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# Simulating the Decay of a Radioactive Element

By Bruce Wilson
Product Manager, Chemistry

Tired of counting pennies to plot a half-life curve? This activity takes less time than counting pennies, uses equipment you already have, involves cooperative group work, and allows your students to run multiple trials.

This activity simulates the decay of a radioactive element. Water flows from a buret following a first-order reaction rate, the same order rate as radioactive decay. As a radioactive substance decays, it forms a new isotope. The amount of water delivered from the buret represents the new "daughter" isotope, whereas the water remaining in the buret represents the amount of undecayed "parent" isotope. Plot both parent and daughter isotope data on the same graph, with mL on the y-axis and time in min on the x-axis. The point where the 2 lines intersect represents the 1st half-life of the parent isotope. Read the 2nd half-life from the graph and use it to assess the accuracy of the graph.

#### Materials

• Buret, 50 mL (with buret clamp and stand)
• Water
• Beaker, 100 mL (or larger)
• Timer (that measures seconds)

#### Procedure (for students)

1. Form a trio with 2 partners. One of you is the timer, another the recorder, and the 3rd the reader.
2. Fill a buret to the top mark (usually 0 mL) with water.
3. Place a beaker under the buret tip.
4. Open the stopcock and adjust the flow rate so that the buret delivers several drops a sec.
5. Without closing the stopcock, place your finger on the buret tip to stop the flow of water.
6. Fill the buret to the top mark and record the volume.
7. When ready to start timing, remove your finger from the buret tip to start the flow of water. Read the volume of water in the buret every 30 sec. Your partner will tell you when to measure the volume. Your other partner will record the value.
8. When the water reaches the zero mark on the buret or when the drop rate is very slow, stop the timer. See Table 1 for sample data.
9. Plot the volume of water delivered from the buret as a function of time. This plot represents the formation of the daughter isotope. Your graph should gently increase along a curve and then approach a horizontal line toward the end of the experiment.
10. To plot the decay of the parent isotope, calculate the amount of water remaining in the buret at each point. For the 1st point, the value is 20.5 mL minus 0 mL; the 2nd point is 20.5 mL minus 3 mL and so on. See Table 1 for examples. Plot this new column of data as a function of time to see the parent isotope's decay.
11. Where the 2 curves intersect is the half-life. In this case, the point occurs at 10.3 mL, 2 min. That's the point where ½ the original volume is delivered from the buret.
12. To test the accuracy of your curve, determine the 2nd half-life. Trace the curve to double the time of the 1st half-life, in this case 4 sec. At 4 sec, the volume remaining in the buret is 4.1 mL. From the 1st half-life, one would estimate this value to be ½ of 10.3 mL or 5.15 mL.
13. Calculate the percent error of your half-life determination as shown:
(5.15 mL – 4.1 mL)/5.15 mL × 100% = 21%
14. Without adjusting the stopcock, repeat the experiment several times and calculate an average half-life for your setup. Determine the percent error of your curve based on your average value.

Table 1: Volume of Water Delivered from a Buret

Time/Minutes Buret Reading/mL Volume Delivered/mL Volume Remaining in Buret/mL
0 0.5 0.0 20.5
0.5 3.5 3.0 17.5
1 6.1 5.6 14.9
1.5 8.6 8.1 12.4
2 10.7 10.2 10.3
2.5 12.6 12.1 8.4
3 14.3 13.8 6.7
3.5 15.7 15.2 5.3
4 16.9 16.4 4.1
4.5 17.9 17.4 3.1
5 18.7 18.2 2.3
5.5 19.3 18.8 1.7
6 19.9 19.4 1.1
6.5 20.4 19.9 0.6
7 20.7 20.2 0.3
7.5 21.0 20.5 0.0

Figure 1: Volume of Water as a Function of Time

#### Experiment tips

• Start the exercise with any volume of water in the buret.
• Just record your starting volume and subtract this amount from the values you read off the buret during the experiment, before you graph your data.
• End the exercise with any volume of water delivered from the buret, as long as the graph generates a curve that ends with a nearly horizontal line.
• If your graph does not approach a horizontal line over the last few points, your experiment ended too soon.
• If there are not enough points on your graph to show a smooth curve, consider reducing the flow-rate of the buret or take readings more often (e.g., every 15 sec rather than every 30 sec).