Describe 2 methods using graphical analysis to determine the half-life of a radioactive isotope.
Answers
Explanation:
Halflife of a Radioisotope
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, N0 is the initial activity, and halflife is the halflile of the isotope.
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 55Fe. You might be presented with something like the following:
"Previous experimental data on 55Fe has been collected. At the start of the experiment the activity was 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 55Fe ."
Estimate the halflife. For the information presented in step 1 you can see that the halflife of 55Fe 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 55Fe would be about 800-900 days.
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 (55Fe), 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.
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.