Chem

CHEM 101

Laboratory Series

Craig Benson

LAB #13: Half-Life of an Element*

Purpose

To gain an understanding of the statistical probabilities underlying the half-life of elements, and to better understand graphs and the presentation of scientific data.

Discussion

Radioactive elements contain nuclei that are unstable. Over time, these unstable nuclei decay, changing into a nucleus with a different number of protons and/or neutrons while releasing radiation. The half-life of an element is the time required for half of the atoms of a radioactive isotope to undergo decay. Some isotopes are relatively stable, undergo decay very slowly, and have extremely long half-lives. Uranium-238 has a half-life of 4.46 billion years! Other isotopes are extremely unstable, and have short half-lives, measured in tiny fractions of seconds.

The isotope francium-233 has a half-life of 22 minutes. That means that if you possessed 10 grams of francium-233, after 22 minutes you would have 5 grams of francium-233, while the remainder of the atoms would have been converted by some decay processes to other elements. After another 22 minutes (44 minutes after the beginning of the experiment), a further half of the atoms will have undergone decay, leaving you with 2.5 grams.

While it is possible to predict the percentage of atoms of an isotope that will undergo decay in a certain time span, it is not possible to predict which individual atoms within a sample will be the ones to undergo decay, as it is a random process at the level of individual atoms. The inability to solve this perplexing problem prompted a frustrated Albert Einstein to say, “God does not play dice with the Universe!”

Materials

· 64 M&M’s® or skittles® or Pennies or Puzzle Pieces

· Paper or plastic cup

Procedure

1. Obtain 64 M&M’s® or skittles® or Pennies or Puzzle Pieces and place them into your paper or plastic cup. Each M&M® or skittle® or Penny or Puzzle Piece represents a single atom of a hypotherical radioactive element (“onecentium”).

2. Cover the top of the cup and shake for 10 seconds, the half-life of our onecentium.

3. After 10 seconds, dump the M&M’s® or skittles® or Pennies or Puzzle Pieces on the table. Pick up ONLY the M&M’s with the “m” or in case of skittles with the “s” showing – these are still radioactive. Count all of the pennies that landed “heads up” or the the candies with “m” or “s”. Record the number in your data table. If you plan to use puzzle pieces, consider the puzzle face as heads up.

4. Return only the “heads up” pennies or puzzle pieces to the cup. In case you are using the M&M’s or skittles, return only the candies showing “m” or “s” to the cup (We assume that the “tails” pennies or puzzle pieces or candy side with no “m” or “s” mark have undergone decay.)

5. Shake the cup, and pour the item (M&M’s® or skittles® or Pennies or Puzzle Pieces) on the table. Once again, Count the pennies or puzzle pieces that landed “heads up” or the the candies with “m” or “s”. Record the number from this trial in your data table. Return these remaining “heads up” pennies or puzzle pieces or the the candies with “m” or “s”. to the cup, shake, and dump them on the counter. Each time, you are eliminating the tails pennies or puzzle pieces or pieces or candy with no “m” or “s” mark as if they had undergone radioactive decay.

6. Repeat this procedure, stacking and recording data after each trial, until there are no “heads up” pennies or puzzle pieces or no “m” or “s” marked candies to return to the cup.

7. Go back to the beginning, and repeat the procedure two more times, recording your data in the next columns of the data table.

Calculations

Calculate the average number of atoms remaining after each half-life and enter it on the data table. The average is the sum of the atoms remaining in each trial divided by the number of trials. Remember that, if you have no atoms remaining in a trial, you include a “0” for that trial in your calculated average.

Create a graph of the decay curve of onecentium on the attached graph paper. Plot the average number of atoms on the y-axis, and the elapsed time on the x-axis. Be sure to determine the appropriate scale of each axis (one box does not necessarily equal one atom). For each half-life, plot the average number of atoms. Be certain to include the 64 atoms you started with.

Add a trendline, by smoothly connecting the datapoints at each half-life. If you cannot connect your datapoints smoothly, your trendline can pass near each point but does not necessarily need to touch each point.

Data Table

Time	Pennies remaining Trial 1	Pennies remaining Trial 2	Pennies remaining Trial 3	Average pennies remaining
0 s	64	64	64	64
10 s
20 s
30 s

Postlab Questions

1. Calculate how many half-lives of a random radioactive sample would elapse before less than one-half of one percent of the initial sample remains.

2. How many half-lives elapsed before your sample of onecentium was gone? Compare this to your answer from Question 1 and explain any differences.

3. Products of radioactive decay can be hazardous to human health. Given the results of your experiment, why is the storage of radioactive waste a concern?

* Courtesy El Diamante High School Department of Chemistry.