#### Radioactive Half-Life 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 follow-up 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 half-life, and use the graph to "age" several samples. The follow-up exercise tests students' understanding by having them generate a C14 decay graph and use it to date a post-ice 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 follow-up 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.

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 half-lives.

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, half-life, 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.

Follow-up 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.

Follow-up comment:

After months of investigation no new evidence or information was turned up. Eventually the police requested a C14 radio-active dating test done on the victim's body and clothes. To their astonishment the test found that for every 100,000,000 C12 atoms present in the man's body and clothes only 3,000 radio-active C14 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: C14 half-life 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 C14 graph on their own.

Additional scenarios you could generate C14 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

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. [Re-mix 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 half-life. Find additional half-life points.

Step 5: This is a stopping place for a class discussion on isotopes, radio-active decay, half-life, 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.