PHY313/CEI544 - Radioactive Decays

PHY313/CEI544

Radioactive Decays

    Li Li, a graduate student in the physics department, will be assisting in this experiment. You will work in groups of 2; you may choose your own lab partner.

    NO FOOD or drink should be brought into the lab. You should wash your hands afterward. This is not because there is much danger in the radioactive material you will get. Instead, it is because the radioactive material is in a dilute acid solution that we hope you will not spill and burn your clothes with. Also cleanliness is required practice in laboratories, and radioactive aspects mandate special care. The concern is that the equipment should be kept clean and free from dust so that it will continue to function in future semesters. The radioactive exposure you will get during the 10 minutes you observe radioactive decays, is similar to that you get from an hour or so of ordinary life in a nominally radiation-free environment, and much less than, for example, you get from a dental x-ray.

    You will be given a geiger counter and a sample which contains a small number of barium (Ba) ions (more specifically, the isotope ¹³⁷Ba) that have been created by decay of a radioactive isotope of cesium (¹³⁷Cs). Cesium is number 55 in the periodic chart of the elements, which means that it has in its nucleus 55 protons. There are various "isotopes" of cesium, one of which has 82 neutrons, or 55+82=137 "nucleons". This isotope is called ¹³⁷Cs. A nucleus of ¹³⁷Cs is unstable and will eventually decay to a lower energy nucleus, ¹³⁷Ba , which has 56 protons and 81 neutrons. Essentially you can say that one of the neutrons changes into a proton, and in the process throws out an electron. The charge on the nucleus increases by 1 quantum of charge, but total charge is "conserved" because the electron carries off -1 quantum of charge. This process is known as "beta decay" because when the process was first discovered, the emitted electron was not yet identified as an electron and was called a "beta ray." The emitted electrons do not travel very far, and are absorbed inside the sample or in the walls of the container. There is also a neutrino emitted, which travels away at the speed of light and is highly unlikely to interact with anything. It can easily penetrate the earth and travel to distant parts of the universe.

It happens that in the beta decay of ¹³⁷Cs, the product (or "daughter") barium nucleus is left in an "excited" state. This decays in a few minutes back to the "ground" state of the barium nucleus, emitting a photon (a quantum of light) of fairly high energy, called a "gamma" ray (technically, gamma rays of energy 0.66 MeV, corresponding to light with wavelength 0.02 Angstroms. The energy of the gamma ray equals the difference between the energy of the excited and ground states of ¹³⁷Ba.) Such a gamma ray interacts weakly with matter, and will usually penetrate the container and fly into the room where it might be absorbed in your geiger counter detector, especially if you put the sample close to the geiger counter. But don't put it too close -- you might accidentally break the fragile "window" of the counter which will destroy the counter.

Before you begin counting gamma rays from the ¹³⁷Ba, you should inspect detector, a box, inside which is hidden a Geiger-Müller tube. Adjust the high voltage to a value near 600 V, and then keep it there throughout your measurments. Measure the room "background" for 10 minutes. You will need this information later to correct your counting measurements of ¹³⁷Ba decays.

We will separate some unstable ¹³⁷Ba atoms from the "parent" ¹³⁷Cs source. This is done by washing the ¹³⁷Cs with dilute hydrochloric acid to dissolve out the barium. We will give you the resulting solution, containing no cesium, only barium. The technical term for this is "milking the cow." The parent ¹³⁷Cs source is the "cow" and the solution we give you is the "milk." The milk contains some excited barium nuclei which were probably created by very recent decays of the cow (Cs) atoms. It also contains some barium atoms in the ground state, which were probably created by less recent decays of cow atoms, and have already emitted a gamma ray and decayed to their ground state. Before too long, the rest of the barium atoms will also decay into their ground state, emitting more gammas, some of which you can measure with your counters. The time required for half the "excited" ¹³⁷Ba nuclei (these are designated as ¹³⁷Ba* nuclei) to decay into ground state ¹³⁷Ba nuclei is called the "half-life." This is what I want you to find out from your measurements. The answer will probably be a few minutes. You should be able to measure the half-life to approximately 10% accuracy. This does not mean that you are only 90% competent. If you and the group that comes after you are both perfectly competent, then the group that comes after you will probably get an answer 10% smaller or bigger than you did. In order to get a more accurate answer, you would have to count many more decays.

As soon as Li Li gives you your sample, put it in the detector, which should be in the "stop" and "reset" mode, showing zero counts. Then promptly move the "count" button of your detector to the "continuous mode" and start timing. At then end of each minute, record the total counts showing on the detector.

After one half-life has elapsed, only 1/2 of the ¹³⁷Ba nuclei remain in the ¹³⁷Ba* form, and 1/2 will have decayed to the ground state. After two half-lives have elapsed, only 1/4 of the ¹³⁷Ba nuclei will be in the ¹³⁷Ba* form, and 3/4 will have decayed to the ground state. After three half-lives, only 1/8 are ¹³⁷Ba*. Therefore, the rate of new counts in the counter will be decreasing with time by corresponding factors. The number of new counts will be proportional to the number left in the unstable ¹³⁷Ba* form. If you make a graph with the horizontal axis being clock time since you start counting, and the vertical axis being the total number of accumulated counts in your counter since you started counting at time "zero", then the vertical axis will show how many ¹³⁷Ba decays have been detected plus how many background events have happened. You should then graph the accumulated number of counts versus time.

How should you determine the half-life from this graph? I will let you think about it. For your first try, you can ignore any correction for background.

When you have finished counting, please give your samples back to Li Li. Also, please give him a copy of your data (60 sec, # of counts, 120 sec, # of counts, etc.) Li Li will add the results of all groups for each 1 min interval. We will study this additive count graph either later in the evening or at the next class.

Cesium decay
Figure 1: The ¹³⁷Cs decay chain.

Lab Writeup:

Please begin with an introductory paragraph. It does not have to be technical, but should include the meaning of the important terms you will use, such as: unstable, decay, gamma...
Next a short section on what you did.
Then a section on results, including graphs.
Finally a short conclusion. What did you learn? Is the lifetime of an excited Ba nucleus in any way analogous to the lifetime of a multicelled organism such as yourself? Do you have any idea why there is a "background" count in this experiment?