Honors Chemistry
Dr. Wilhelm
Half-Life of an Element
Background Information:
Half-life is the time required for half of the atoms of a radioactive isotope to undergo
decay. Some isotopes are very stable, undergo decay very slowly and have extremely
long half-lives. Uranium-238 has a half-life of 4.46 billion years. Other isotopes are
extremely unstable and have short half-lives. The isotope francium-233 has a half-life of
22 minutes.
While it is possible to predict the percentage of atoms of an isotope that will undergo
decay in a certain time span, it is not possible to predict which individual atoms within a
sample will be the ones to undergo decay. The purpose of this lab is to gain an
understanding of the statistical probabilities underlying the half-life of elements.
Pre-lab questions:
1. Is radioactive decay and extensive property (relies on external forces) or and
intensive property (independent of external conditions)?
2. What is carbon dating and how does it rely on radioactive decay and the half-life
of Carbon-14?
Procedure:
1. Prepare a data table containing two columns (Trial Number, Number of HeadsUp Pennies) and 10 rows. You will need three such tables in order to repeat this
experiment three times.
2. Place 50 atoms (pennies) into a paper cup
3. Cover the top of the cup and shake for 10 seconds
4. Carefully dump the pennies on the lab table. Take all the pennies that landed
“heads-up” and place them in a stack. Record the number in your data table.
5. Return all the remaining pennies into the cup. Repeat steps 1-3, keeping the new,
“heads-up” pennies in a separate stack. Record this data in your data table.
6. Repeat this procedure, stacking and recording after each trial until there are no
“tails-up” pennies to return to the cup.
7. Go back to the beginning and repeat the entire process, creating a new data table.
8. Repeat the process a third time, again recording your data in an entirely new data
table.
Data and Observations:
You should have three data tables in your lab book, each reporting:
Trial #
1
Etc.
# Heads-up Pennies
Calculations and Graphs:
1. Mark a piece of graph paper into quarter in preparation for making four graphs.
2. Create three bar graphs, representing the stacks of “heads-up” pennies. The
number of pennies should be the y-axis, and the number of trials the x-axis. Label
each graph according to which data table is being represented.
3. Calculate an average number of pennies for each of the trials by adding the
number of pennies in the “heads-up” stacks for each trial and dividing by three.
Record you work in a table, like shown below:
4. Create a fourth graph that represents the data in the table of averages, with the
trial # on the x-axis and the average on the y-axis.
Summary Table:
Trial #
Total Heads-up
(tables 1,2,&3)
Average Heads-up
(Total/3)
1
2
Etc.
Conclusion: include a response to the following questions in your conclusion. Explain!
1. How does this lab relate to the radioactive half-life concept?
2. Did your results illustrate and approximate “halving” of the pennies after each trial?
3. Which set of result would provide the best model of half-life?
a. Your results from a single data table?
b. Your average results of all three data tables?
c. The average results for all lab groups in the class put together?
Lab Report:
Your report should include a formal write up using the guidelines in your handbook.
Don’t forget to include you pre-lab questions, data table and graphs and follow-up
questions in your final report.
Due date: __________________________________
Follow-up Questions:
1. The half-life of carbon-14 is 5715 years. If an animal bone contains 20.0 grams
of carbon-14 when the animal dies, how many grams will be left in 17145 yrs (3
half-lives)?
2. If the half-life of francium-233 is 22 minutes, how much time must elapse in
order for 60.0 grams of a 64.0 gram sample to undergo decay? In other words,
after how many minutes will you only have 4 grams of the original isotope
remaining?
3. Would the amount of time you spent shaking the coins change the percentage that
landed “heads-up”?
Reference: http://www.sciencegeek.net/Chemistry/chempdfs/Halflife.pdf