Rock of Ages- A Half-life Analog
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.
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:

  • Gallon Ziplock bags
  • M&M's
  • Reese's Pieces
  • Paper
  • Pencil and two colored pencils
  • Graph Paper

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 group¹s 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 group¹s 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 Reese¹s 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.

Shake # / Total Parent Atoms / Total Daughter Atoms / Number of Half-Lives / Calculated Age (Years)
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15

Graphing Data: Prepare a graph by labeling the X-axis with half-life (______)
and the Y-axis with radioactive elements ( ______).
Graph the following data using two different colored pencils.

  1. Number of Half-lives VS. Total Parent Atoms.
  2. Number of Half-lives VS. Daughter Atoms.

Analysis and Conclusion:

  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 (0.5) X1/2 (0.5) 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? Explain your answer.
  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.)