In this activity, you will apply the scientific method to to investigate radioactive decay and its application to radiometric dating. . The activity involves experimentation using a web-based interactive simulation.
After completing the background reading for this assignment, go to the “Radioactive Dating
Game” simulation on the PhET simulations website at:
http://phet.colorado.edu/en/simulation/radioactive-dating-game. Click the play arrow on
the simulation graphic to run the web-based simulation or click DOWNLOAD to run the
simulation locally on your device.
Simulation requirements: This interactive simulation is optimized for use on computers
(MACs or PCs) and may not run on some tablets, notebooks, cell phones, or other devices.
Running the simulation will require an updated version of Java software (free). If you do not
or are not sure if you have Java on your computer, go to the Java Website. If you cannot get
the simulation to run, consult The PhET Simulation Troubleshooting Guide on the course
website.
2. Explore and experiment on the four different tabs (areas) of the simulation. While
experimenting, think about how the concepts of radioactive decay are being illustrated in
the simulation.
a. Half-Life tab – Observe a sample of radioactive atoms decaying – carbon-14, uranium-
238, or ? (a custom-made radioactive atom). Clicking on the add 10 button adds 10
atoms at a time to the decay area. There are 100 atoms in the bucket; so, clicking the
add 10 button 10 times empties the bucket into the decay area. Observe the pie chart
and time graph as atoms decay. You can pause or step the simulation as atoms decay,
and Reset the simulation, using buttons at the bottom of the screen.
b. Decay Rates tab – Similar to the half-life tab, but different! Atom choices are carbon-14
and uranium-238. The bucket has a total of 1,000 atoms. Drag the slide bar on the
bucket to the right to increase the number of atoms added to the decay area. Observe
the pie chart and time graph as atoms decay. Note that the graph for the Decay Rates
tab provides different information than the graph for the Half-Life tab. You can pause or
step the simulation as atoms decay, and Reset the simulation, using buttons at the
bottom of the screen.
c. Measurement tab – Use a probe to virtually measure the amount of radioactive
material within an object or in the atmosphere. The probe can be set to detect the
decay of either carbon-14 or uranium-238 atoms. Follow prompts on the screen to run a
simulation of a tree growing and dying, or of a volcano erupting and creating a rock, and
then measuring the decay of atoms within each object.
d. Dating Game tab – Use a probe to virtually measure the percentage of radioactive
atoms remaining within various objects and estimate the ages of objects by applying the
concept of half-life. The probe can be set to either detect carbon-14, uranium-238, or
other “mystery” elements that may be contained in the objects. Drag the probe over an
object, select which element to measure, and then slide the arrow on the graph to
match the percentage of atoms measured by the probe. The time (t) shown for the
matching percentage can then be entered as the estimate in years of the object’s age.
e. Pause button ( I I ) – Simulation is running when this is showing; press to pause the
simulation.
f. Play arrow ( > ) – Simulation is paused when this is showing; press to run the
simulation.
3. After getting oriented to the simulation, follow the steps below to perform four different
experiments. Before beginning, be prepared to write down hypotheses and observations
for the experiments.
Experiments
Experiment 1: Half-Life
In this experiment, you will visualize the radioactive decay of atoms and investigate the concept
of half-life.
Before completing the experiment, write down a hypothesis, based on your current
understanding, that makes specific predictions for how the decay of a radioactive substance will
progress over time.
1. Experiment setup: click on the Half-Life tab at the top of the simulation screen.
2. Experiment procedure:
Construct a table like the one below. Complete the following steps for parts I and II of the
experiment to complete the table.
Part I – Carbon-14
a. Make sure that Carbon-14 is selected in the Choose Isotope box. Click the pause
button ( I I ) at the bottom of the screen so that it shows the play arrow ( > ). Click
the Add 10 button below the Bucket o’ Atoms ten times to empty the bucket and
place 100 carbon-14 atoms in the decay area.
b. The half-life of carbon-14 is about 5,700 years. Based on the definition of half-life, if
you left these 100 carbon-14 atoms to sit around for 5,700 years, what would you
predict to be the number of carbon-14 atoms that would radioactively decay
during that time? Write your answer down.
c. Click the play arrow. As the simulation runs, carefully observe what is happening to
the carbon-14 atoms in the decay area, and the graphs at the top of the screen (both
the pie chart and the time graph).
d. After all atoms have decayed, click the pause button, and the Reset All Nuclei
button in the decay area.
e. Repeat steps c and d until you have a good idea of what is going on. Then, write
down a specific description of what you observed happening, both in the decay
area and on the pie chart and time graph, while the simulation is in play mode.
f. Repeat step c again, but this time, watch the graph at the top of the window
carefully, and click “pause” when Time reaches 5,700 years, i.e., when the carbon-
14 atom moving across the graph reaches the dashed line labeled Half-Life. If you
don’t pause the simulation on or very close to the dashed line, click the Reset All
Nuclei button and repeat step c again.
g. Once you have paused the simulation in the correct spot, record the number of
carbon-14 nuclei that have decayed into nitrogen-14 (the number next to #14N, to
the left of the pie chart).
h. Click the Reset All Nuclei button in the decay area.
i. Repeat steps f through h for two more trials, to record a total of three values for
step g.
Part II – Uranium-238
a. Click Reset All below the Choose Isotope box, then yes in the box that pops up. Click
on the radio button for Uranium-238 in the Choose Isotope box. Click the pause
button at the bottom of the screen so that it shows the play arrow. Click the Add 10
button ten times to empty the bucket and place 100 Uranium-238 atoms in the
decay area.
b. The half-life of Uranium-238 is 4.5 billion years!* Based on the definition of half-life,
if you left these 100 Uranium-238 atoms to sit around for 4.5 billion years, write
down your prediction of the number of Uranium-238 atoms that will radioactively
decay over that time.
c. Click the play arrow. Watch the graph at the top of the window carefully, and click
pause when Time reaches 4.5 billion years, i.e., when the Uranium-238 atom
moving across the graph reaches the dashed line labeled Half Life. If you don’t pause
the simulation on or very close to the dashed line, click the Reset All Nuclei button
and repeat step c.
d. Once you have paused the simulation in the correct spot, record the number of
Uranium-238 nuclei that have decayed into Lead-206 (the number next to #206Pb to
the left of the pie chart).
e. Click the Reset All Nuclei button in the decay area.
f. Repeat steps c through e for two more trials, to record a total of three values for
step d.
Number of atoms that have
decayed when
Time = Half LifeRadioactive
Element
Number of atoms in
the sample at Time = 0
Prediction of # atoms that
will decay when time
reaches one half-life Trial #1 Trial #2 Trial #3
Carbon-14 100
Uranium-238 100
Experiment 1 – Results and Conclusions
1. In Part I of the experiment (and in nature), carbon-14 radioactively decays to nitrogen-14.
Based on what you read in Chapter 12 of The Sciences about the three types of radioactive
decay, name the specific type of radioactive decay taking place in Part I of the experiment.
2. Based on your observations and data collected while conducting Experiment 1:
a. Formulate a written discussion that describes the nature of radioactive decay – i.e., is
the process random, exact, or something else, and can you make any analogies between
radioactive decay and other processes you observe in your everyday life?
b. Does the data collected in parts I and II of the experiment validate or negate the
concept of radioactive half-life? Support this conclusion by formulating a written
comparison between your predictions from step b for the number of atoms that will
radioactively decay over one half-life and the values you recorded in the trials.
* Unlike carbon-14, which undergoes only one radioactive decay to reach the stable nitrogen-14, uranium-238 undergoes many
decays into many intermediate unstable elements before finally getting to the stable element lead-206. (See the decay chain
for uranium-238 in Chapter 12 for details).
Experiment 2: Decay Rates
In this experiment, you will again visualize the radioactive decay of atoms, and you will also
make some additional quantitative measurements of the decay. Your hypothesis from
Experiment 1 also applies to this experiment.
1. Experiment setup: click on the Decay Rates tab at the top of the simulation screen.
2. Experiment procedure:
Construct a table like the one below. Complete the following steps for parts I and II of the
experiment to complete the table.
Part I – Carbon-14
a. Click the Reset All button below the Choose Isotope box.
b. In the Choose Isotope area, click the button next to carbon-14.
c. Drag the slide bar on the bucket of atoms all the way to the right. This will put 1,000
radioactive nuclei into the decay area. When you let go of the slide bar, the simulation
will start right away. Watch the graph at the bottom of the screen until all atoms have
decayed.
d. From the graph, record the percentage of carbon-14 nuclei remaining at times
equivalent to 1, 2, and 3 half-lives of carbon-14 (a total of three percentage values).
Recall that the half-life of Carbon-14 is about 5700 years.
Part II – Uranium-238
a. In the Choose Isotope area on the right side of the screen, click the button next to
Uranium-238.
b. Repeat step c of Part I for uranium-238.
c. From the graph, record the percentage of uranium-238 nuclei remaining at times
equivalent to 1, 2, and 3 half-lives of uranium-238 (a total of three percentage values).
Recall that the half-life of uranium-238 is about 4.5 billion years.
Percentage of the element remaining after:Radioactive
Element 1 half-life 2 half-lives 3 half-lives
Carbon-14
Uranium-238
Experiment 2 – Results and Conclusions
Does the data collected in parts I and II of the experiment validate or negate the concept of
radioactive half-life? Support this conclusion by discussing the trends in the number of
radioactive nuclei remaining after 1, 2, and then three half-lives had passed.
Experiment 3: Measurement
In this experiment, you will use a probe to detect the decay of radioactive material within a
rock and a tree.
Before completing the experiment, write down a hypothesis, based on your current
understanding, that predicts how the simulation should be utilized to detect each object’s age.
1. Experiment setup: click on the Measurement tab at the top of the simulation screen.
2. Experiment procedure:
Part I – Tree
a. Under Choose an Object, click on the button for Tree. In the Probe Type box, click on
the buttons for Carbon-14, and Objects. This sets up a probe to measure radioactive
decay of any carbon-14 in the tree. Note that the probe can only detect the element for
which it is set.
b. Click Plant Tree at the bottom of the screen. As the simulation runs, observe that the
tree grows and lives for about 1,200 years, then dies and begins to decay. Observe the
probe reading (upper left box) and graph (upper right box) at the top of the screen
showing the percentage of carbon-14 in the tree over time. Write down your
observations of what is taking place in the visual scenario, the probe reading, and the
graph.
c. Click either of the two Reset buttons on the screen. In the Probe Type box, set the
probe to measure uranium-238 instead of carbon-14. So, now the probe is detecting the
decay of any uranium-238 in the tree.
d. Click Plant Tree and again observe the probe reading and graph as the simulation runs.
Write down your observations of the probe reading and graph.
Part II – Volcanic Rock
a. Click either of the two Reset buttons on the screen.
b. Under Choose an Object, click the button for Rock. Keep the probe type set on
Uranium-238.
c. Click Erupt Volcano and observe the volcano creating and ejecting very hot igneous
rocks. As the simulation runs, observe the probe reading and graph showing the
percentage of uranium-238 in the rock over time. Write down your observations of
what is taking place in the visual scenario, the probe reading, and the graph.
d. Click either of the two Reset buttons on the screen. In the Probe Type box, set the
probe to measure the decay of carbon-14 instead of uranium-238. So, now the probe is
detecting the decay of carbon-14 in the rock.
e. Click Erupt Volcano and again observe the probe reading and graph as the simulation
runs. Write down your observations of the probe reading and graph.
Answer questions 1–5 below to help you formulate some results and conclusions for this
experiment. You may need to do some additional experimentation to answer the questions.
1. Explain what happened when the probe was used to measure uranium-238 in the tree
and carbon-14 in the rock.
2. At what point in the simulation does the probe detect a decrease in the carbon-14 in the
tree? Explain why this is the case.
3. At what point in the simulation does the probe detect a decrease in uranium-238 in the
rock? Explain why this is the case.
4. When the amount of carbon-14 in the tree has decreased to 50 percent, approximately
how many years have passed since the tree died?
5. When the amount of uranium-238 in the rock has decreased to 50 percent,
approximately how many years have passed since the volcano erupted?
Experiment 3 – Results and Conclusions
Formulate a written conclusion for how the probes in the simulation should be properly utilized
to detect the ages of each object. Support your conclusion with your observations while
conducting the experiment and answers to the above questions.
Experiment 4: Dating Game
In this experiment, you will determine the age of various objects using a probe that can be set
to detect the radioactive decay of various elements. Your hypothesis from Experiment 3 also
applies to this experiment.
1. Experiment setup: Click on the Dating Game tab at the top of the simulation screen. Verify
that the Objects button is clicked below the Probe Type box.
2. Experiment procedure:
Construct a table like the one below. Complete the following steps to complete the table:
a. Set the Probe Type to either Carbon-14 or Uranium-238, as appropriate for the object
you are measuring, based on your findings in Experiment 3.
b. Drag the probe directly over the object. The box in the upper left, above Probe Type,
will show the percentage of the radioactive element that remains in the item, based on
the level of radioactivity being detected by the probe.
c. Drag the green arrow on the graph to the right or left, until the percentage in the box on
the graph matches the percentage of element in the object. Once you have the arrow
positioned correctly, enter – in the Estimate the age… box – the time (t) shown, as the
estimate for the age of the rock or fossil. Click Check Estimate to see if your estimate is
correct.
Practice completing the above steps using this example:
1) Let’s determine the age of the dead tree. Since this is a once-living thing, set the
Probe Type to Carbon-14.
2) Drag the probe over of the tree, and then look at the probe reading: it detects 97.4%
of carbon-14 remaining in the dead tree.
3) Drag the green arrows on the graph to the right or left until you land on a carbon-14
percentage of 97.4%, matching the reading from the probe. When the graph reads
97.4%, it shows that time (t) equals 220 years.
4) Type “220” into the box that says Estimate age of dead tree: and click Check
Estimate. You should see a green smiley face, indicating that you have correctly
figured out the age of the dead tree, 220 years. This means that the tree died 220
years ago.
TIPS:
The estimate for the age of an object must be entered in years. So, if t = 134.8 MY on
the graph, which means 134.8 million years, you would enter the number 134,800,000
as the estimate in years for the age of a rock. The estimates do not have to be exact to
be registered as correct, but it must be close. For example, if 134,000,000 were entered
for the above example, the simulation would return a green smiley face for a correct
estimate
For the items on the list marked with an *, you should discover that neither carbon-14
nor uranium-238 will work to determine the item’s age. Select Custom for the Probe
Type, and experiment to find an element from the drop-down menu that returns a
probe reading other than 0.0%. Note that for each of the Custom elements, only the
half-life of the element is given, not the name of the element
Object Being Measured Element Detected
to Determine Age
Age
(Years)
Animal skull
House
Living tree
Dead tree
Bone
Wooden cup
Large human skull
Fish bones
Rock 1
Rock 3
Rock 5
Fish fossil*
Dinosaur skull*
Trilobite*
Small human skull
Answer questions 1–5 below to help you formulate some results and conclusions for this
experiment. You may need to do some additional experimentation to answer the questions.
1. Explain the differences in carbon-14 readings in the living tree versus the dead tree.
2. Explain why some of the items detect carbon-14 and not uranium-238, and vice-versa.
3. Explain why the probe could not detect carbon-14 or uranium-238 in the fish fossil,
dinosaur skull, or trilobite, but could detect one of the Custom elements in each of
those items.
4. Explain why the probe detected uranium-238 in Rocks 1, 3, and 5, but the probe
detected the Custom 100 my element in only Rocks 1 and 3, and not Rock 5?
5. Explain why the probe set to Carbon-14 gives a reading of 100% in the living trees.
Experiment 4 – Results and Conclusions
1. Based on your observations while conducting the experiment and your answers to the
questions above, formulate a written discussion that explains how to properly use the
simulation to determine the age of:
A. The rocks
B. The items that contain once-living material
2. Include in your explanation which element the probe should be set to and why, and how
to use the slider on the graph to determine the age.
Activity Submission
1. Create a document containing a report for each experiment. Your document should contain
four paragraphs, one for each experiment.
a. Title each paragraph with the corresponding name for each experiment, as it is stated in
the headings for the experiments above (e.g., Experiment 1: Half-Life).
b. For each experiment report:
i. Clearly and succinctly present your hypothesis for the experiment.
ii. Based on the information prompted for in the experiment’s Procedure and Results
and Conclusions section, clearly and succinctly summarize your observations,
results, and conclusions for the experiment, and include any data collected and
calculations made.
iii. Clearly and succinctly evaluate the correctness of your hypothesis based on the
information presented in part ii above.
c. Include your full name and the date you completed the activity at the top of the
document.
