
Count the pennies you removed and record this number in Table 1 under Trial 1. Also record the number of heads-up pennies that are left.
Repeat steps 2 through 4 until there are no pennies left in the container.
Repeat steps 1 through 5 and record your data in Table 1 under Trial 2.
Calculate the averages for each time period and record these numbers in Table 1.
Graph the average data from Table 1 on Graph 1. Use one colored pencil to graph the number of heads-up pennies against time. Make a key for the graph that shows this color as Radioactive Isotopes. Using a different color of pencil, plot the number of tails-up pennies against time. In your key, show this color as Stable Atoms.
Copy the averages from Table 1 into Table 2 under Group 1.
Then, record the averages obtained by other groups in your class in Table 2.
Determine the totals for the combined data from all groups in Table 2.
Graph this combined data in Graph 2 in the same way as you graphed your group's data in step 8.

Data and Observations

Table 1

	Trial 1 A B		Trial 2 C D		Averages
Shaking Time	Number of Heads-up Remaining	Number of Tails-up Removed	Number of Heads-up Remaining	Number of Tails-up Removed	Columns A and C (H)	Columns B and D (T)
After 20 s
After 40 s
After 60 s
After 80 s
After 100 s
After 120 s
After 140 s

Table 2

Group Average	Start		20 s		40 s		60 s		80 s		100 s		120 s		140 s
Group Average	H*	T*	H	T	H	T	H	T	H	T	H	T	H	T	H	T
Group 1	100	0
Group 2	100	0
Group 3	100	0
Group 4	100	0
Group 5	100	0
Group 6	100	0
Group 7	100	0
Group 8	100	0
Totals

*Note: H = heads, T = tails

Questions and Conclusions

In this model, what represented the process of radioactive decay?
Which side of the penny represented the unstable isotope? Which side represented the stable atom?
In this model, what was the half-life of the pennies? Explain.
What can you conclude about the total number of atoms that decay during any half-life period of the pennies?
Why were more accurate results obtained when the data from all groups was combined and graphed?
If your half-life model had decayed perfectly, how many atoms of the radioactive isotope should have been left after 80 seconds of shaking?
If you started with 256 radioactive pennies, how many would be stable after 60 seconds of shaking?

Strategy Check

_____ Can you make a model that illustrates the half-life of an imaginary isotope?

_____ Can you graph and interpret data of the isotope's half-life?