9th Grade Physical Science
Unit 5: The Power of the Nucleus
#5D Nuclear Radiation: Using Radioactive Half-Life as a Clock
#5D
To Begin
How we use radioactive C-14 in carbon dating.
All living organisms use carbon. Let’s say that in our atmosphere right now, 10% of all carbon is the
isotope C-14 and 90% is the isotope C-12. Even though C-14 is unstable and decays to more stable
N-14, the ratio of C-14 to C-12 stays fairly constant because C-14 is constantly being generated by
reactions in the atmosphere caused by cosmic rays.
That means that all living organisms today have that same ratio of
C-14/C-12 in their tissues/bodies. When an organism dies, it no longer will be
adding carbon to its tissues. Using our example, the C-14 in its body starts out at a
10% level but will decay by one-half in 5,730 years.
Let’s say we find a sword with a wooden handle in a cave and we suspect it is from
the days of the Roman Empire. We can actually find out when the sword was
made! We can analyze the carbon in the wood and determine the current ratio of
C-14 to C-12 (let’s say it has a ratio of 7/93). Since we know that the ratio of C-14/C-12 in a living tree
should be 10/90 AND we know the half-life (50% in 5730 years), then using the appropriate
mathematical equation, we can actually calculate when the tree died!! (of course, we make the
assumption that the wooden handle was carved from the tree soon after the tree died.)
Purpose
• Students will understand that radioactive dating using a particular radioactive isotope only works
for objects that contain that radioactive isotope.
• Students will be able to determine the relative ages of objects that using radioactive half-life.
Process
1. Using Google and Chrome, enter “phET radioactive dating game” into the search box. Choose the
first website displayed. Click ‘Download now’ to open the simulation onto your desktop.
2. Click on tab for Decay Rates. Select Carbon-14. Using the graph (or the text above), complete the
following statement:
The estimated half-life for C-14 is ___________ years.
Complete this statement also:
C-14 decays to N-14 through __________decay. (hint: does the mass change or not?).
Data Table 1. Decay of C-14
3. Move the bucket slider all the way to the right. This will
place 1000 C-14 atoms onto the screen.
a. Click ‘Pause’ to stop the C-14 decay. Click on ‘Reset All
Nuclei’.
b. Click ‘Play’ to start the C-14 decay. Click ‘Pause’ before
you get to the first half-life.
c. Use the Step ( ) button to stop decay at exactly one half-life.
After 1 half-life, how many C-14 atoms of the 1000 original
remain? Record this in Data Table 1. Decay of C-14.
# of
HalfLives
0
1
2
3
# of C-14 atoms Remaining
Aver
Trial
Trial
Trial
age
#1
#2
#3
1000
1000
1000
1000
d. Use the Pause/Play and Step buttons to reach two half-lives. After two half-lives, how many C14 atoms remain? Record this in Data Table 1. Decay of C-14.
e. Do the same for three half-lives. Repeat 3 trials for C-14 and calculate the average.
4. Select Uranium-238. Using the graph, complete the
following statement in your notebook: the estimated halflife for U-238 is _________ years. (You can always check
your estimate by checking online.) Complete this
statement also: U-238 decays to Pb-206 through a series
of both ___________ and ___________ decay.
Data Table 2. Decay of U-238
# of
HalfLives
5. Repeat Steps 3 (a-e) with uranium-238, and put your data
into Data Table 2. Decay of Uranium-238.
0
1
2
3
# of U-238 atoms Remaining
Aver
Trial
Trial #2
Trial
age
#1
#3
1000
1000
1000
1000
6. Based on the results of in your 2 Data Tables for C-14 and U-238 decay, explain the meaning of the
word “half-life” in one sentence to your partner. Add this sentence to your comp book.
7. Now choose the Measurement tab.
a. Under Probe Type, select Uranium-238 and Objects. Under Choose an Object, select Rock.
b. Click on Erupt Volcano. Cool the Rock and let the simulation run. Pay close attention: What % of the
original uranium remains when you reach 1 half-life?__________ How many years did this
take?___________________
c. Under Probe Type, select Carbon-14 and Objects. Under Choose an Object, select Tree.
d. Click on Plant Tree. Pause when it is fully grown. How old is the tree?__________
e. Notice that the amount of C-14 is at 100%. Remember, for every atom of C-14 that decays a new one is
taken up by the living tree as it grows.
f. Kill the Tree and let the simulation run. Pay close attention: When the % remaining reaches 50%, how
many years have gone by? ______________ Subtract the 2 numbers…this is the half-life of C-14…how long it
takes for 50% to decay. How many years did this take?______________
g. Discuss with your partner why U-238 is used to measure the age of rocks while C-14 is used to measure
the age of the tree trunk?
8. If you have time, choose the Dating Game tab. There are objects on the surface and in the five layers
beneath the surface. There are both rocks and fossils in each layer.
9. Select the Carbon-14 detector. Notice the graph with shows the decay curve for C-14. You can slide the
green hours back and forth along the curve to establish the % C-14 and the time for any point. The half-life
for carbon-14 is approximately 5,700 years. Move the probe to each fossil; the % C-14 remaining is shown.
Use the graph to estimate the age of the fossils by finding the time that corresponds to the % given.
10. Repeat #9 using the Uranium-238 detector to estimate the rock ages.
11. Some animal fossils are too old to be able to estimate their ages with C-14. Show your partner how you can
estimate the ages of these animal fossils by using the ages of the rocks around them.
Practice
1. The half-life of Potassium-40 is 1.25 billion years. This means 50% of the parent atom decays to the daughter
atom in 1.25 billion years. Potassium-40 (parent atom) decays to Argon-40 (daughter atom).
Rock “Sample A” has a ratio of potassium to argon of 25:75. When rocks are first formed from volcanic
eruptions, the ratio of potassium to argon is 100:0 (there is no argon in the rock at that moment). Estimate
how long ago rock Sample A was formed? Explain your reasoning .