The Half-life of M&Mium

Purpose: To study a half-life analogy, and to apply it to radioactive decay analysis.

Materials: gallon Ziplock bags, cups, M&M’s, Reeses Pieces, paper, pencil, graph paper

Background:

Radioactive decay analysis allows researchers to determine the length of time an element will remain in a certain radioactive state. This is important because nuclear power plants must know how long their waste products will need to be stored, as well as how long the material they are stored in must last in the environment to avoid leaks. With the passing of years since the Chernobyl disaster it is also crucial to know how long radioactive substances will stay in the environment before decaying into less harmful elements. Today’s large scale “model” will also 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.

In radiometric dating, different isotopes are used depending on the predicted age of the rocks. Samarium-deodymium dating is for very old rocks since these 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 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 or 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 organisms. A very accurate age can be determined. The daughter atoms (Nitrogen-14) are lost to the atmosphere as elemental nitrogen.

Procedure:

  1. Place the M&M’s in the ziplock bag and seal it. These candy pieces represent the radioactive parents of the element M&Mium. Count your total number of Parent Atoms. Record this number in the data table under “Total parent atoms” next to Shake # 0 (this represents zero time when no time has passed).
  1. Shake the bag for several seconds and lay it flat on the table. Carefully open the bag and remove only the candy pieces with the “M” showing. Count the number of theseParent Atoms which have decayed to a new element, the Daughter Element. Do not place them back in the bag. Put them in the empty cup. Record this number in the data table under the column “Total Daughter Atoms.”

3. Count up how many “Total Parent Atoms” (M&M’s) are still left in the bag and record in the “Total Parent Atoms” column. Then fill in the “Number of Half-lives” that have occurred. If it is shake #1, then 1 half-life of time has just occurred.

4. Now count out the number of Reeses Pieces that matches the number of decayed parent atoms that you just removed from the baggie. Place these in the baggie with the rest of your atoms, and seal the bag. These will represent the newly formed Daughter Atoms. These daughter atoms are not the same elementthat we started with, thus are represented by white M&M’s so that we can tell them apart from our still remaining parent atoms (regular colored M&M’s). In other words, the number of atoms we start with must match the number of atoms we end with, even though they may be atoms of different elements now.

5. Before going on to the next shake or half-life of time, calculate the age in years in the last two columns on the data table. To do this you must know the half-life of the parent atoms or element (# of years it takes for half an amount (mass or # of atoms) of parent element to decay (transmute) into a daughter element). For example for both Carbon-14 atoms and Potassium-40 atoms at 0 half-lives, no time has passed so 0 years will be put into the data table in that row. Now if our M&M’s were really Carbon-14 atoms, after about 5730 years about one-half of the parent atoms (regular colored M&M’s) would decay into the nitrogen daughter atoms (white M&M’s). After another half-life of time (2nd shake), another 5730 years would be added to the previous amount of time. Or simply multiply the half-life time of the element by whichever half-life or “shake” you are on.

6. Repeat steps 2 through 5 until you have only one Parent Atom (regular colored M&M) left. When filling in the “Total # of Parent Atoms Remaining” column make sure to subtract the number that has decayed after each shake from your previous value in this column, and add this number to the previous “Total # of Daughter Atoms” column. After every half-life or “shake” you should be able to add these two columns together and get the total number of atoms you started this activity with. The number of atoms does not change throughout the nuclear decay process, they simply change from one element into another in this case.

7. When you are finished, have your teacher check your table, then you may munch on the M&M’s while working on the graphs and questions.

Data Summary: (enter your data in the data table)

Graphing Your Data:

Using the graph paper provided, prepare a graph by labeling the X-axis with “number of half-lives (shakes) and the Y-axis with “number of atoms”. On the graph plot the two lines, and draw a line of best fit (a curve in this case) that appropriately shows the change in the number of parent and daughter atoms over time (remember a half-life is time). Make a key on the graph to show which line is which, add color.

Line 1: # of Parent Atoms vs. Number of Half-lives (shakes)

Line 2: # of Daughter Atoms vs. Number of Half-lives (shakes)

The title of graph should be “The Effect of Time on Radioactive Decay”.

A second graph just like the graph described above should be prepared using Excel.

The Half-life of M&Mium

Student Tasks:

Student 1 (______) is responsible for keeping track of the Parent Atoms. These will be represented by the M&M’s.

Student 2 (______) is responsible for counting the daughter atoms. Reeses Pieces will be used for these.

Student 3 (______) is responsible for getting the graph paper and organizing the group’s graphing activity which will be done by all.

Procedure:

  1. Place the M&M’s in the zipolock bag and seal it.The M&M’s represent the ______.

Your group’s total number of Parent Atoms = ______.

  1. Place the M&M’s in the bag and shake for several seconds.Open it and remove only the candy pieces with the “M” showing. These are Parent atoms which decayed to a new element, the Daughter element.
  2. Count the remaining and removed Parent Atoms. Record the number in the data table. Put the removed Parent Atoms in the cup – not back in the bag. (DO NOT EAT THEM YET!)

Teacher signature______(necessary to continue)

  1. Replace the removed Parent Atoms with an equal number of Reeses Pieces. These new candy pieces are the Daughter atoms.
  2. Record the number of Daughter atoms added in the data table. Check your progress. The total number of M&M’s and Reeses Pieces in the bag must be the same as the number of M&M’s you started with.
  3. Seal the bag and shake for several seconds.Open it, count and remove only the candy pieces with the “M” showing. Fill in your data table. Put the removed Parent Atoms in the cup. (DO NOT EAT THEM YET!)
  4. Replace the removed Parent Atoms with the same number of Daughter atoms.
  5. Teacher signature______(necessary to continue)
  6. Repeat the procedure until all of the Parent Atoms have changed into Daughter atoms. This is the decay process.
  7. At each step record the Parent Atoms removed and the Daughter Atoms added.

Graphing: Prepare a graphby 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

Data Table:

shake number / total parent atoms remaining (M&M’s) / total daughter atoms formed (Reeses Pieces) / number of half-lives that have passed / calculated time for decay process to occur (years)
carbon-14 (5730 years) / potassium-40 (1.3 billion years)
0 / 0 / 0 / 0 / 0
1
2
3
4
5
6
7
8
9
10
11

Analysis Questions:

  1. Approximately what percent of the remaining PARENT Atoms did you remove after each half-life or “shake”? Why?
  1. Each shake represents a "half-life" for the PARENT Atoms. What does half-life mean? (Put this meaning in your own words. Check what the introduction has to say.)
  1. How many half-lives did your radioactive Parent Atoms sample undergo?
  2. Looking at your completed data table, if the Parent Atoms were carbon-14 atoms, approximately how many years would have passed during the first 3 half-lives of the decay process?
  1. If the parent atoms were potassium-40 atoms, approximately how many years would have passed during the first 3 half-lives in the decay process?
  1. If you started with 1000 "M&M's", would the half-life change? Please explain.
  1. Would the total number of half-lives or “shakes” that the Parent Atoms go through change if you started with more of the original Parent Atoms? Why or why not?
  1. 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 ½ × ½ over and over. Do you ever get to zero?

Will a small amount of the Parent Atom always remain?

Why is the “lifetime” of a radioactive sample not a meaningful concept due to this finding?

  1. 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.)
  1. Before the spent (used) fuel rods are removed from a nuclear reactor site, they are placed in a deep pool of water and kept under water for a minimum of several months. Why is the world finding it difficult to find a place to store radioactive wastes once they are removed from these pools of water?

Conclusion Summary: