Lab 14. RADIOACTIVITY 14.1. Guiding Question What are the properties of different types of nuclear radiation? How does nucelar decay proceed over time? 14.2. Equipment 1. ST360 Radiation Counter, G-M probe with sample holder, beta source, gamma source, paper, plastic, lead, and meter stick (or other length measurement device). 2. 100 dice, cup, great patience 3. Calculator or spreadsheet, worksheet 14.3. Background Radioactive materials are ubiquitous. For example, some smoke detectors contain 241 Am while bananas contain 40 K. However, the radioactive nature of these materials cannot ordinarily be recognized by human senses. Hence, specialized detectors are needed to measure the presence of radioactive species. Types of decay Nuclei of radioactive substances are unstable and emit various types of radiation with differing properties. The type of radiation a particular nucleus emits will depend upon which decay process is energetically favorable. Sometimes more than one process may be energetically favorable and thus different particles can be emitted by different nuclei of the same isotope. Alpha decay and beta decay are two common forms of radioactive decay. In alpha decay, the unstable parent nucleus emits an alpha particle which is simply a 4 He nucleus (2 protons and 2 neutrons). The resulting daughter nucleus now has two fewer protons and therefore is a different chemical element. In beta decay, the unstable parent nucleus emits a beta particle, which is an electron. In doing this, the resulting daughter nucleus has one additional proton. Gamma rays, which have no mass, result as a consequence of a nucleus de-exciting. Gamma rays frequently are emitted after other decay processes such as beta decay that result in an excited nucleus. Alpha particles, beta particles, and gamma radiation have different properties. For example, gamma rays are much more penetrating than alpha particles. In addition, the charges of these species differ.
The intensity of radiation drops off quickly as the distance between the source and the detector increases. Specifically, if there is no absorption of the radiation, the intensity of radiation varies with the inverse square of the distance between the radiation source and the detector. So if one doubles the distance between the source and the detector, the detector will see only one forth of the radiation that it saw at the original distance. If material between the source and detector, such as air or shielding, absorbs radiation, even less of the radiation will reach the detector. Decay kinetics During any period of time, an unstable nucleus has some chance that it will decay. The decay probability depends only on what particular isotope the nucleus is, that is, on the number of protons and neutrons it contains. The probability does not change with time: a five-year old nucleus of cobalt-60 has exactly the same chance of decaying in the next minute as a three-day old cobalt-60 nucleus. If both nuclei survive the next minute, their chances of decaying in the following minute will still be exactly the same as their chances were in the previous minute. The rate of decay for a radioactive isotope is often expressed in terms of half life: the time for one half of a radioactive quantity to decay. Half life is the inverse of the probability of decay in a particular time interval: a nucleus with a high probability of decay in a 1-minute period has a short half life, while a nucleus that is very unlikely to decay in the same period has a correspondingly longer half life. Each radioactive isotope has its own characteristic half life t 1/2. For example, the most common naturally occurring isotope of uranium, uranium-238, decays into thorium-234 with a half life of 4.51 10 9 years. This means that only half of an original amount of 238 U remains after this time. After another 4.51 10 9 years half of this decays, leaving only one fourth of the original amount remaining. Compare this with the decay of polonium-214, which has a half life of 1.6 10-4 seconds. With such a short half life, any sample of polonium-214 will quickly disintegrate. Quantitatively, if the initial amount of a radionuclide is N 0, the amount N remaining after time t is given by N = N 0 e t where is the radionuclide s decay constant. This can be expressed in terms of the half-life if we recognize that N = N 0 /2 when t = t 1/2 : N = N 0 e t N 0 2 = N 0 e t 1/2 1 = 2 e t 1/2 = 1 e t 1/2 2 = e t 1/2 ln(2) = t 1/2 = ln(2) t 1/2 2
Inverting the kinetic equation N = N 0 e t allows us to determine the time that has elapsed since the amount of radionuclide N 0 was isolated from the remaining amount N. N = N 0 e t N 0 N = e t t = ln( N 0 N) ( ) t = ln N 0 N ( ) () ln N = t 0 N 1/2 ln 2 14.4. Activities There are three activities in this lab. You may do them in any order. A. Nuclear Counting Only beta and gamma sources will be used for this experiment. The G-M probe is a Geiger-Müller tube that interfaces with the ST360 Radiation Counter. The G-M probe operates at approximately 900 V. The end of the probe has a fragile window made of mica of thickness 2 mg/cm 2. The GM probe will fail if the mica window gets punctured or experiences microscopic cracking. The ST360 Radiation Counter is a combination unit containing a nuclear scaler, timer, high voltage supply, and a computer interface. Your instructor will show you how to use the detector and software. 1. Move all radiation sources at least 5 meters from the radiation detector. Collect a background count for 3 minutes. Repeat this step two more times. Record the data in the table below. Background Count #1 cpm Background Count #2 cpm Background Count #3 cpm Average Background Count Rate cpm 2. Using the beta source, determine the count rate at 4 distances from the detector. Record your data below. 3
Count Rate (cpm) Distance from Source d (cm) 1/d 2 3. Plot count rate versus 1/d 2. 4. Move the beta detector to within 2 cm of the source. Record the distance between the source and the detector. Record the count rate of the beta source with nothing between the source and the detector. Place a sheet of paper between the beta source and the detector. Record the count rate. Remove the sheet of paper and place a sheet of plastic between the beta source and the detector. Record the count rate. Remove the sheet of plastic and place a sheet of lead between the beta source and the detector. Record the count rate. 4
5. Remove the beta source and replace it with a gamma source. Record the distance between the source and the detector. Record the count rate of the gamma source with nothing between the source and the detector. Place a sheet of paper between the gamma source and the detector. Record the count rate. Remove the sheet of paper and place a sheet of plastic between the gamma source and the detector. Record the count rate. Remove the sheet of plastic and place a sheet of lead between the gamma source and the detector. Record the count rate. Source Beta Gamma Distance d (cm) Count Rate No shielding Count Rate Paper Questions 1. Why aren t the three background count rates identical? Count Rate Plastic Count Rate Lead 2. Which type of radiation is most penetrating? 3. Does the unshielded count rate follow 1/d 2? B. To Half or to Hold In this activity, you will investigate a hypothetical nuclide represented by a six-sided die. The process of decay is simulated by rolling a large number of dice. If a die rolls 1, it is considered to have decayed and is removed from the pile. By tabulating and graphing the number of dice remaining in the sample after each successive roll, you can estimate the nuclide s half-life. 1. Shake the dice in the cup and roll them onto a flat surface. 2. Count the dice that rolled 1 and record this number under Removed in Table 1. 3. Remove the 1 dice in a pile off to the side. 4. Gather the remaining dice back into the cup and roll them again. 5. Repeat steps 2-4 until all dice have been set aside, or you have completed 50 rolls. 5
Table 1. Simulated radioactive decay Throw Removed Remaining Throw Removed Remaining 0 1 26 2 27 3 28 4 29 5 30 6 31 7 32 8 33 9 34 10 35 11 36 12 37 13 38 14 39 15 40 16 41 17 42 18 43 19 44 20 45 21 46 22 47 23 48 24 49 25 50 6
6. Plot the number of cubes remaining vs. the number of throws for each substance on a graph. dice remaining 0 Questions: 1. In terms of throws, what is the half-life of a die? number of throws 2. Is the line in your graph straight or does it curve? 3. The rate of decay is defined as Rate of decay = nuclei/ t = slope of the plot. Is this rate constant, or does it change over time? 7
C. Radioactive Dating Since its discovery in the early 1900's, radioactivity has been used in many ways. These include radiometric dating (determining the age of the solar system, Earth, geologic events, age of human artifacts, etc.), atomic bombs, nuclear power, and medical imaging. In this exercise you will explore radiometric dating. With each radioactive decay, an atom of one element, the parent, is transformed into an atom of a different element, the daughter.. Over time, the number of parent atoms N p decreases and the number of daughter atoms N d increases. If the present-day ratio of daughter atoms to parent atoms (N d /N p ) is measured and the decay rate is known, then the length of time the parent has been decaying can be calculated. In this sort of situation, we do not independently know the initial amount of parent N 0. However, if the initial sample did not contain any daughter and that neither parent nor daughter entered or left the sample during the decay, N 0 = N p + N d. Then t = t 1/2 ln N 0 ( N p ) ln 2 () = t 1/2 ln N + N p d N ln 2 p ln 1+ N d N p = t 1/2 ln 2 Use this formula to complete the table below. ( ) Event/Material N d /N p Parent t 1/2 (yr) Half-lives Age (yr) a. Meteorites 1.01 b. Oldest known Earth rock 0.78 c. Single-celled life 0.56 d. Oldest hard-shelled fossil 0.07 e. Last Ice age 2.00 f. Great Flood of Black Sea 1.40 g. Egyptian pyramids 0.75 () () 238 U 4.51 l0 9 238 U 4.51 l0 9 238 U 4.51 l0 9 238 U 4.51 l0 9 14 C 5730 14 C 5730 14 C 5730 8