10.4 Half-Life. Investigation. 290 Unit C Radioactivity

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1 .4 Half-Life Figure Pitchblende, the major uranium ore, is a heavy mineral that contains uranium oxides, lead, and trace amounts of other radioactive elements. Pierre and Marie Curie found radium and polonium in pitchblende residues. B Investigation The Half-Life of Popcorn To perform this investigation, turn to page 3. In this investigation, you will simulate the radioactive decay using popcorn kernels. A sample of radioactive material, such as uranium ore (Figure ), contains an immense number of radioactive atoms, any of which can undergo radioactive decay. The decay of a nucleus is an individual random event. The rate of radioactive decay of a sample is not affected by physical or chemical changes, including temperature and pressure. In addition, the age of a nucleus does not affect the probability that it will decay. Although there is no way of determining when an individual nucleus will decay, we can predict the average rate of decay for a large number of nuclei. In the beginning, there are a large number of radioactive parent nuclei and, therefore, there will be a high rate of decay per second. As time passes and parent nuclei decay, there will be fewer and fewer parent nuclei, and more and more daughter nuclei. Over time, both the number of parent nuclei present and the rate of decay will decrease. The number of decays per second of a sample is known as the activity of the sample and is measured in becquerels (Bq). A becquerel is equal to one decay per second. The average length of time for half of the parent nuclei in a sample to decay is called the half-life. The half-life is different for different isotopes, but is a constant number for a given isotope. B Investigation The activity of a sample depends on the size of the sample (how many radioactive nuclei were present initially) and the age of the sample (how many radioactive nuclei are left). However, for any sample, the number of parent nuclei left in the sample and the activity level of the sample always follow the curves shown in Figures 2 and 3. These curves are for a fictitious (made up) radioactive source. Number of Parent Nuclei versus Time 35 Activity Level versus Time Number of parent nuclei Activity level (Bq) Time Figure 2 Parent nuclei decay curve Time Figure 3 Activity curve 29 Unit C Radioactivity

2 Both curves have an identical shape. You can see from the figures that the sample has a half-life of 5 units of time. The number of parent nuclei goes from to 5 to 25 to 2.5 to 6.25 at times of, 5,, 5, and 2 time units. Similarly, the activity level of the sample goes from 32 to 6 to 8 to 4 to 2 at times of, 5,, 5, and 2 time units. Some radioactive isotopes are used in medicine. For example, the radioactive isotope thallium-2 can be injected into a patient s bloodstream where it is carried to the patient s heart. A camera detects the radiation given off from the decay of thallium-2 and produces an image of the heart (Figure 4). Comparison of scans made during exercise and at rest may show areas of the heart not receiving adequate blood flow. Figure 5 shows how the activity level of an injection of thallium-2 decreases. LEARNING TIP A line graph can be used to show a trend over a period of time. Ask yourself, What information is presented on the left side and along the bottom of Figure 5? What has happened to thallium-2 over a period of time? 2 Activity Level of Thallium-2 versus Time Activity level (MBq) Figure 4 A thallium scan of a normal heart Time (min) Figure 5 Activity of thallium-2 We can use the graph to determine the half-life of thallium-2. The initial activity of 2 MBq is reduced to 6 MBq after.3 min. This means that the half-life is.3 min. Note that the half-life is so short that most of the thallium will decay quickly and not stay in the blood for much time. As every half-life passes, the number of parent nuclei present and the activity level decreases by half. To find out how many half-lives have passed, divide the time by the half-life of the isotope. Table shows how these fractions can be expressed. Table Number of half-lives n Fraction remaining Exponential notation Calculating Half-Lives Using Fractions n.4 Half-Life 29

3 Another way to calculate the amount of the parent nuclei remaining is to use percentages. The original amount is %. Therefore, we can calculate the amount left after every half-life by dividing the previous amount by two. Table 2 shows the percentage left after the first five half-lives. This table can be used for problems calculating the amount of parent nuclei left. Can you determine the percentage that would be left after six half-lives? Table 2 Calculating Half-Lives Using Percentages Number of half-lives Percent remaining 5 % 25 % 2.5 % 6.25 % 3.25 % SAMPLE PROBLEM Use Half-life to Determine the Time Passed Cesium-24 has a half-life of 3 s. A sample of cesium-24 in a laboratory has an initial mass of 2 mg. (a) Calculate the amount of time it will take for the sample to decay to 5 mg. (b) Calculate how much cesium-24 will remain after 93 s. Mass of cesium-24 (mg) Mass of Cesium-24 versus Time Time (s) Figure 6 Decay curve for cesium-24 Solutions (a) First determine how many half-lives have passed. This can be done using either the fraction or percentage method. Fraction Method Percentage Method The fraction left is The percent left is % 25 % 2 5 By using either method, we can see that two half-lives have passed. Now calculate the total amount of time that has passed. Since two half-lives have passed, the total time that has passed will be 2 3 s 62 s. Figure 6 shows a graph of the mass time. From the graph, we can see that at about 62 s, the mass is reduced to 5 mg. This is in agreement with the calculated solution. (b) Since the half-life of cesium-24 is 3 s, we can determine the number of half-lives: number of half-lives to tal t half- ime life 9 3 s 3 3 half-lives s Now calculate the mass (m) remaining. This can be done using either the fraction or percentage method. Fraction Method Percentage Method m 2 3 (2 mg) After three half-lives, there is 2.5 % remaining % m 2.5 mg m % 2 mg m 2.5 mg The mass remaining is 2.5 mg. We can also see on the graph that the approximate mass remaining is about 2.5 mg. 292 Unit C Radioactivity

4 Practice A sample of fluorine-8 in a laboratory has an initial mass of 5 mg. Fluorine-8 has a half-life of.8 h. Figure 7 shows the decay curve for fluorine-8. (a) Calculate the amount of time it will take for the initial mass of fluorine-8 to be reduced from 5 mg to 2.5 mg. You can use the graph to confirm your answer. (b) Calculate what mass of fluorine-8 remains after 5.4 h. You can use the graph to confirm your answer. Mass of fluorine-8 (mg) Mass of Fluorine-8 versus Time Time (h) Figure 7 Decay curve for fluorine-8 SAMPLE PROBLEM 2 Determine the Activity Level Using Half-life Radium- has a half-life of 6. A material containing radium- has an activity of 5 MBq. (a) Determine what the activity level will be in the material after 8. (b) How many earlier was the activity level in the material 2 MBq? Solutions (a) First, determine the number of half-lives. 8 y ears 5 half-lives 6 h alf-life Now determine the activity level. activity 5 MBq MBq After 8, the activity level will be 6 MBq. (b) The activity level of 5 MBq is one-quarter the activity level of 2 MBq. 2 2 This represents a period of two half-lives. 4 We can calculate the amount of time as t The activity level was 2 MBq 32 earlier. Practice Silicon-32 has a half-life of 6. A material containing silicon-32 has an activity of 8 MBq. (a) Determine what the activity level of the material will be after 32. (b) How many earlier was the activity level of the material 64 MBq?.4 Half-Life 293

5 Table 3 Decay Decay Series of Uranium-238 Half-life U 9 Th 4 2He Th 9 Pa e 24 d 9Pa 92 U e 6.7 h 92 U 23 9 Th 4 2He Th 88 Ra 4 2He Ra 86 Rn 4 2 He 6 86Rn 84 Po 4 2 He 3.8 d 84Po 82 Pb 4 2 He 3. min 82Pb 83 Bi e 27 min 83Bi 84 Po e 2 min 84Po 82 Pb 4 2 He.6 4 s 82Pb 83 Bi e 22 83Bi 84 Po e 5 d 84Po Pb 4 2 He 38 d Figure 9 The remains of a human were found in glacial ice in the Alps. Scientists used carbon-4 dating to determine that he lived about 53 ago. Decay Series In biological families, a parent can have a daughter. After time passes, the daughter becomes a parent and produces another generation. In a similar way, a radioactive parent nucleus produces a daughter nucleus, which can also be radioactively unstable. In turn, the daughter nucleus becomes a parent nucleus, which continues the sequence of events. When radioactive nuclei form such a chain, it is called a decay series. The decay series always ends in the formation of a stable isotope. For example, uranium-238 forms a decay series ending with the stable isotope lead-26 as shown in Table 3. Note that some of the isotopes have very short half-lives. However, uranium-238 has a half-life of about 4.5 billion. The decay series of uranium-238 provides some isotopes that would not otherwise be present on Earth. The decay series of uranium-238 can be graphed as shown in Figure 8. Mass number Pb- Pb- Pb- 26 Bi- Bi- Po- Po- Po Atomic number Radioactive Dating Decay Series of Uranium-238 Rn- = decay = decay Since radioactive isotopes decay according to their half-lives, it is possible to date materials using appropriate isotopes. Carbon-4 is a radioactive isotope that can be used to date material that was once alive (Figure 9). Almost all naturally occurring carbon is carbon-2. However, an extremely small fraction of carbon (about one atom in a trillion) is carbon-4. The half-life of carbon-4 is 573. With this half-life, there should be no carbon-4 Ra- Figure 8 Uranium-238 is changed into lead-26 in a decay series of 4 steps. Th- Th- 23 Pa- U- 238 U- 294 Unit C Radioactivity

6 left on Earth, which is about 4.5 billion old. However, our Sun and all the stars in the universe produce cosmic radiation. Energetic neutrons are part of cosmic radiation, and the neutrons combine with nitrogen in the upper atmosphere to form carbon-4 and a proton according to the following nuclear equation: 4 7 N n 4 6 C p This process keeps the level of carbon-4 constant on Earth and in living organisms. When an organism dies, the amount of carbon-4 in the organism starts to decrease as it radioactively decays, and no new carbon-4 enters the organism through eating or respiration. Carbon-4 has a half-life of 573, which means that the ratio of carbon-4 in an organism decreases by half every 573. Figure shows the decay curve for carbon-4. It is clear from the graph that carbon-4 can only be used to date objects less than 4 old. With a more accurate graph (or by calculation), the useful time range can be extended to about 6. Note that carbon-4 dating will only date things that were once alive. GO Other isotopes can be used to date things that are more than 6 old or that were never alive. For example, uranium-235 decays to lead-27 with a half-life of 74 million, and uranium-238 decays to lead-26 with a half-life of 4.46 billion. Dating materials using two different isotopes make the age estimates very accurate. Uranium-238 has been used to determine that the oldest rocks that have been dated on Earth are about 4 billion old. Amount of carbon-4 left (%) Percentage of Carbon-4 Left versus Time Time (thousands of ) Figure Decay curve for carbon-4 To find out more about carbon-4 dating go to To test your skills on half-life and radioactive dating, go to GO SAMPLE PROBLEM 3 Use Radioactive Dating to Determine the Age of a Sample A piece of leather was found to have 2.5 % of its original carbon-4 present. Determine the age of the leather using Figure and by calculation. Solution From the graph, we can see that the time is approximately 7. The decrease from % to 2.5 % is a ratio of 2. 5 % % 8 23 Therefore, the time taken is half-lives 7 9 h alf-life The piece of leather is approximately 7 2 old. Practice A bone fragment was found to have 25 % of its original carbon-4 present. Determine the age of the bone fragment using Figure and by calculation..4 Half-Life 295

7 .4 CHECK YOUR Understanding Number of nitrogen-3 atoms (thousands). How are the terms activity and becquerel related? 2. What is the activity level of the following samples? (a) 36 decays in 42 s (b) 35 decays in 35 min (c) 45 decays in 7.5 min (d) 2 decays in 3 h (e) 25 decays in 55 min and 7 s 3. Nitrogen-3 decays to produce carbon-3. A laboratory sample contains 5 nitrogen-3 atoms. Use the decay curve for the sample over time shown in Figure to answer the following questions Decay of Nitrogen-3 Atoms versus Time Time (min) Figure Decay curve for nitrogen-3 4. A radioactive isotope source has a mass of 2 µg. If the isotope had a half-life of 2 s, what would be the mass of the isotope after 2 min? 5. Beryllium-7 has a half-life of 53 d. A sample was observed for min and there were decays. (a) What is the activity level of the sample? (b) What will the activity level of the sample be after 265 d? (c) After how many days will the activity level of the sample be 2 Bq? (d) What was the activity level 6 d before the sample was observed? (e) How many days earlier was the activity level eight times greater than the observed level? 6. A granite rock is thought to be about two billion old. Why is it not possible to determine the age of the rock using carbon-4 dating? 7. A hair sample has 8 % of its original carbon-4 present. What is the age of the sample? 8. A bone fragment has lost 75 % of its original carbon-4. What is the age of the bone fragment? 9. An organic sample is old. What percentage of the original carbon-4 is still present in the sample? (a) How many nitrogen-3 atoms will be left after 6 min? (b) How many carbon-3 atoms will be present after 25 min? (c) What is the half-life of nitrogen-3? (d) How many nitrogen-3 atoms will be present after 4 min? 296 Unit C Radioactivity

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