Title: Rock of Ages- A Half-life Analog

Author:
 Steve Bower, Waunakee High School, 100 School Drive, Waunakee, WI 53597
sbower@waunakee.k12.wi.us

Grades:  6-12

Overview of Lesson: This exercise studies a half-life analogy and applies it to radioactive decay analysis. This large scale model will clarify how radiometric age dating is used to accurately date once living organisms or the age of rocks. The Parent atom and Daughter atom relationship will be examined.

Suggested Time:
 45 minutes for data and graphing

Students' Prior Knowledge: Students should be familiar with the concepts of perimeter and area and also with using a grid for measuring.
(Previous lessons on mapping and scale from this site are helpful).

Background Information: In radiometric dating, different isotopes are used depending on the predicted age of the rocks. Samarium-deodymium dating is used for very old rocks since these elements have a half-life of 108 billion years. Potassium/Argon dating is good for rocks 100,000 years old since Potassium 40 has a half-life of 1.3 billion years! And finally, Uranium/Lead dating since U-238 has a half-life of 4.47 billion years. It is used for dating zircon crystals in igneous rocks.

By comparing the percentage of an original element (parent atom) to the percentage of the decay element (daughter atom), the age of a rock can be calculated. The ratio of the two atom types is a direct function of its age because when the rock was formed, it had all parent atoms and no daughters.

Radiocarbon dating uses Carbon-14 which has a half-life of 5730 years. This is used for organic things such as wood, human artifacts made from once living organisms, and modern bone. Modern isotopic counting techniques (accelerator mass spectrometer) can date things as old as 70,000 years. This is done by counting individual C-14 atoms (the parents) remaining in the once living organism. A very accurate age can be determined. The daughter atoms (Nitrogen-14) are lost to the atmosphere as elemental nitrogen.

Materials:
Student Activity: This lab has four parts: acquiring data, recording data, graphing data, and interpreting data. Each student will have a specific task during this lab. Everyone must complete the data table and graphs.

Student Tasks: Work in groups of three.
Person one (_________________) is responsible for keeping track of the number of Parent Atoms. These will be represented by the M&M's.

Person two (________________) is responsible for counting the Daughter Atoms. Reeses Pieces will be used for these.

Person three (_________________) is responsible for getting graph paper and organizing the groupıs graphing activity which will be done by all.

Procedure:
  1. Place the M&M's (supplied by your teacher) in the ziplock bag and seal it. These candy pieces represent the ______________________.
    Your groupıs total number of Parent Atoms = ______________________.

  2. Shake the bag for several seconds and lay it on the table. Open it and remove only the candy pieces with the "M" showing. These are the Parent Atoms which transmute (decay) to a new element, the Daughter element.

  3. Count the remaining and removed Parent Atoms. Record the numbers in the data table below. Do not put the removed Parent Atoms back in the bag. (DO NOT EAT THEM YET!)
    Teacher Signature: ____________________ (necessary to continue)

  4. Replace the removed Parent Atoms with an equal number of Reeseıs Pieces. These new candy pieces are the Daughter Atoms.

  5. Record the number of Daughter Atoms added in the table below. Check your progress. The total number of M&M's and Reese's Pieces in your bag must be the same as the number of M&M's you started with.

  6. Seal the bag and shake it for several seconds. Open it. Count and remove only the Parent Atoms with the "M" showing. Fill in your data table. Do not put the removed Parent Atoms back in the bag. (DO NOT EAT THEM YET!)

  7. Replace the Parent Atoms you removed with the same number of Daughter Atoms.
    Teacher Signature: ____________________ (necessary to continue)

  8. Repeat the above procedure until all of the Parent Atoms have changed into Daughter atoms. This process is called transmutation.

    At each step record the Parent Atoms removed and the Daughter Atoms added.

    Data Table
    shake    Total            Total        Number of      Calculated age (years)
    #        parent           daughter     half-lives        
             atoms            atoms                       
    
    0             0            0           C-14           K-40
    
    1
    
    2
    
    3
    
    4
    
    5
    
    6
    
    7
    
    8
    
    9
    
    10
    
    11 
    
Graphing Data: Prepare a graph by labeling the X-axis with half-life (_____________ )
and the Y-axis with radioactive elements ( _______________).
Complete both graphs.
  1. Number of Half-lives VS. Total Parent Atoms.
  2. Number of Half-lives VS. Daughter Atoms.
When you complete your graph, write your data on the board for each student to copy.

Summing Up:
  1. Approximately what percent of the remaining PARENT Atoms did you remove after each shake? Why?

  2. Each shake represents a "half-life" for the "M&M" PARENT Atoms. What does half-life mean? (Put this meaning in your own words. Check what your book has to say.)

  3. If you started with 100 "M&M's", would the half-life change? Please explain.

  4. Use a calculator to complete this question. In nature, Parent Atoms decay into Daughter Atoms in a predictable mathematical order. Half-life is defined as; "The time required for half of any given amount of a radioactive substance (Parent Atoms) to decay into another substance (Daughter Atoms)".

    Try multiplying 1/2 X1/2 over and over to determine if you ever get to zero.

    1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2

    Will a small amount of the Parent Atom always remain? Yes or No

  5. Carbon-14 has a half-life of 5730 years. How old would a real fossil be after eight Carbon-14 half-lives? Show your work. (Hint: Refer to your graph for help.

Teacher Notes: Carbon-14 analysis of organic materials is of keen interest to paleontologists and the lay person alike. Recent development in the uses of accelerator mass spectrometry has greatly extended the usefulness of this technique. Currently, single atoms of C-14 can be counted and dates pushing 70,000 seem to be the limit. The element carbon has three isotopes, carbon- 12, carbon-13 and carbon-14.

Both C-12 and C-13 are stable isotopes (C-12 has 6 neutrons and C-13 has 7 neutrons in the nucleus), however C-14 is unstable and radioactive. It decays through the loss of an electron (beta decay) into its daughter element, elemental nitrogen-14. The half-life of C-14 is 5730 years and is the time it takes any given amount of C-14 to change back to N-14.

Carbon -12 and 13 make up the vast majority of the carbon reserves in the Earthıs oceans, atmosphere, fresh water and biosphere. This carbon exchange reserve consists of over forty trillion metric tons. Of that total, a mere sixty tons is C-14.

Due to the short half-life of C-14, the entire reserve would be exhausted in a few thousand years. Therefore, in order for C-14 to be used it must be continually renewed. This renewal happens when cosmic rays bombard the upper atmosphere and convert small quantities of nitrogen into C-14. As C-14 is lost through decay it is being created at a constant rate which creates a steady amount of C-14, the 60 tons mentioned before.

Since all green plants use carbon as basic building blocks during the process of photosynthesis, C-14 is present plant materials and animals who directly or indirectly depend on them. Once an animal or plant dies, the amount of C-14 in their tissues is not replaced. The C-14 begins to diminish at a constant rate. After 5730 years, half of the original amount has changed into N-14.

A theoretical difficulty with using C-14 is the assumption that the rate of cosmic radiation striking the Earth's upper atmosphere has remained constant over time. Clearly fluctuations have occurred, however enough is known about these changing rates for them to be allowed for.

Student Procedure: Have students work in groups of three and assign each a task. Have them write their names in the blanks and answer the questions #1. The total number of Parent Atoms will vary from group to group. A small plastic or paper cup filled about half way will yield about 25 plain "M&M".

The Teacher signatures serve two purposes. The first is to slow them down until each student has a chance to read the background. The second is to allow you a chance to see to it they understand the difference between parent and daughter atoms.

The second Teacher signature is a moment in time when you check if they are replacing the parent atoms with daughter atoms. This is when each group is given an equal number of Reeses Pieces which will be used as Daughter atoms.

Please note: This step is important because students must be reminded of the Law of Conservation of Mass. Atoms are neither created or destroyed. Parent atoms change into Daughter atoms and in this lab, students physically replace the parents with daughters. This models the Law of Conservation of Mass.

Date Table: Each shake represents a half-life. The total parent atoms will vary from group to group depending on the number of M&M's each is given. The Parent Atom data table column is wide enough so students can enter their group data and class totals. By completing both, the students begin to realize the significance of the definition of half-life when it mentions, "any given amount of radioactive material". No matter how much they begin with the calculated age remains the same for each parent atom.

The Calculated Age column is to be used by students to calculate the half-life years for two isotopes of different elements. The C-14 data will be used for studentıs to analyze the age of organic materials and the K-40 data will be used for the analysis of the age of rocks.

Graphing the Data: Students can use traditional methods to graph the data or computer programs to assist. In either case, it is recommended each student has his/her own graph. The parent and daughter curves must be labeled. Since the curve will be used for all types of decay, labeling them is not necessary.

Summing Up:
  1. 50%, Each candy piece has two sides, therefore the chances of either side landing face up is 50%.
  2. Half-life is defined as the amount of time necessary for half of any given amount of radioactive material (parent atom) to decay into another atom (daughter atom).
  3. The half-life will not change. One can start with "any given amount".
  4. Yes, a small amount of the parent Atom will remain. This concept is successive halves. No matter how far you multiply, a fraction of the whole will remain. In the case of C-14, eventually only a single atom will remain.
  5. 5730 years X 8 = 45840 years.
National Science Education Program Standards:
A: All elements of the K-12 science program must be consistent with the other National Science Education Standards and with one another and developed within and across grade levels to meet a clearly stated set of goals.

B: The program of study in science for all students should be developmentally appropriate, interesting, and relevant to students' lives; emphasize student understanding through inquiry; and be connected with other school subjects.

D: The K-12 science program must give students access to appropriate and sufficient resources, including quality teachers, time, and materials and equipment, adequate and safe space, and the community.

E: All students in the K-12 science program must have equitable access to opportunities to achieve the National Science Education Standards.

F: Schools must work as communities that encourage, support, and sustain teachers as they implement an effective science program.

National Science Teaching Standards:
A: Teachers of science plan an inquiry-based science program for their students.*

D: Teachers of science design and manage learning environments that provide students with the time, space, and resources needed for learning science. *

National Science Assessment Standards:
B: Achievement and opportunity to learn science must be assessed.

D: Assessment practices must be fair.

National Science Content Standards:
K-4: As a result of activities in grades K-4, all students should develop,
A - (Science Inquiry): abilities necessary to do science inquiry and understanding about science inquiry.

D - (Earth and Space Science): an understanding of properties of earth materials.

5-8: As a result of activities in grades 5-8 all students should develop,
A - (Science Inquiry): abilities necessary to do scientific inquiry and understandings about scientific inquiry.

D - (Earth and Space Science): an understanding of Earth's history.

E - (Science and Technology): understandings about science and technology.

G - (History and Nature of Science): science as a human endeavor, the nature of science and the history of science.

9-12: As a result of activities in grades 9-12, all students should develop,
A - (Science Inquiry): abilities necessary to do scientific inquiry and understandings about scientific inquiry.

C - (Life Science): an understanding of biological evolution.

D - (Earth and Space Science): an understanding of the origin and evolution of the earth system.

E - (Science and Technology): abilities of technological design and understanding about science and technology.

G - (History and Nature of Science): an understanding of science as a human endeavor, nature of scientific knowledge and historical perspectives.

Wisconsin State Science Standards:
A4.2
http://www.dpi.state.wi.us/standards/scia4.html
When faced with a science-related problem decide what evidence, models, or explanations previously studied can be used to better understand what is happening now.

C4.2
http://www.dpi.state.wi.us/standards/scic4.html
Use the science content being learned to ask questions, plan investigations, make observations, make predictions, and of explanations

C4.4
http://www.dpi.state.wi.us/standards/scic4.html
Use simple science equipment (including rulers, and computers) safely and effectively to collect data relevant to questions and investigations.

C4.5
http://www.dpi.state.wi.us/standards/scic4.html
Use data they have collected to develop explanations and answer questions generated by investigations.

C4.6
http://www.dpi.state.wi.us/standards/scic4.html
Communicate results of their investigations in ways their audiences will understand by using charts, graphs, drawings, written descriptions, and various other means.

Wisconsin Math Standards:
A.4.3
http://www.dpi.state.wi.us/standards/matha4.html
Connect mathematical learning with other subjects, personal experiences, current events, and personal interests: use math in a way to understand the other areas of the curriculum (e.g., measurement in science, map skills in social studies).

D.4.5
http://www.dpi.state.wi.us/standards/mathd4.html
Determine measurements by using basic relationships (such as perimeter and area) and approximate measurements by using estimation techniques.