Introduction
Download the TI-82 simulation program.
Download the TI-83 simulation program.
Unstable nuclei continually undergo a process of disintegration
called radioactive decay. Although it is impossible to tell exactly
which nuclei in a sample will disintegrate, it is possible to
predict, on average, the percentage 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 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:
In this exercise, you will calculate the decay constant and half-life of a sample in a simulation.
Instructions
1. Make a table in your lab notebook to record the elapsed time and nuclei count for a decaying sample. Be sure to record data as the sample runs. Begin the simulation by selecting HALFLIFE from the program menu on your TI-82/83. Begin the simulation by selecting ENTER.
2. Enter the number of trials as 10, and select ENTER. The number of trials is equivalent to the number of time increments that will pass as the sample decays. The simulation will give you a graphic of a decaying sample. Note the pattern of decay. Create a data table and record the elapse time and value of N in your notebook. Do not forget No. When the ELAPSE TIME=10, select ENTER.
3. Create a graph from your data for number of nuclei vs. elapsed time, using time as the independent variable.
4. Use the trace feature to determine the time at No/2 . This value corresponds to the half-life of the sample. Record this value as t1/2 in your lab notebook.
5. Calculate and record the decay constant, , using the
formula given in the introduction section.
6. Load your derived equation into Y1, and graph the equation.
6. Use the statistic features of the calculator to calculate an exponential relationship for your data and plot the equation as Y2. Graph.
Save the graph as homework to be printed later.
Questions
1. What did you notice about the pattern of decay for your sample?
2. Give a physical explanation for the pattern you witnessed in the sample's decay.
3. Explain any differences between the plots of Y1 and Y2.