**Purpose**

The purpose of this experiment is to determine the halflife of a radioisotope. Halflife is defined as the time it takes for one half of the atoms in a radioactive sample to decay. Data will be collected on the activity of a radioactive isotope vs. elapsed time. The halflife will then be determined by two different types of graphical analysis.

**Discussion**

Radioactive decay is random process that simulates a first order rate process. The only "constant" in such a process is the time it takes for the activity to drop from any value to one-half that value. This is referred to as the "halflife" of the isotope. The mathematical equation that describes this process is: ; where **N** is the activity at time** t, N _{0}** is the initial activity, and

Since experiments of this type can take a long time to complete we will simulate the experiment on the computer with a small program written in Javascript. The program will not only simulate the decay on several isotopes but also simulate the experimental errors which would normally occur during the collection of this kind of data (in other words the actions of your lab partner in addition to counting errors).

From the data collected you will be able to determine the true activity and log of the true activity of the isotope. The halflife of the isotope can then be determined with two different plots: true Activitv vs. time, and log(true activity) vs. time. In order to collect enough data points to determine the halflife by plotting activity vs. time, the program will force you to collect data over about two halflives. Also, the program will also not allow the collection of more than 30 data points. It is recommended that the experimental parameters be such that between 12 to 20 data points are collected. This will give you enough data points to average out experimental counting errors, which are simulated by the program.

**Procedure**

- Select an isotope from the pop-up menu. After you select an isotope information will be presented to allow you to estimate the halflife of your isotope. You need to estimate the halflife of the isotope so that you can determine how long to simulate the experiment and how often to collect data. For example, suppose you picked the isotope
. You might be presented with something like the following:^{55}Fe*"Previous experimental data on*has been collected. At the start of the experiment the activity was^{55}Fe**1000**. After**690**days the activity was**615**. At this time there was an equipment failure and the experiment was not completed. Use this information to estimate the halflife of."^{55}Fe

- Estimate the halflife. For the information presented in step 1 you can see that the halflife of
is longer than 690 days because in that time period the activity did not drop to one-half of the starting value, which was 1000. (Note: Had the reading dropped down to about 500 in that time period then the halflife would have been close to 690 days.) A good estimate for the halflife of^{55}Fewould be about 800-900 days.^{55}Fe - Fill in the experimental parameters. These parameters are given below:
- How many days do you want to run this experiment?
- How often do you want to take readings?
- For how many minutes each day do you want to take a reading (Max of 10)?

- Using our estimate of 800 days for the halflife of the example above (
), we would want to run the experiment for about 1600 to 1800 days. If we enter 1600 for the length of the experiment (first experimental parameter) we would want to take readings every 100 days (second experimental parameter). This would give us 16 data points to plot. If we were to take readings every 50 days we would collect more than 30 data points which is not allowed.^{55}Fe - Click on the Run Experiment Button. If you are presented with error dialogs you will have to correct the experimental parameters entered in step 3. Remember, the experimental parameters must not allow for more than 30 data points to be taken and must result in data being taken over about two halflives. This will ensure that there are enough data points to determine the halflife.
- Print out the page and process the data.

You may want to print out this page before proceeding so that you have the information above as well as the questions that need to be answered on your lab report. When you are ready to do the experiment follow the link below.

**Questions**

- Make a plot of true activity vs. time and determine the halflife from the plot by using the definition of halflife: the time it takes for the activity to drop from some intitial value to one-half that value. Show on your graph how you obtained the halflife from the plot. (True activity is the observed activity, in counts per minute, minus the background activity.)
- Inspection of the formula given in the discussion above reveals that a plot of
**log N**vs**time**gives a linear plot with a slope equal to . Make a plot of**log (true activity)**vs.**time**and determine the halflife from this plot by setting the slope of the graph equal to . - Average the results from questions 1 and 2 , if necessary, and compare the halflife obtained with the actual value given by the HANDBOOK OF CHEMISTRY AND PHYSICS. Calculate the relative error in your value.

Questions? Comments?? Patrick Gormley | |