Chapter 10 Nuclear Physics 10.1 Nuclear Structure and Stability 10.1.1 Atomic Number and Nucleon Number 10.2 Radioactivity and Radioactive Decay 10.2.1 Types of Radioactive Decay 10.2.2 Predicting the Half-Life of a Radioactive Isotope 10.2.3 Experiment: Measuring the Half-Life of a Radioactive Isotope 10.2.4 Radioactive Decay Series 10.3 Nuclear Fission and Nuclear Reactors 10.3.1 Nuclear Fission 10.3.2 The Nuclear Power Plant 10.4 Nuclear Fusion 10.4.1 Nuclear Fission vs. Nuclear Fusion
182 CHAPTER 10. NUCLEAR PHYSICS 10.1 Nuclear Structure and Stability 10.1.1 Atomic Number and Nucleon Number 1. Write the following isotopes in A ZX notation. The number of neutrons in the nucleus is given in parentheses. (a) Carbon (7) (b) Zinc (36) (c) Radon (136) (d) Uranium (147) 2. Using a periodic table, identify the following elements and calculate how many neutrons are in the nucleus. (a) 24 11X (b) 65 29X (c) 131 53 X (d) 212 84 X 3. Two atoms have the same nucleon number. Are both atoms necessarily the same element?
10.2. RADIOACTIVITY AND RADIOACTIVE DECAY 183 10.2 Radioactivity and Radioactive Decay 10.2.1 Types of Radioactive Decay 1. Write out the decay process for each of the following isotopes: (a) α decay of 216 84 Po (b) β decay of 137 55 Cs (c) β + decay of 22 11Na (d) γ decay of 152 66 Dy 2. The chart below shows the masses of several nucleii and nuclear particles. Use the chart to answer the following questions: Particle/Nucleus Mass (amu) proton 1.007825 α 4.002603 206 80 Hg 205.977499 210 82 Pb 209.984163 210 83 Bi 209.984120 234 90 Th 234.043593 237 91 Pa 237.051140 238 92 U 238.050784
184 CHAPTER 10. NUCLEAR PHYSICS (a) 238 92 U decays by α decay. One question that is reasonable to ask is Why does 238 92 U emit an α particle rather than a single proton? Write an equation for each decay process and then calculate the energy of the parent nucleus and products for each reation. Is emission of a single proton feasible? Why or why not? 3. 210 82 Pb can decay either through α decay or β decay. Write a reaction for each of these processes and calculate the enrgy released upon transumtation of lead in each case.
10.2. RADIOACTIVITY AND RADIOACTIVE DECAY 185 10.2.2 Predicting the Half-Life of a Radioactive Isotope Suppose you have a collection of 400 cubes in which each cube has 5 white sides and 1 black side. 1. Assume that each cube represents a radioactive nucleus. If you rolled the cube some time during a one minute period, what is the probability that a black side will come up? 2. Suppose you roll a collection of N(0) = 420 cubes during a one minute period. In this roll, how many of the cubes should have a black side facing up? This is the number of decayed nucleii N. 3. How many undecayed dice are left after 1 minute? This is your value for N(1). 4. If you remove the decayed dice and roll the remaining N(1) dice, how many will decay in the next minute? How many will remain? 5. In Excel, create a spreadsheet to calculate N(t) and the decay rate N/ t for the first thirty minutes of decay.
186 CHAPTER 10. NUCLEAR PHYSICS 6. Plot N(t) vs. t and fit it with an exponential function. According to this fit, what is the decay constant of this isotope? 7. Based on the decay constant from your fit, what is the half life of this isotope? 8. Suppose instead of a nucleus decaying when a black side was rolled, it decayed when a white side was rolled? How would this affect the decay rate and the half-life of the isotope? 10.2.3 Experiment: Measuring the Half-Life of a Radioactive Isotope Equipment: 420 cubes, each with one black side Experiment: 1. Divide the cubes among your self and your classmates. Record N(0) = 420 in your spreadsheet. 2. Roll all four hundred twenty cubes during the first minute. Remove the decayed cubes and record the number of undecayed cubes in your spreadsheet. 3. Repeat this 29 more times and fill the results into your spreadsheet.
10.2. RADIOACTIVITY AND RADIOACTIVE DECAY 187 4. Plot N(t) as a function of time and again calculate the half life of the isotope. Does it agree with your theoretical prediction? Calculate the percent error. Is there way to modify the experiment so that the half-life would be closer to the predicted value? Attach your graph in the space below.
188 CHAPTER 10. NUCLEAR PHYSICS 10.2.4 Radioactive Decay Series In the figure below, fill in the missing information into the decay sequence. 232 Th 14 billion years!? 6.7 years " 228 Ac 6.1 hours? 220 Rn 55 s?? 3.7 days! 228 Th 1.9 years!?.16 s! 212 Pb 11 hours " " 216 At 164 µs?! 208 Tl? 61 minutes 3.1 minutes? " 212 Po 0.3 µs!? stable Figure 10.1
10.3. NUCLEAR FISSION AND NUCLEAR REACTORS 189 10.3 Nuclear Fission and Nuclear Reactors 10.3.1 Nuclear Fission 1. Go to the website phet.colorado.edu/simulations/sims.php?sim=nuclear_fission and click Run Now. A Java applet should load and run on your computer. 2. Select the Chain Reaction tab. The first screeen you see has a single 235 92 U nucleus. Fire the neutron gun and observe the reaction. Describe your observations in the space below. 3. Write a reaction for the process you observed assuming one of the daughter products is 141 56 Ba. 4. Now change the number of 235 92 U nuclei to 0 and the number of 238 92 U nucleii to 1. Fire the neutron gun at the 238 92 U nucleus (you may need to tilt the gun). Describe your observations in the space below.
190 CHAPTER 10. NUCLEAR PHYSICS 5. Write a nuclear reaction for the process you observed. 6. Which isotope of uranium undergoes fission according to your observations? 7. Now try different combinations of 235 92 U and 238 92 U nucleii. When do you get a chain reaction? 8. The natural abundance of 235 92 U is less than 1%. According to your observations, can naturally occuring urnaium be used to carry out a chain reaction? Why or why not? 10.3.2 The Nuclear Power Plant 1. In the same simulation that you used in the last activity, click on the Nuclear Reactor tab.
10.3. NUCLEAR FISSION AND NUCLEAR REACTORS 191 2. Begin with the control rods all the way in and fire the neutrons. What happens to the reactor? Describe your observations of the temperature, energy output and power output below. Reset the nucleii. 3. Now pull the control rods all the way out and fire the neutrons. What happens to the reactor? Describe your observations of the temperature, energy output and power output below. Reset the nucleii. 4. The goal of a nuclear power plant is to keep a fairly constant output power while keeping the temperature low enough not to damage the reactor. In this simulation you want to keep the temeperature at or below the gray region. Run the simulation and attempt to keep the power constant and the temperature under control. In the space below, describe how you had to move the control rods to achieve this.
192 CHAPTER 10. NUCLEAR PHYSICS 10.4 Nuclear Fusion 10.4.1 Nuclear Fission vs. Nuclear Fusion Particle/Nucleus Mass (amu) 1 0n 1.0087 2 1H 2.0141 3 1H 3.0161 4 2He 4.0026 140 54 Xe 139.922 94 38 Sr 93.915 235 92 U 235.044 1. Calculate the amount of energy released for the following reaction using the values in the table above: 1 0n + 238 92 U 140 54 Xe + 94 38 Sr + 2 1 0n
10.4. NUCLEAR FUSION 193 2. Calculate the amount of energy released for the following reaction using the values in the table above: 2 1H + 3 1 H 4 2 He + 1 0 n 3. Which reaction produces the most energy per reaction? 4. In a kilogram of hydrogen there are 6.0 10 26 atoms while in a kilogram of uranium there are 2.6 10 24 atoms. On a per kilogram of fuel basis, which reaction is more efficient? 5. Which process would be the best for a nuclear power plant? Explain your reasoning.