# CHEM 121 Cascadia C College Alpha Decay & Radioactive Dating Game Lab Report

Chem 121
Alpha Decay and Half-life
Aim: To determine the half-life of an isotope from radioactivity decay data.
Theory: A nucleus of a radioactive element that emits an α-particle transforms into a nucleus of
another element. The nucleus of the so-called ‘parent’ element loses two neutrons and two protons
(helium nucleus). Therefore, the mass number (A) decreases by 4 and the atomic number (Z)
decreases by 2. The nucleus formed by this decay is called the ‘daughter’ nucleus. We may express
such a nuclear decay by the nuclear reaction equation;
A
A−4
4
ZX → Z−2Y + 2He
(parent) (daughter) (α-particle)
The radioactive decay law enables us to determine a relationship between the half-life of a
radioactive element and the decay constant.
If a sample of a radioactive element initially contains N0 atoms, after an interval of one half-life the
sample will contain N/2 atoms that are still radioactive. Since the radioactivity decay is exponential,
we can write that
N(t) = N0e-t
where  is the decay constant and t is how long (time) the sample has decayed. Solving this equation
for the half-life t1/2 we can write (Don’t worry about the math we did to get this equation.)
t1/2 = 0.693/
To explore radioactive decay, perform the following exercises with the alpha decay simulation.
Procedure:
1. Navigate to https://phet.colorado.edu/en/simulation/alpha-decay , and click on the triangle
button. The window below should appear.
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Chem 121
2. In the right panel of the screen, click to “Custom” and get the diagram below.
3. Adjust the half-life to any value you want between 0.5-1sec. using the double-sided green
arrow.
4. Click the Stop “ ” button at the bottom of the screen so the simulation will not run
immediately. Click the “Add 10” button until the bucket is empty. The screen should look
similar to the one below.
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5. Note the numbers in the upper panel. The top number is the number of radioactive
(undecayed) atoms. The display will show 99 atoms at the start of the simulation. Click the
“ ” button to start the simulation. The atoms in the simulation will begin to decay. Record
the number of radioactive atoms at 0.5 sec intervals in the table below. (You will be
approximating where 0.5 second intervals occur.)
6. Repeat the measurement 4 more times. Calculate the average for each time point.
Time (s)
N
Number of
Undecayed
Atoms
Average
0
99
99
99
99
99
99
0.5
1.0
1.5
2.0
2.5
3.0
7. Draw a graph of the average number of undecayed atoms (N, y-axis) vs. time (sec, x-axis).
8. Calculate values of ln N for the average number of decayed atoms and write them in the table
below.
Time (s)
N, Average
Number of
undecayed atoms
ln N
0
0.5
1.0
1.5
2.0
2.5
3.0
99
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9. Draw a graph of ln N vs time and calculate its slope. The negative of the slope is known as
decay constant, 𝜆.
− = ln N/t1/2 = slope
10. Using the relationship below, calculate the actual half-life of the parent nucleus.
t1/2 = 0.693/
t1/2 = _____ sec
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Purpose: Use the radioactive decay rate and parent/daughter element ratios of carbon-14 and
uranium-238 to determine the ages of different objects.
Procedure:
Game.
2. Click on tab for Decay Rates
3. Select Carbon-14. Using the graph,
estimate the half-life for 14C. t1/2 =
_________ years.
Bucket
Slider
4. Click on the Start/Stop so the
simulation will not run the 14C decay
immediately.
5. Click on Reset All Nuclei. Move the
bucket slider all the way to the right.
Start/Stop
14
This will place 1000 C atoms onto the screen.
button
Step
button
a. Click on the Start/Stop to start the 14C decay. Stop the decay as you get close to one halflife.
b. Use the Step button to stop the decay at one half-life.
• After 1 half-life, how many 14C atoms of the 1000 original remain? _______
c. Use the Start/Stop and Step buttons to reach two half-lives. After two half-lives, how
many 14C atoms remain? ________
• What fraction of 14C atoms present at 1 half-life remain after 2 half-lives? _______
d. Use the Start/Stop and Step buttons to reach three half-lives. After three half-lives, how
many 14C atoms remain? ________
• What fraction of 14C atoms present at 2 half-lives remain after 3 half-lives? _______
e. Repeat Steps (a) to (d) with uranium-238.
• Estimated half-life for 238U is _________ years.
• After 1 half-life, how many 238U atoms of the 1000 original remain? _______
• What fraction of 238U atoms present at 1 half-life remain after 2 half-lives? _______
• What fraction of 238U atoms present at 2 half-lives remain after 3 half-lives?
_______
f. Based on the results of 5a to 5e, explain the meaning of the word “half-life” in one
sentence.
The half-life is ___________________________________________________________.
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6. Click on the Measurement tab.
7. Under Probe Type, select Uranium-238 and
Objects. Under Choose an Object, select
Rock.
8. Click on Erupt Volcano. Let the simulation
run until you reach 1 half-life. What % of the
original uranium remains? _________. How
many years did this take? ____________
9. Under Probe Type, select Carbon-14 and
Objects. Under Choose an Object, select
Tree.
10. Click on Plant Tree. Let the simulation run until you reach 1 half-life. What % of the
original carbon remains? _________. How many years did this take? ____________
11. Explain why uranium-238 is used to measure the age of rocks while carbon-14 is used to
measure the age of the tree trunk?
12. Click on Dating Game tab. There are
objects on the surface and in the five
layers containing rocks and fossils beneath
the surface.
13. Select the Carbon-14 detector. Move the
Geiger counter (the detector) to each fossil
and record the % of original in the table
below
14. On the ½ life graph, move the green arrow
right or left until the % of original matches
the reading on the detector. Record the
estimated age for each fossil in the table. Determining the age of some older fossils may not
be possible using the graph. Estimate the age using what you know about half-lives.
15. Repeat Steps 13 and 14 using the Uranium-238 detector to estimate the rock ages.
16. Using what you have learned in this activity, summarize how 14C and 238U dating together
can be used to determine fossil ages.
Table:
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Object
Measured using
C-14 or U-238?
% of Original
Measured Age
yrs
Animal Skull
Living Tree
Distant Living Tree
House
Bone
Wooden Cup
1st human skull
2nd human skull
Fish Bones
Fish Fossil 1
Rock 1
Dinosaur Skull
Rock 2
Trilobite
Rock 3
Rock 4
Rock 5
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Purpose of Lab:
Conclusions
By performing this lab, I learned (describe any new techniques, new equipment, the identity of an
unknown, or a connection to a chemical concept that you learned from this lab.)
By performing this lab, I have formulated the following question that can be tested experimentally.
(State the question and briefly describe how you would experimentally test the question.)
This lab relates to (specifically explain which of the topics, terms, theories, or laws that you have
previously learned that this lab connects with.)
This lab relates to (provide specific examples from the “everyday world” or your personal life that
can be connected with what you learned in this lab and explain how they relate.)
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