Workshop: Detecting & Measuring Background Radiation & Potassium Chloride Count Rates, Lab Reports of Physics

Download Workshop: Detecting & Measuring Background Radiation & Potassium Chloride Count Rates and more Lab Reports Physics in PDF only on Docsity! Radioactivity Workshop #12 Physics 102 April 17-19, 2008 Name: ___________________ Name of Instructor: _______________ Name(s) of Lab Partner(s):________________Time/Day of Workshop: ________ Review As you know, atoms consist of a nucleus at its center, plus electrons bound to it. The nucleus holds the positive charge of the atom. This charge results from the fact that protons are one of its two inhabitants. Each proton is positively charged. Its charge-magnitude is equal to that of the electron. The nucleus has a second inhabitant, called the neutron. The neutron has zero electric charge. Most atoms in nature are neutral. In a neutral atom, the number of electrons bound to the nucleus is equal to the number of protons within the nucleus. As an example, consider hydrogen. By definition, all hydrogen atoms contain one proton in its nucleus. The most prevalent form of hydrogen contains zero neutrons in its nucleus. This is “ordinary” hydrogen. Its symbol is 1H1. The subscript is the number of protons (one) in the nucleus. The superscript is the sum total of protons and neutrons (also one). If a hydrogen nucleus contains 1 neutron, we call the nucleus deuterium. Hence, its symbol is 2H1, as there are two particles in the nucleus. If the nucleus contains two neutrons, it is called tritium. The symbol, then, is 3H1. The term isotope denotes nuclei that contain the same number of protons, but differing numbers of neutrons. Thus, ordinary hydrogen, deuterium, and tritium are all isotopes of hydrogen, as the nuclei of all three contain just one proton. Consider again the three isotopes of hydrogen – ordinary, deuterium and tritium. It happens that the tritium nucleus is unstable. It breaks up, (called decay) spontaneously. It decays into 3He2. In the process of this change, an electron is released. The electron is one example of what is called a beta particle. Whenever a nucleus spontaneously emits a particle, the nucleus is termed radioactive. Hence, tritium is an example of a radioactive nucleus. Another element with radioactive isotopes is potassium (symbol K). About 93% of the potassium on earth is of the isotope 39K19. This means there are 19 protons (this defines potassium) and that the sum of the number of protons and neutrons is 39. 1 This prevalent isotope is not radioactive. But 0.012% of all potassium on the earth is the isotope 40K19. This isotope is radioactive. Note that it has one more neutron (twenty one) than does 39K19. When 40K19 undergoes radioactive decay, a high-energy beta particle (electron) is emitted from its nucleus. One of its neutrons is transformed into a proton. What is the resulting nucleus? Since there are now 20 protons, the nucleus is now represented by the symbol 40Ca20. Note that calcium (symbol Ca) is defined by the fact that there are 20 protons in its nucleus. Note: the superscript does not change - a neutron is transformed into a proton, leaving their sum unchanged. Also, 40Ca20 is stable. Every second of the day, your body is bombarded by high energy radiation. Its origin is from the sun, or from other celestial objects. You cannot escape this radiation. This radiation is called background radiation. Today, you will investigate this radiation. You will then investigate some properties of radioactive 40K19. Equipment: Potassium chloride, Geiger tubes, counters, a ruler, a calculator. Set of barriers: paper, cardboard, aluminum foil, aluminum slab, and lead slab. Potassium Chloride. Purpose: To learn methods for detecting and counting background radiation and also detecting particles emitted by deliberately-placed radioactive sources. Also, to learn some of the properties of radioactivity. Part A. Geiger Counter Setup Familiarize yourself with the Geiger counter. It is a device that is sensitive to high energy particles. If a high energy particle enters the counter, it produces ions in the gas that fill the tube. These ions then produce an electrical pulse. The electrical pulse then produces an audio pulse, and also registers a count on the counter. Plug in the counter. Make sure that the switch on the back is set to 900 [V], and that the audio is in the ON position. Set the count mode to Continuous. Turn on the Geiger counter. You should hear beeps. Each beep corresponds to the passage of a high energy particle passing through the tube. If you do not hear beeps, bring it to the attention of your instructor. 2 Chart 1: The Graph of Count-Rate versus distance from radioactive source to the Geiger Tube 5 Part D: Computing the KCl Count-Rate. The data you have collected (when KCl was on a shelf) includes more than the radiation from KCl. It also includes radiation from the background. To get the rate from just KCl, it is necessary to subtract out the background rate. i) Refer to your results from Part B, for the background rate. Note the average value of your results for this entry. Then compute and record the “background-subtracted” count- rate (for KCl alone). Note: The uncertainty-rate is the same as you found in Table 2. Table 3: Background Subtraction of the KCl Count-rates Shelf Distance Total Count-rate Background Count-rate Uncertainty Position (cm) counts per minute rate for KCl alone rate 1 2 3 4 6 ii) On Chart 2, given on the next page, graph the “background-subtracted” count-rate versus d. iii) Do you observe that the KCl count-rate increases, decreases, or remains the same as d increases? iv) If you found that the count-rate changes as d changes, is the change linear or non- linear? Note: When we say that a change is linear, it means the following: You make a change in one variable. Call it ∆x. Then, you observe the change resulting in the other variable. Call this change ∆y. You then repeat the process, using the same ∆x, but starting at some other value of x. If you get the same value for ∆y as before, then the dependence is linear. This must be true, no matter what value of x you start with. Graphically, it means that the graph is a straight line. 6 Chart 2 7 6. In the graph of Question 5, the straight-line graph represents a linear decrease with d. In contrast, the curved graph represents a dependence of the vertical coordinate on d that varies as 1/d2. Which of these two dependences, (if either) would you expect for radioactive decay? To answer this question, first consider, for a moment another problem. Paint is sprayed from a paint gun. Examine the paint that squirts out in a particular cone that emanates from the gun. It is intercepted by a square placed at varying distances from the gun. This is illustrated in the Figure below. Suppose that we position the patch so that it is on a sphere of radius one meter from the gun. The paint then travels one meter. Suppose that it then happens to produce a patch of paint that is 1 millimeter thick. How thick would the patch of paint be, if the experiment is done instead with the patch at a distance of two meters from the gun? Explain. 10 7. Based on the analogy with the paint spray problem, what dependence do you expect for the KCl count-rate on d? Why? 8. From inspection of your graph in Chart 2, is your data roughly consistent with your answer to Question 7? Explain how you came to your conclusion. 11 9. A characteristic time that tells you how unstable is a radioactive nucleus is the half- life, denoted as T1/2. This is the time it takes for half of an original quantity of a radioactive isotope to decay. For example, radium-226 (radium with a total of 226 protons and neutrons) has a half-life of 1,620 years. This means that half of any given specimen of radium-226 will be converted into other elements by the end of 1,620 years. In contrast, 40K19 has a much longer half-life of 1,260,000,000 years or 1.26 x 109 years. Suppose you succeed in assembling 1 kilogram of pure 40K19. The graph below gives the mass remaining, as time varies. Fill in the values on the time axis at the points indicated by the dashed lines. 10. Draw a rough sketch (qualitative, not quantitative) on the above graph to indicate the amount of radium-226 remaining, as time varies. Again, assume we start with 1 kilogram of radium-226. 11. The mean life τ of a radioactive nucleus can be defined by the relation τ = T1/2/0.693. More precisely, τ is the average lifetime of a radioactive nucleus. 12