Determination of Half-Life

During the sixth lab, you learned that radioactive decay is a random process. That is, there is no way to predict when an individual radioactive atom will decay. However, statistically, we can determine the amount of time it will take for a certain fraction of the radioactive atoms originally present in the sample to decay. If this fraction is arbitrarily chosen as one-half, the time interval is known as the half-life . 

For example, consider the radioisotope iodine-131, which has a half-life of 8.04 days. If 1 gram of I-131 is present initially, after one half-life (8.04 days), ½ gram will be present. After 8.04 more days, ½ of the ½ gram will be present (for a total of 

gram). After another 8.04 days (or a total of three half-lives), ½ of the ¼ will be 

present, for a total of 1/8 gram. The progression continues in this fashion indefinitely. Plotting a graph of the amount of a radioisotope present against the number of elapsed half-lives yields the attached graph (see last page). 

Another way to view the half-life is to think of it as the time it takes for the 

activity of a radioisotope to decrease by ½. In the case of I-131, the activity of the sample will decrease by ½ every 8.04 days. A graph of activity against elapsed half-lives will be identical to that described above, except that the vertical axis will represent the fraction of original activity remaining, rather than fraction of the original number of radioactive atoms. 

Determining half-life is one method of identifying a particular radioisotope (because each radioisotope has a different half-life). With an unknown source, one may determine its half-life and then match the experimental value with tabulated values in the literature to identify the source. In this experiment, we will start with a radioisotope that has been artificially created in the UMass Lowell Research Reactor and determine its half-life. 

Laboratory 7: Determination of Half-Life 

Procedure: 

Measure the sample gross counting rate every 30 seconds for approximately seven minutes (the instructor will facilitate this). 

Data: 

Tabulate and graph the data using elapsed time on the horizontal axis and the gross 

counting rate on the vertical axis. Estimate the half-life from this data. 

Discussion: 

Using your graph, what is the estimated half-life of Aluminum-28? 

3 minutes 

Would you be able to perform this experiment with a long-lived radioisotope such as Uranium-238 (4.5 billion-year half-life)? Why or why not? 

No, it will not be possible. A difficulty may arise in the mass determination of the base material if the chemical state of the element is not exactly defined. The composition of uranium oxides, for example, varies with the conditions in which it is produced and stored and therefore the oxygen/uranium ratio may vary. 

The Al-28 source was artificially created by subjecting Al-27 to neutron radiation in a process known as activation. A fraction of the Al-27 nuclei in the sample absorbed the neutrons and were transformed into radioactive Al-28; the sample was activated. Discuss at least one application of neutron activation analysis in depth. 

Neutron activation analysis is a nuclear process that allows precise identification and quantification of elements in a vast amount of materials (Hamidatou et al., 2013) . 

This technique has found application in chemistry as well as other research fields such as geology, forensic science, archaeology, medicine and environmental monitoring. 

In environmental monitoring the neutron activation analysis can be used to determine the nitrogen content in plants. For the determination of the nitrogen content in plants, 14 MeV neutron activation analysis was used based on the determination of the elemental concentration by measuring the area of the gamma-radiation of the radionuclide13N as a result of14N(n, 2n)13N reaction (Hamidatou et al., 2013) . Three methods were tested in order to obtain quantitative results: comparator method, method for absolute determination of the neutron flux and monitor method. Using the monitor method, results for nitrogen content in plant species were obtained-for beans 74.8% and for maize 1.8%. The precision of determination is ±10%. The possible sources of errors are analyzed. The efficiency of the Ge(Li) detector has been determined using a combined γ-source in the energy interval 120–1400 keV with precision of 4.5%. The sensitivity achieved was 4 mg or 47 imp/mg per min. 

Reference

Hamidatou, L., Slamene, H., Akhal, T., & Zouranen, B. (2013, March 13).  Concepts, instrumentation and techniques of neutron activation analysis . IntechOpen - Open Science Open Minds | IntechOpen.  https://www.intechopen.com/books/imaging-and-radioanalytical-techniques-in-interdisciplinary-research-fundamentals-and-cutting-edge-applications/concepts-instrumentation-and-techniques-of-neutron-activation-analysis