Determining a Fossil’s Age
Problem: How can you simulate radioactive half-life?
Hypothesis: If we use pennies, then we can simulate a radioactive half-life.
Data/ Observation:
Number of
Trial 1- number Trial 2- number Trial 3- number Totals- number
Shakes (Half
of heads (K 40
of heads (K 40
of heads (K 40
of heads (K 40
Lives)
atoms left)
atoms left)
atoms left)
atoms left)
Average
0
100
100
100
100
100
1
49
48
57
154
51.3
2
29
18
27
74
24.6
3
10
7
13
30
10
4
5
2
7
14
4.6
5
4
2
5
11
3.6
Analysis:
1. What symbol represented an atom of K40 in this experiment? What symbol represented an
atom of Ar 40?
The heads of the pennies represented K 40, and the tails of the pennies represented Ar 40.
2. Compare the numbers of protons and neutrons of K 40 and Ar 40. (Consult the Periodic Chart
in the Appendix for help.) Can Ar 40 change back to K 40? Explain your answer, pointing out
what procedural part of the experiment supports your answer.
K 40 has 19 protons and 21 neutrons, since K, which is potassium, in the periodic table, has an atomic
number of 19. Because an atomic number is the number of protons, so K 40 has 19 protons, and 19
subtracted from 40 is 21, so K 40 has 21 neutrons. So K 40 has 19 protons and 21 neutrons.
Ar 40 has an atomic mass of 18, so it has 18 protons and 22 neutrons. Therefore, Ar 40 cannot go
back to K 40. It does not have enough protons. Also, once K 40 decays into Ar 40, it can’t ever go back. K
40 decays into Ar 40 and can’t go back. We showed this in our procedure by not allowing the tails to go
back into the shoebox after they flipped over. When we shook the shoebox and a penny flipped to the
tails side, we had to take the penny out and could not put it back in the box, just as K 40 cannot go back
to Ar 40.
3. Define the term half-life. What procedural part of the simulation represented a half-life period
of time in the experiment?
A half-life is the amount of time it takes for half of a substance to decay. In our procedure, the shaking
of the shoebox simulated a half-life period of time. Every time we shook the box, there was a 50/50
chance, a half chance that the penny would flip either to heads or to tails. If it flipped to tails, it
“decayed”, and if it stayed at heads, it was still the rock. In every trial, we shook the box 0, 1,2, 3, 4, and
5 times. So, for example, after we shook it once, about half of it would turn over to tails, and we would
take those out. So for the second time we would shake it, there would only be half left, and we would
decrease approximately half of that much, since about half of the pennies left in there was estimated to
turn over to tails.
4. Explain how scientists use radioactive dating to approximate a fossil’s age.
Scientists use radioactive dating to approximate a fossil’s age; they use K 40 and Ar 40, because they
know that K 40 will decay into Ar 40 in 1.3 billion years. So when they find a rock, and they see K 40 and
Ar 40 in it, and they see that half of that rock has decayed from K 40 to Ar 40 by half, they will know that
it has been 1.3 billion years. If there is more decay to that rock, they will use the knowledge of half-lives
and decay rates to add up to how old the fossil actually is.
5. You are attempting to determine the age of a rock sample. Use your graph to read the rock’s
age if it has:
a. 70% of its original K 40 amount
The rock is about 0.2167 billion years old.
b. 35% of its original K 40 amount
The rock is about 8.45 billion years old.
c. 10% of its original K 40 amount
The rock is about 11.7 billion years old.
Conclusion:
In this lab, we simulated radioactive half-lives with 100 pennies and a shoebox. We placed 100
pennies “heads” up in the shoebox. Then, we covered the shoebox and shook it once, then opened the
box and took out the pennies that were facing “tails” up. We counted the number of “heads” left, and
recorded that into our data tables. We repeated this process, increasing the number of shakes each time
by one, until five shakes. So the number of pennies kept decreasing as the number of shakes increased
because we would keep pulling out the pennies facing “tails” up. We did three trials of shaking the
shoebox of pennies, and our data shows that, in each trial, when we shook it zero times, we had 100
“heads up” pennies. After we shook it one time, the numbers decreased by about 50. When we shook it
twice, the numbers went down again by about 25. After three shakes, the numbers decreased by about
15. After four shakes, the numbers went down again by about 5. At five shakes, the numbers went down
by about 1. This data implies that, at every half-life, there will be a less amount of decrease. It will
decrease even less as each level of shaking grows. In a way, this data does support my hypothesis
because I hypothesized that the pennies would be able to help us simulate a radioactive half-life, and it
did. However, my hypothesis was not very specific, so I was partially correct, but not entirely right.
This lab has helped me better understand how half-lives work. I had a vague understanding before,
but this lab has helped to clear it up for me. I now understand that it is not always perfectly half and half
decay and normal, but that there is a 50/50 probability chance of it decaying. This lab relates to what we
are learning in class because we are learning about half-lives and how scientists perform radiometric
dating. This lab has helped me to grasp the concept of radiometric dating, and how half-lives work; I also
now can’t forget that scientists use K 40 and Ar 40 to find the age of fossils, since K 40 is many times
found in fossils, and it decays to Ar 40. Since scientists know that the half-life of K 40 to Ar 40 is 1.3
billion years, they can automatically know, when they see half of K 40 and half of Ar 40, that the fossil is
1.3 billion years old.