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Lesson Plans
I'm Late, I'm Late, for a Radioactive Date!
Using Radioactive Decay and
Primary Sources to Date the Shroud of Turin
OverviewProcedure for teachersStudent Resources and Materials

Prep for Teachers

Set the Pink Panther Theme to play on the tape recorder or CD player. If possible, make a tape with the song playing over and over, or program the CD player to repeat. This way you can start the tape as students enter and have it playing low when the students are working.

Prior to the teaching, bookmark all of the Web sites used in the lesson. Load Adobe Acrobat Reader to view standards, and Netscape Communicator 4 or Microsoft Internet Explorer 4 with JavaScript enabled to use the Virtual Dating site and the decay calculator. To make class management easier, you may decide to go to the teacher site and print out all the pages (this way you will know who is almost done and who is having a hard time).

CUE the videotape Math Vantage, "Data: What Does It Mean?" to the picture of the narrator with the prairie dog in the background, where the narrator says, "Environmental biologists are concerned with populations other than people." This is located directly after the picture of Texas.

CUE the videotape Religion & Ethics NewsWeekly, Show #133 to the picture of the narrator with the sign "Shroud of Turin," where the narrator says, "The Shroud of Turin goes on public display in Italy this weekend for the first time in twenty years."

CUE the videotape Exponential and Logarithmic Functions, Episode #3 to the picture of the periodic table (on a can) and where the narrator says, "One type of Plutonium -- Plutonium 243 -- has a half life of five hours." Make copies of Student Sheets #1, #2, #3, #4.1, and #4.2.

When using media, provide students with a FOCUS FOR MEDIA INTERACTION, a specific task to complete and/or information to identify during or after viewing of video segments, Web sites, or other multimedia elements.

Introductory Activities

Setting the Stage
Step 1:

To set the scene, play the Pink Panther Theme. As students come in, break them into groups of three or four and give each Student Sheet #1. Ask your students to explain the following. Are the three graphs on the sheet related? Make up a story telling how they are or are not related. Put these answers on their data sheet. Give students some discussion time. After three minutes ask why we are playing the Pink Panther music. (Tell students we are playing the music to indicate that we will play the part of scientific detectives. We first want to sharpen their skills with this small problem.)

Are these three graphs related? (The graphs are related. Ferrets eat prairie dogs and burrowing owls use their dens. Don't give students the answer now. They will discover the answers during the video.) Let's use a videotape to discover this.

Step 2:

Provide students with a FOCUS FOR MEDIA INTERACTION, asking them to determine if the graphs give us all the information. Students will have to use their listening skills and answer the question after hearing some videotape narration. START the videotape Math Vantage, "Data: What Does It Mean?" on the picture of the narrator with the prairie dog in the background, where the narrator says, "Environmental biologists are concerned with populations other than people." This is located directly after the picture of Texas. PLAY THE VIDEO WITH THE SOUND ON AND COVER THE TV SCREEN. PLAY the video until you hear the narrator say, "By only looking at the graphs, we could misinterpret the data and make false assumptions." PAUSE the tape. Ask the students if graphs can give us all the information. Ask what else we need to do to get information. (The students should see that the graphs alone could not give all the information. We can get information by doing research on the Internet or by using an encyclopedia. It is OK if students don't see that now; they should after the next section. The graphs on Student Sheet #1 have a different y interval than on the video.)

Ask students if they think that seeing the video would give them any more information. REWIND and REPLAY the video clip to CHECK the students' predictions. Provide students with a FOCUS FOR MEDIA INTERACTION, asking them to see if watching the video would give them any more information. Discuss.

(Note the differences between the prairie dog graph on the worksheet and the video. They have two different scales. The prairie dog graph on the worksheet could be misleading. Let this go if students don't pick it up now. You will tie this together after the next couple of clips.)

Step 3:

Provide students with a FOCUS FOR MEDIA INTERACTION, asking them to write the answers for the following three questions on Student Sheet #1. RESUME PLAY and PAUSE when the narrator says, "You may not know what causes what just by looking at a graph."

Why did the prairie dog decline? (Increased agriculture, pest control, disease)

Why did the ferret decline? (Ferrets feed almost exclusively on the prairie dog.)

Why did the burrowing owl decline? (Burrowing owls are dependent on the prairie dog for nest sites.)

Ask students again if graphs can give us all the information. Discuss that if you didn't understand the relationships within the ecosystem then, you couldn't fully explain why the three were declining.

Step 4:

Provide students with a FOCUS FOR MEDIA INTERACTION, asking them to make a prediction and to write down why they believe that graphs can sometimes be misleading. RESUME PLAY and STOP when the narrator says, "If you don't, you'll get a distorted picture of the situation." Why can graphs sometimes be misleading? (The scales chosen for the graph can create different pictures. If the interval is not even for the scale, you get a distorted picture of the situation. Ask the students to remember the prairie dog graph on the worksheet and the prairie dog graph in the video. The scales didn't match. The prairie dog population appears to be decreasing more slowly than it actually is.) Now that we are warmed up, we want to look at our problem.

Learning Activities

Step 1:

Now that we have practiced looking at data and discovered how data can be misinterpreted depending on its presentation, we will look at a real-life problem. This problem centers on data and how it is read and interpreted. We want to discover if mistakes were made when determining the origin date of the Shroud of Turin. Before we go any further, we first need to collect information and find out more about our problem, and to do that we will be watching a couple of video clips. Give students Student Sheet #2.

Step 2:

Provide students with a FOCUS FOR MEDIA INTERACTION, asking them to answer the following two questions. What is the Shroud of Turin? What is the controversy surrounding it? START the videotape Religion & Ethics NewsWeekly, Episode #133 on the picture of the narrator with a sign reading "Shroud of Turin," where the narrator says, "The Shroud of Turin goes on public display in Italy this weekend for the first time in twenty years." PLAY the video until you hear the narrator say, "...and as Mary Alice Williams reports, modern science and faith continue to collide in the search for the truth." PAUSE the tape. (Note: you are using the video as a primary source of information.)

Ask your students, "What is the Shroud of Turin?" (Ancient linen cloth with the faint image of a crucified man.) What is the controversy? (Some people believe this linen is the burial cloth of Jesus Christ, which would make it nearly 2000 years old. In 1988 carbon dating placed the age of the cloth in the Middle Ages. However, no modern technology has been able to replicate the image on the cloth.) Note: Students may not get all the information initially, but as the video elaborates, the controversy should become clearer.

Provide students with a FOCUS FOR MEDIA INTERACTION, asking them to determine what has happened to the shroud throughout history, and what the view is of the scientist (microscoper) Walter McCrone. PLAY the video and PAUSE when you hear Walter McCrone say, "I am faced by the fact that my microscope tells me that it is not the real shroud of Christ." CHECK for comprehension. Ask students what has happened to the shroud throughout history. (The Shroud has survived several changes of power, a flood and three major fires.) Ask students what Walter McCrone's viewpoint is. (Walter McCrone says, "Everything I saw says it is paint...my microscope tells me that it is not the real shroud of Christ.")

Provide students with a FOCUS FOR MEDIA INTERACTION, asking them to determine what the opposite point of view is from Walter McCrone's. PLAY the video and PAUSE when you hear the narrator say, "The shroud itself is, in effect, a photographic negative, and no technology has been able to replicate that." CHECK for comprehension, and ask students what the opposite point of view is. (The opposite point of view is that the Shroud is not a painting, but a genuine religious relic. No one can explain how it was produced in medieval times. It has no brush strokes, no artistic method, and it displays none of the textile technology or laws of physiology known in medieval times. No one can explain its photographic properties, which could not be replicated with the technology at the time. The shroud is a photographic negative, and no technology has been able to replicate that.) Let's hear from another expert.

Provide students with a FOCUS FOR MEDIA INTERACTION, asking them to answer the following: What is the viewpoint of author and historian Ian Wilson, and what is the carbon 14 date for the shroud? PLAY the video and STOP when you hear Ian Wilson say, "What the carbon-dating scientists were doing, quite unwittingly, was dating both original linen from the shroud and also a microbiological accumulation that had grown up through the centuries." CHECK for student comprehension. What is the carbon date for the shroud? (In the middle of the thirteenth century.) What is Ian Wilson's viewpoint? (Ian Wilson doesn't understand how we can explain how the Shroud was produced at that time. The technology didn't exist. Someone would have to understand photography to produce the Shroud. He says that the scientists didn't date just the shroud, but also the microbiological accumulation that has grown up through the centuries.)

Provide students with a FOCUS FOR MEDIA INTERACTION, asking them what they believe Walter McCrone's reaction to Ian Wilson's viewpoint will be. Listen to this section for both Walter McCrone's and Ian Wilson's responses. PLAY the video and STOP when you hear Ian Wilson say, "That really comes down to being the bottom line." CHECK for comprehension. What does Walter McCrone say? (Walter McCrone says that the amount of material that would have to be present for the shroud to be dated first century rather then fourteenth would be double the weight of the shroud itself.)

What does Ian Wilson say? (Wilson says the section that was carbon dated was stained, its carbon date skewed by fire or a radiant photodynamic event.)

Provide students with a FOCUS FOR MEDIA INTERACTION, asking students to determine what the DNA scientists have discovered about the Shroud. PLAY the video, and STOP when you hear the narrator say, "The scientists might have determined if the man was Jewish, even if the DNA was only maternal." What did the DNA scientists discover about The Shroud? (The sample is a human male with strands of DNA. Note: certain genes have a higher probability of occurrence in Jews of that time and living in that area. If the shroud is real, then the specimens should show only maternal DNA according to the theory of the Virgin Birth.)

Provide students with a FOCUS FOR MEDIA INTERACTION, asking them to explain if the Catholic Church supports this Shroud of Turin story. Also, do students think that Ian Wilson was a religious fanatic? PLAY the video and STOP when you hear the Ian Wilson say, "...like a twentieth-century doubting Thomas examining the wound of Jesus." Discuss student responses. (The Catholic Church has no opinion on the Shroud, and believes it should be valued for turning the faithful to what is really holy. Ian Wilson was an agnostic and now has converted because of the shroud.)

Provide students with a FOCUS FOR MEDIA INTERACTION, asking students to watch the last segment and summarize the problem. PLAY the video and STOP when you hear the narrator say, "There is at least a possibility that it could be cloned. A living human replica of the original source." Discuss student responses. (The problem is that, no matter how many times we radioactively date the Shroud, there is no explaining how a three-dimensional, heat-resistant indelible image was transferred to linen two millennia ago.)

Ask students what questions they would need answered before they could draw conclusions about this problem. (What is half-life? What is the half-life of carbon 14? What is the amount of carbon 14 present in normal living samples? Did microbiological contamination (fire, dust, etc.) in any way affect the result of the carbon 14 dating?) Tell students that they will first discover what half-life is and how it is used.

Step 3:

Provide students with a FOCUS FOR MEDIA INTERACTION, asking them to determine what half-life is, and how it is used. START the videotape Exponential and Logarithmic Functions, Episode #3 at the picture of the periodic table (on a can), where the narrator says, "One type of Plutonium, Plutonium 243, has a half life of five hours." PLAY the video and PAUSE when you hear the narrator say, "Let's calculate in a step-by-step process the total mass left after 30 hours." CHECK for comprehension. What is half-life? (The time it takes for one half of the mass of a radioactive substance to decay.) How is half-life used? (Students may not be able to determine this yet. Let them discover this. Don't give the answer yet. It is used to determine the age of radioactive substances.) What is the half-life of Plutonium 243? (Five hours.)

Give students Student Sheet #3, and ask them to figure out the following. If you are starting with 100 grams of Pu, how much will you have after five hours? (Don't give the answer. It will be given in the videotape. The answer is 50 grams, which is one half of 100 grams.)

Step 4:

TURN DOWN THE SOUND before you PLAY the next segment. ASK A STUDENT TO SUPPLY THE NARRATION for the next segment. Provide students with a FOCUS FOR MEDIA INTERACTION, asking them to tell how much plutonium will be left after five hours, what percent will be left, and how you could figure this out. START the videotape and PAUSE when you see mass 50 grams on the screen. Discuss. (Students should say that it took five hours for the mass to decrease to 50 grams. The formula is what you start with times 1/2, or 100 g x 1/2.) As you can see in the upper left corner, 1/2 of the original mass is left and 1/2 of the original mass has changed.) REWIND the last segment, and REPLAY it WITH SOUND to CHECK comprehension. (Note: You decide if this is needed. You may want to try it at least once.)

TURN DOWN THE SOUND before you PLAY the next segment. ASK ANOTHER STUDENT TO SUPPLY THE NARRATION for the next segment. Provide students with a FOCUS FOR MEDIA INTERACTION, asking them to tell how much plutonium will be left after ten hours, what percent will be left, and how you could figure this out? Students should use Student Sheet #3 to record their answers. START the videotape and PAUSE when you see mass 25 grams on the screen. Discuss. (Students should say that it took ten hours for the mass to decrease to 25 grams. This is half of 50, which is what was left after the first half-life. The formula is what you start with times 1/4 or 100 g x (1/2)2. As you can see in the upper left corner 1/4 of the original mass is left and 3/4 of the original mass has changed.) REWIND and REPLAY WITH SOUND to CHECK comprehension. (Note: if students get all information it is not necessary to rewind. This will be true of the next section also.)

TURN DOWN THE SOUND before you PLAY the next segment. ASK ANOTHER STUDENT TO SUPPLY THE NARRATION for the next segment. Provide students with a FOCUS FOR MEDIA INTERACTION, asking them to tell how much Plutonium will be left after fifteen hours, what percent will be left and how could you figure this out? Students should use Student Sheet #3 to record their answers. START the videotape and PAUSE when you see mass 12.5 grams on the screen. Discuss. (Student should say that it took fifteen hours for the mass to decrease to 12.5 grams. This is half of 25, which is what was left after the second half-life. The formula is what you start with times 1/8 or 100 g x (1/2)3. As you can see in the upper left corner, 1/8 of the original mass is left and 7/8 of the original mass has changed.) REWIND and REPLAY WITH SOUND to CHECK comprehension.

TURN DOWN THE SOUND before you PLAY the next segment. ASK ANOTHER STUDENT TO SUPPLY THE NARRATION for the next segment. Provide students with a FOCUS FOR MEDIA INTERACTION, asking them to predict the general formula for radioactive decay and explain the formula. START the videotape and PAUSE when you see the letter "n" as an exponent in the formula. What is the formula for radioactive decay? (When M is the mass left after n time periods, the formula is M= 100 g x (1/2)n.) Ask students how they could determine this. Ask students to finish the chart on Student Sheet #3. Give three minutes.

Discuss all but the last answer, which will use the videotape. Show the relationship between the formula and determining the problem step by step. 50g is 1 half-life, which is 5 years, which is 1/2 or 50% of the original mass. This is 100 g x (1/2)1. 25g is 2 half-lives, which is 10 years, which is 1/4 or 25% of the original mass. This is 100 g x (1/2)2. 12.5g is 3 half-lives, which is 15 years, which is 1/8 or 12.5% of the original mass. This is 100 g x (1/2)3. 6.25g is 4 half-lives, which is 20 years, which is 1/16 or 6.25% of the original mass. This is 100 g x (1/2)4. 3.125g is 5 half-lives, which is 25 years, which is 1/32 or 3.125% of the original mass. This is 100 g x (1/2)5. 1.5625g is 6 half-lives, which is 30 years, which is 1/64 or 1.5625% of the original mass. This is 100 g x (1/2)6.

TURN DOWN THE SOUND before you PLAY the next segment. ASK ANOTHER STUDENT TO SUPPLY THE NARRATION for the next segment. Provide students with a FOCUS FOR MEDIA INTERACTION, asking them to tell how much plutonium will be left after thirty hours, what percent will be left, and how you could figure this out. START the videotape and PAUSE when you see mass 1.5625 grams on the screen. Discuss. (Student should say that it took thirty hours for the mass to decrease to 1.5625 grams. The formula is the amount you start with multiplied by 1/8 or 100 g x (1/2)3. As you can see in the upper left corner, 1/64 of the original mass is left and 63/64 of the original mass has changed. OPTION: student can substitute into the formula and solve.) REWIND and REPLAY WITH SOUND to CHECK comprehension if necessary.

Step 5:

The site http://vcourseware.sonoma.edu/VirtualDating/index.html will be used for the next step. Students are seated at a computer. Provide students with a FOCUS FOR MEDIA INTERACTION, asking them to answer the rest of the questions on the Student Sheet #3. If you print the sheets from the teacher Web site earlier, you will be able to see how fast each student is progressing. This will take about twenty to thirty minutes. When students finish, they will get a certificate from the site. As students finish, have them help students who are having problems. Discuss the answers with your students.

Answers are as follows:

  1. Generated in the upper atmosphere, C-14 makes up only 0.00000000010% of all carbon atoms.
  2. Because of interaction and exchange with atmosphere and oceans, all living tissue maintains a fixed proportion of C-14. After death, the amount of C-14 begins to decrease.
  3. A C-14 date estimates the time since the death of once-living things, up to about 50,000 years.
  4. What fraction of original C-14 can be found in a sample after 10 HL? (.1%)
  5. Why is the daughter product, N-14, not retained by a specimen? (N-14 is a gas and escapes as it forms.)
  6. Use the decay calculator to determine the age of a rock that has 87% of its mass. (1203yBP)
  7. Use the calculations for the above in BP, substitute it into the calculator, and determine the date in A.D. (749 A.D.)
  8. Explain why the amount of C-14 produced in the Earth's upper atmosphere from cosmic rays striking N-14 is or is not constant over time. (It turns out that the production of C-14 changes somewhat from year to year because of variations in incoming cosmic radiation. Increased solar flare activity increases C-14 with higher amounts of C-14 found in organisms that lived during those times. We have developed calibration curves using tree rings to compensate.)
  9. What would be the age if you used the calibration or correction curves for the time in question 6? (950 A.D.)
Step 6:

Each group of four students will now pursue a specific investigation and report their findings back to the class. Hand out Student Sheets #4.1 and #4.2: Group Investigations. We now know about C-14, but we need to know what was done with the shroud to see if the results are valid. All students will go to the site www.shroud.com/nature.htm and then go to part of the article to answer their questions. Provide students with a FOCUS FOR MEDIA INTERACTION, asking them to answer the questions designated for their group on the Student Sheet #4. Students are to answer their questions and then be able to report back to the group. All students must have the answers. This will take 5 - 10 minutes. The questions and answers for each group are as follows:

Group 1 will go to the section called Measurement Procedures and answer these two questions: How did each of the sites clean their samples? How many samples did they make from the original cut? (All laboratories cleaned it microscopically. The Oxford Group cleaned each samples using a vacuum pipette, followed by cleaning in petroleum ether. Then, they divided the sample into three. Each was treated with hot strong acid, hot base, and again acid, with rinsing in between. Two of the three samples were then bleached. (Oxford had three samples -- each is 1/3.) The Zurich group precleaned each sample in an ultrasonic bath. They then split the sample in half. They saved the second half until the first half was done. The first half was subdivided into three portions. One third received no further treatment; one third was submitted to a weak acid at room temperature, weak base, and again acid, with rinsing in between. The final third was given a hot strong acid, base, acid, rinsing in between. After the first set of measurements revealed no evidence of contamination, the second set was split into two portions, to which the weak and strong chemical treatments were applied. (Zurich had five samples - 1/3, 1/3, 1/3, 1/4, 1/4.) The Arizona group split each sample into four subsamples. One pair of each textile was treated with dilute acid, dilute base, and again acid, with rinsing in between. The second pair was treated with detergent, distilled water, weak acid, another detergent, Soxhlet extraction with ethanol, and distilled water at 70 C in an ultrasonic bath. [Arizona had four samples - each 1/4))

Group 2 will go to the section called Controls and address the following: Controls are used to avoid conflicting results. Identify each of the samples as a variable or control. Tell the type of fabric and the age of the sample. Look at the previous paragraph and tell the type of cloth of the Shroud. Do all the samples match? (Sample 1 Experimental Shroud -- distinctive three-to-one herringbone twill weave of the shroud could not be matched in the controls. Sample 2. Control Linen -- eleventh to twelfth centuries AD. Sample 3. Control Linen -- 110 B.C. - A.D. 75. Sample 4. Control Threads -- A.D. 1290 - 1310. No, the samples do not match.)

Group 3 will go to the section Removal of Samples from the Shroud and answer the following questions: What was the size of the one sample taken from the shroud? (10mm x 70mm) This one sample was divided into three samples of what size? (Mass approximately 50mg) On what date was the sample taken? (April 21, 1988) Which laboratories did this as a blind study? (None) Which labs did part of the study as a blind study? (Oxford and Zurich, after combustion to gas, recoded the samples so that the staff making the measurements did not know the identity of the samples.)

Group 4 will go to Table 1 Basic Data and answer the following questions: For Arizona in sample one, what was the range of data and what was the average? (High value 701, low value 591, range 110, and average 646 yBP) For Oxford in sample one, what was the range of data and what was the average? (High value 795, low value 730, range 65, and average 750 yBP) For Zurich in sample one, what was the range of data and what was the average? (High value 733, low value 635, range 98, and average 676 yBP) Which lab has the highest range and has the largest or smallest value? (Arizona -- smallest)

Group 5 will go to Table 1 Basic Data and answer the following questions: For Arizona in sample three, what was the range of data and what was the average? (High value 2041, low value 1838, range 203, and average 1995 yBP) For Oxford in sample three, what was the range of data and what was the average? (High value 1990, low value 1955, range 35, and average 1980 yBP) For Zurich in sample three, what was the range of data and what was the average? (High value 1984, low value 1886, range 98 and average 1940 yBP) Which lab has the highest range and has the largest or smallest value? (Arizona -- largest)
Group Questions:

What was the size of each sample tested by each laboratory? (Oxford 50/3 mg, Arizona 50/4 mg, Zurich 50/6 mg and 50/4 mg)

How much radiocarbon is there in a 50/4 mg sample? (Carbon is about half the weight of carbohydrates and proteins, so divide the sample by half -- 6.25mg. C-14 is 1 x 10-10 of the weight of carbon, so move the decimal 4 places to the right and use the prefix nm.-- 0.000625 ng)

Is there any truth to the following quote? "The laboratory that has larger samples had less variation in the dates." Explain. (True: a smaller sample has less C-14 and a small mistake can cause a larger difference.)

Which lab did not do the experiment as a blind study? (All but Zurich and Oxford did it as a blind study half way through. Arizona did not.)

Let us suppose that Zurich was the only station that was correct. How old would the sample 1 (the Shroud of Turin) be? (You did this problem on Student Sheet #3 Questions #6, 7, 9. It would be dated 950 A.D.)

Did microbiological contamination (fire, dust, etc.) in any way affect the result of the carbon-14 dating? (No it does not appear to.)

To summarize, tell students that the more we know, the more we realize we don't know. Using radiocarbon dating, the Shroud of Turin does appear to date back to the Middle Ages. It does not appear to be contaminated by any microbiological accumulations, or by the fire, as the sample was taken away from the charred area. But the fire has not been disproved. Could it have caused a drying out and cooking of the sample and thus changed the radioactive date? A radiant photodynamic event has also not been disproved. This is outside our human experience, so it may or may not be able to be studied.

Culminating Activitie

Radioactive Decay Model


Step 1:

Go to www.exploratorium.edu/snacks/radioactive_decay.html and give students graph paper. Provide students with a FOCUS FOR MEDIA INTERACTION, asking them to read the sections entitled "The Materials," "The Assembly," and "To Do," and determine they will need and what they will do. Discuss. Students will need a shoebox and cover, 100 pennies, a pencil, and two sheets of graph paper. They will put all pennies in the shoebox, shake the box, and then remove all the "tails" and place them in one column at the edge of the table. Then they will shake the box again, remove all the "tails" again, and place them in a second column, and complete the activity following the directions on the Web site.

Step 2:

Make a data table at the top righthand corner of the graph paper. This graph should have four columns showing # of tosses starting at 0 to the end, total # of heads remaining starting at 100 and going to 0, total # of tails produced starting at 0 and going to 100, # of tails produced during each shake. Set up a graph and plot the data.

Step 3:

The teacher should discuss the following:

What does the decay curve look like? (Exponential decrease -- it gets half as big each time.) Why didn't we use nickels to represent the product produced during the decay of C-14? (The product is N14, which is a gas. This gas diffuses into the atmosphere.) How many time periods is represented by one shake of the box? (One half-life.) How could we have made this lab more accurate? (Average the class data.)

Step 4:

Plot the product curve, or the total number of tails as a second line on the graph. What does this look like? (It is the reciprocal of the decay curve. It increases instead of decreasing as time goes on.) Where do the two graphs intersect? (At the half-life.)

Step 5: Alternate or Additional Activity

Have students decide what constitutes an "upside-down" or inverted tails side of a penny. How perfectly "upside-down" does the image on the tails side need to be to be qualified as inverted? Draw pictures of the limits of what it could look like. Repeat the experiment, but only remove the tails that "certifiably" upside-down according to the class's definition. Repeat the experiment as you did above but with the new twist. Keep track of the amounts as you did in the above lab but this time average the class data. Have students set up an individual data table and a class data table. Plot the decay curve and the product curve. What is the difference? (The "heads" decay curve is shallower, as is the upside-down "tails" product curve. Depending on the students' definition of an upside-down tails, the results will change. The class must agree on the definition so that the class total will make sense.) What is the half-life? (The point where the two curves intersect.)

Cross-Curricular Activities

SOCIAL STUDIES/LANGUAGE ARTS
Assign students to a debate. Is the Shroud of Turin real or a fake? (You may question or defend the accuracy of the new radiocarbon dating using very small amounts.)

DRAMA
Assign a group of students to write and perform a play or dance showing the radioactive decay of an element.

SCIENCE/MATH
Go to http://ehs.ucsc.edu/rs/decay.html. Provide students with a FOCUS FOR MEDIA INTERACTION, asking them to substitute the following information into the calculator -- mass 0.000625 (ng) nCi, check C-14, 1/1/100 for the start date and 1/1/1950 for the current date. What is the amount left? (.0005 ng.) Use a start date of 1/1/800. Is there a difference? (Not that we can see.) Use the following two start dates and tell if there is a difference 1/1/900 and 1/1/1940. (Not that we can see.) How accurate is this computer for small amounts of C-14? (Not that accurate.) Change the start amount to 100 (like 100%) and use two start dates: 1/1/100 and 1/1/1300. What is the difference now? (You get twice the product but this does not mean the sample must be twice as big.)

How old is the earth and which radioactive elements do we use to date the earth? (4.6 billion years and we use the U238 / Pb206 ratio in rocks. Students should try to interpolate the decay.)

SCIENCE
Why is radioactive iodine used to treat diseases of the thyroid gland? What are the decay products of radioactive iodine?

MATH
Use the products produced by radioactive decay and determine the formula for the exponential increase.


Community Conections

Visit your local college or university's Web site and ask a geologist if they wouldn't mind answering your students' emails on the dating of rocks using radioisotopes for one week.

Invite a forensic scientist in your community to talk about how they perform carbon dating. (Use email if they can't come in person.)

Invite police detectives to come to your class and discuss cases they have had that used radiocarbon dating. (Use email if they can't come in person.)