Materials Included In Kit

Additional Materials Required

Lab Hints

• Have students use only a small piece of tape to attach each tile to the storyboard. This will allow students to modify the arrangement of the tiles, as needed, and will permit the tiles to be reused.
• In addition to potassium-40 decay, the decay of uranium-238 to stable lead-206 has also been used to estimate the age of rocks.

Answers to Questions

1. How and where is carbon-14 produced?

   Cosmic rays from space collide with atoms in the upper atmosphere to produce high energy neutrons. The neutrons collide with nitrogen-14 atoms to produce carbon-14 and release a proton.

   {12625_Answers_Equation_8}
2. How is carbon-14 different from carbon-12? Give two differences.

   Carbon-14 has two more neutrons in its nucleus than carbon-12 and it is radioactive.

3. If more and more C-14 is constantly being produced, why doesn’t its concentration in the atmosphere keep increasing?

   As more radioactive 14C is produced, the rate of decay of 14C increases until the rate at which 14C is produced equals the rate at which it decays.

4. Explain the “cup” analogy used in the puzzle (Part I).

   As water drips into the cup, it slowly trickles out the bottom. Because the rate of filling the cup is initially greater than the rate at which water leaks out of the cup, the volume of water in the cup increases. As the amount of water increases, the leak rate increases. This continues until a steady-state volume of water is reached (when the rate at which water drips into the cup is equal to the rate at which water leaks out of the cup.

5. Explain the pathway by which C-14 is incorporated into our bodies.

   The carbon-14 produced in the upper atmosphere is incorporated into CO₂. This ¹⁴CO₂ is distributed evenly throughout the atmosphere. Plants absorb ¹⁴CO₂ during photosynthesis. Some animals eat the plants, other animals eat those animals, and carbon-14 becomes evenly distributed throughout the food chain.

6. If we are constantly taking in more and more C-14, why doesn’t its concentration in our bodies keep increasing?

   As with the atmosphere, the rate of ingestion just equals the rate of decay.

7. As far as C-14 is concerned, what is the significance of death?

   No more uptake of carbon atoms occurs. The ratio of C-14 to C-12 decreases because carbon-14 starts to decrease at a constant rate due to radioactive decay.

8. For each of the following, decide whether or not C-14 dating could be used.

   ___Yes___To determine the age of a wooden axe handle believed to be 10,000–13,000 years old.
   ___No___ To determine the age of the oldest living pine tree believed to be 5,000–10,000 years old.
   ___Yes___ To determine the age of an animal skin believed to be 3,000–4,000 years old.
   ___No___ To verify the age of a man claimed to be 6,493 years old.
   ___No___ To determine the time of death of a murder victim who was found last Tuesday.
   ___No___ To determine the age of a wooden spear, believed to be 100,000–120,000 years old.

9. If a newly cut piece of wood gives a Geiger tube reading of 124 cpm (counts per minute) and an artifact from the same type of wood gives a reading of 31 cpm, how old is the artifact?

   One half of 124 equals 62 (1 half-life). One half of 62 equals 31 (2 half-lives). Two half-lives equals two times 5730 yrs or 11,460 yrs. The age of the artifact dates to 11,500 yrs – 2000 = 9500 B.C.

10. C-14 is not the only isotope used for radioactive dating. List some others and explain why they might be better suited in some cases. Hint: Consult reference sources.

    Potassium-40 is used because its half-life (1.3 x 10⁹ years) is much longer than that of carbon-14. This allows the dating of rocks and geological formations that are billions of years old. The age of the Earth has been estimated based on the decay of uranium-238 and thorium-232 isotopes.

11. In the puzzle, the spear is labeled 5200 B.C. Show the exact math that gives this number.

    The age of the spear, t, is equal to:
    t = –8270 ln(13.6 cpm/32.5 cpm) yrs
    t = 7,200 yrs old
    7,200–2,007 = 5,193 B.C. (Approx. 5200 B.C.)

Teacher Handouts

12625_Teacher1.pdf

12625_Teacher2.pdf

References

We are grateful to Bob Becker, Kirkwood High School, Kirkwood, MO, for providing us with the idea and instructions for this activity. This activity has been adapted from Nuclear Chemistry, Volume 18 in the Flinn ChemTopic™ Labs series; Cesa, I., Editor; Flinn Scientific: Batavia, IL (2006).

Introduction

Archaeologists and geologists have been able to reconstruct some of the ancient history of the Earth by “dating” various artifacts. The predictable process of nuclear decay can be used to date objects made of wood or cloth based on the amount of radioactive carbon-14 contained in the object.

Concepts

• Cosmic rays
• Radioactive decay
• Half-life
• Isotope ratios

Background

Cosmic rays continually bombard the upper atmosphere of the Earth. The rays collide with gases producing neutrons, which in turn collide with nitrogen atoms to produce carbon-14 and knock out a proton (Equation 1).

Carbon-14 is radioactive and decays to nitrogen-14 by beta decay (Equation 2). The half-life, t_½, of carbon-14 is 5,730 years. The amount of carbon-14 in the atmosphere remains relatively constant over time. This is because the rate at which carbon-14 is produced is approximately equal to the rate at which it decays.

During photosynthesis, plants take up carbon-14, along with the much more abundant isotopes carbon-12 and carbon-13, in the form of carbon dioxide. The carbon-14 is incorporated into starch molecules in plants. Plants are consumed by plant-eating animals, which are then consumed by carnivores. Over time, this will cause living organisms to achieve a steady-state ratio of carbon-14 to carbon-12, which remains constant until the organism dies. At the time of death, the level of carbon-14 is approximately the same as the ratio of atmospheric carbon-14. After an organism dies, the number of carbon-14 atoms is depleted due to radio active decay, causing the carbon-14 to carbon-12 ratio to decrease. If the ratio of carbon-14 to carbon-12 is known for a similar living organism, the age of an artifact can be determined. This is done by measuring the amount of carbon-14 in similar size samples of both the living organism and the artifact.

As time passes, the amount of carbon-14 in an artifact decreases according to the decay rate equation; Where

¹⁴C_o = initial amount of carbon-14
¹⁴C_t = amount of carbon-14 after time t
k = rate constant for carbon-14 decay.

The rate constant for radioactive decay is related to the half-life: For carbon-14 (t_½ = 5730 yrs), the value of the rate constant k is equal to {12625_Background_Equation_7} Rearranging Equation 3 to solve for t gives Since the radioactivity of carbon-14 is directly related to the number of carbon-14 atoms, the measured radioactivity (A) in counts per minute can be substituted into Equation 5. Equation 5 is then simplified to Equation 6: By measuring the carbon-14 activity in similar sample sizes of organic material for both the current organism and the artifact, the age of the artifact can be calculated.

After approximately six half-lifes have passed (6 x 5730, or 35,000 years), the activity of carbon-14 is reduced to near background radiation levels. Unless very sophisticated instrumentation is used, this limits the dating of artifacts by carbon-14 measurements to those less than 35,000 years old. To date objects of much greater age, a different naturally occurring radioactive isotope with a much longer half-life is used. One such isotope that is used for rocks and minerals is potassium-40. Potassium-40 decays by beta emission to argon-40, with a half-life of 1.3 x 10⁹ years. Since argon is a noble gas not naturally found in rock formations, the only source of trapped argon in minerals would be the result of potassium-40 decay. By determining the ratio of argon-40 to potassium-40, the age of a rock and everything deposited around it, may be determined.

Experiment Overview

The purpose of this activity is to solve a carbon-14 dating puzzle by arranging a set of story tiles and picture tiles in a logical sequence to explain the process of carbon-14 dating.

Materials

Procedure

1. Obtain four sheets of blank paper and connect them in the “landscape” direction using a glue stick. Make a one-half inch overlap for each seam. This will be the “storyboard.”
   {12625_Procedure_Figure_1}
2. Cut out or obtain the 21 story tiles and the 21 picture tiles.
3. Read each story tile, then arrange the story tiles in a logical sequence to create a story-line that explains the process of carbon-14 dating. Hint: The story line has been divided into three parts (I, II and III), and each tile has been labeled I, II or III to show where it belongs.
4. Once the story-tile sequence has been determined, use tape or glue to attach the story tiles in order to the storyboard.
5. Match the picture tiles to their corresponding story tiles and tape or glue them to the story board just below the story tiles. The result should resemble a narrative comic strip.
6. Use the story line and the background data to answer the Discussion Questions.

Student Worksheet PDF

12625_Student1.pdf