# Science

Hands-On Labs SM-1 Lab Manual

99

EXPERIMENT 13: Radioactive Decay Read the entire experiment and organize time, materials, and work space before beginning.

Remember to review the safety sections and wear goggles when appropriate.

Objectives: To simulate the decay of a hypothetical radioactive element; To graph the results of the simulated decay; and To determine the half-life and decay constant of the element. Materials: Student Provides: Coffee cup Paper, pen, tape Computer with spreadsheet software From LabPaq: Split peas Discussion and Review: Certain elements are made up of atoms whose nuclei are naturally unstable. These elements are said to be radioactive. The nucleus within an atom of a radioactive element will decay into the stable atomic nucleus of another element by emitting or capturing atomic particles. The unstable element is called the “parent” element and the stable element is called the “daughter” element. The continuous process of disintegration of unstable radioactive nuclei is called radioactive decay. It is impossible to predict which particular nuclei and when any one of the nuclei in a sample will disintegrate. However, it is possible to predict the average rate of nuclei that will decay during a given time period. This percentage, expressed as a decimal, is called the decay constant, . Mathematically, the decay process is modeled exponentially:

where No is the original number of nuclei present and N is the number of nuclei present at time t. The half-life, t1/2 of a radioactive sample is the time required for one half of the nuclei present to decay. If the above exponential equation is solved for t when N = No /2, the result is (Remember “ln” refers to the natural log):

We will assume that once an unstable “parent” decays the resulting “daughter” is stable and can emit no more particles. In more complicated cases the daughter might be unstable as well but we will not deal with that situation now.

Hands-On Labs SM-1 Lab Manual

100

PROCEDURES: In this exercise, you will calculate the decay constant and half-life of a sample using split peas to simulate the decay of radioactive nuclei. Peas lying on their flat side will be “parents” representing nuclei not yet decayed. Peas lying on their rounded side will be “daughters” representing the decayed nuclei. Each trial represents one unit of time. We assume a time interval of 2 minutes for each trial, but since this is a simulation, we could have assumed any time interval we wanted. 1. Set up a data table as follows to record your observations. Data Table: Trials Time –

minutes Parents = Peas lying flat

# per trial Daughters = Peas on rounded side

# per trial cumulative # 0 0 50 0 0 1 2 2 4 3 6 4 8 Etc. 0 50

2. Tape several sheets of white paper to your work table. Having this white background

will make counting the peas easier. 3. Count out exactly 50 individual split peas and put them into a coffee cup. Record 50

peas under time trial 0 on the data table. 4. Cover the cup with your hand, shake the contents for several seconds, and pour the

peas from the cup onto the paper in such a way that a single layer of peas is formed. 5. Count the number of parent peas lying on their flat side, and the number of daughter

peas lying on the rounded side. Record these values under Trial 1 of the Data Table. 6. Set the daughters aside, but put the parent peas from the trial back into the cup.

Shake as before and pour them back onto the paper for another trial. 7. Again, count and record both the flat lying parent peas and the rounded-edge lying

daughter peas. For the parents, record only the number of peas counted. For the daughters, you should record the number counted, then add that number to the previous count so that a running cumulative total of daughters can also be recorded. See the example on the following page for clarification.

8. Repeat this process until no split peas are remaining.

Hands-On Labs SM-1 Lab Manual

101

Example: The example below assumes that for trial 1 you had 23 flat lying parents and 27 daughter peas lying on the rounded sides. Next, you used only the 23 parents for trial 2 and got 12 parents and 11 daughters. Under trial 2, you record the 12 parents and 11 daughters, then add the 11 daughters to the previous count of 27 for a cumulative total of 38 daughters. Example DATA TABLE: Trials Time –

minutes Parents = Peas lying flat

# per trial Daughters = Peas on rounded side

# per trial cumulative # 0 0 50 0 0 1 2 23 27 27 2 4 12 11 38 3 6 4 8

Graphing: 1. Graph the results of your experiment. Plot the number of parent atoms (peas)

remaining after each trial on the y-axis. Plot the time on the x-axis. 2. Construct another graph. Plot the number of daughter atoms (peas) after each

observation on the y-axis. Plot the time of the observation on the x-axis. 3. Explain the difference in the two graphs. 4. Determine the half-life of this hypothetical element from your graph.

5. Using the equation calculate the decay constant: (ln 2 = 0.693) λ = 0.693/ t ½ Remember “ln” refers to the natural log.

- SM-1 Manual COLOR 105 08-17-07.pdf