Teaching Radioactive Decay:
Radioactive HalfLife and Dating Techniques
Daniel Gray
Target age or ability group:
 This activity has proven effective for high school biology students of all ability groups. (Some lower level students need help with the math but they can understand the concept properly.)

Class time required:
 The activity takes about an hour of student work plus discussion time. The followup activity takes twenty minutes to half an hour.

Overview of activity:
 Students generate a radioactive decay table for an imaginary element (designed to simplify the math), use their data to plot a decay graph, develop the concept of halflife, and use the graph to "age" several samples. The followup exercise tests students' understanding by having them generate a C14 decay graph and use it to date a postice age murder.

Teacher instructions:
 My students are familiar with simulations introducing complicated subject matter. They know that they will be expected to apply a simplified model like this one to a more complex situation in a followup exercise. You will get a better response from students not familiar with this learning technique if you explain what you are doing before you start.
For each group you will need to provide a container with 900 pinto beans and 100 M&M's to simulate the 1 to 10 ratio of radioactive isotope to stable isotope. There must be exactly 100 M&M's for this exercise to work correctly. You don't need exactly 900 beans; the students never count them. I find the mass of 100 beans and use it to estimate 900 beans.
The class will need six bags of "radioactive atoms" (between 5 and 100 M&M's in a bag). These bags represent the remains of various people/ organisms. A bag contains only the radioactive portion of the sample that was found along with 900 stable atoms.

Teacher Guide: Radioactive Decay Simulation
Scenario I use to start this activity. (redesign
to match your situation). The recent rash of deaths from eating
the school food has been partially solved (students get a kick
out of anything dumping on cafeteria food). Apparently water from
the school well that the cooks have been using contains relatively
high levels of a previously unknown radioactive element that is
fatal if ingested regularly over several weeks. The element has
been named Monument Mountium in tribute to our school and those
who died here. Those of you who have survived the cafeteria food
(or who were smart enough to bring your own lunch) have been assigned
to discover as much about this new element as you can. Today's
task is to determine the decay rate of Monument Mountium (MM).
We need this information so we can determine just how large a
dangerous dose of MM is and how long it will take for MM to "disappear."
At this point you should read the student direction sheet (page
13). What follows below is an amplification of various aspects
of selected steps from the student sheet:
Step 2: Eating the "decayed" M&M's is part
of the lab's appeal.
Step 3: During the third step some students will want
to calculate the decaying atoms away to "nothing." Encourage
them to do so. Their data will let you demonstrate why there is
an upper limit to aging substances accurately with a particular
radioactive isotope. The students table should be similar to:
Have students who object to "partial atoms" in this
column do the alternate calculation based on 1,000,000 total atoms
and 100,000 rather than 100 radioactive atoms.
Step 4: Thirty data points will make a good graph that
shows the asymptote of the curve and allows the students to see
four halflives.
Step 5: Discussion. During the students work and/or as
a separate step after the graphs are completed, have the students
explain what they have figured out about radioactive decay, halflife,
isotopes, etc. from the exercise. Have them explain how they think
scientists could use radioactive decay to determine time since
an organism's death. Design a way for all students to demonstrate
understanding by this point. Catch conceptual problems here or
the rest of the activity will not teach what it is designed to
teach. This is a stop point if you have short class periods. Here
I often have students gather library information about radioactive
decay to share the next day.
Followup assignment
Use this assignment to see if the students can transfer what they
should have learned to a new situation. The situation presented
is based on a true archaeological find but has been embellished
to make a more useful scenario.
NEWS FLASH  Finland: above the Arctic Circle
The body of a man wearing the traditional clothes of the snow
plains nomads was found at the bottom of one of the many peat
bogs that remain from the last glacial retreat. He had a stone
ax buried in the back of his skull. The ax was made in the ancient
nomad style, stone chipped to a sharp edge and bound by leather
strips to a forked branch. Because of the victim's dress and the
unusual murder weapon, the police are assuming this homicide involves
a clan dispute among the wandering deep snow people, the reindeer
herders, who still maintain their ancient territorial ways.
The acid in the bog has "tanned" the man's body, preserving
it well. Although the man's skin is wrinkled and pulled tightly
over his bones, his features are still distinguishable and his
clothes and internal organs are still intact and available for
police analysis. The withered condition of the body has convinced
the police that the homicide happened at least 10 years ago. Forensic
evidence shows that the man was killed elsewhere, dragged to the
bog and then thrown in, presumably to hide the crime. Anyone having
pertinent information or knowing of any of the reindeer herders
who have disappeared, are urged to contact the police.
Followup comment:
After months of investigation no new evidence or information was
turned up. Eventually the police requested a C^{14}
radioactive dating test done on the victim's body and clothes.
To their astonishment the test found that for every 100,000,000
C^{12} atoms present in the man's body and clothes
only 3,000 radioactive C^{14} atoms were present
instead of the 10,000 atoms expected for a recently deceased person.
This has greatly confused the police who had assumed that the
murder was a recent event.
How long ago did the murder take place? ________________
If your class can do it, give them the minimum information needed:
C^{14} halflife is approximately 5,700 years,
and let them create their own table, graph and solution to the
problem. Some of my classes need the following table but all of
them can generate the C^{14} graph on their own.
Additional scenarios you could generate C^{14}
questions from:
 The "Ice Man" discovered in the Alps
 Burial grounds of American Indians in your area
 Mummies (or clothes, woven baskets, etc.) from ancient burials:
Egyptian pyramids, royal tombs in China, mummies in Chile
 Boat remains from Lief Erickson's journey to NA
 Archaeologists from the future sifting through our "sanitary
landfills"
STUDENT DIRECTIONS
Radioactive Decay Simulation
You need a beaker containing 1000 atoms.
[Beans = stable isotope; M&M's = radioactive isotope.]
Step 1: Count the number of radioactive atoms. Subtract
from 1000 to get the number of stable atoms. Determine the ratio
of the radioactive atoms to the stable atoms. [Remix the beans
and M&M's after counting.]
Step 2: Remove 1 M&M (representing radioactive decay)
every 10 years for 100 years. Determine the decay rate for a 100
year period.
Step 3: Attached is a table with two columns, "years
since death" and "no. of radioactive atoms remaining."
Two data points are already recorded for you. Continue removing
10% of the radioactive atoms (M&M's) every 100 years for 3000
years. Record your results in the table.
Step 4: Plot these data on a graph and draw the curve
connecting them. When were half the radioactive atoms gone. Decide
what is meant by an element's radioactive halflife. Find additional
halflife points.
Step 5: This is a stopping place for a class discussion
on isotopes, radioactive decay, halflife, and how you can use
them to determine when an organism died.
Step 6: Get the bags of "radioactive atoms"
(M&M's) representing samples from various dead organisms.,
Count the number of atoms remaining in each bag and use your table
and graph to determine how long ago the organism died.
Follow up assignment
Show what you learned about radioactive dating by making the appropriate
C^{14} table and graph and then use them to determine
the age of the Finnish murder victim.
Data Sheet
On to Time Conceptualization
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