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Chapter 10
Nuclear Physics
10.1 Nuclear Structure and Stability
10.1.1 Activity: Atomic Number and Nucleon Number
10.2 Radioactivity and Radioactive Decay
10.2.1 Activity: Types of Radioactive Decay
10.2.2 Activity: Predicting the Half-Life of a Radioactive Isotope
10.2.3 Experiment: Measuring the Half-Life of a Radioactive Isotope
10.2.4 Activity: 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 Activity: Atomic Number and Nucleon Number
Activity:
1. Write the following isotopes in AZX 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 neutronsare in the nucleus.
(a) 2411X
(b) 6529X
(c) 13153 X
(d) 21284 X
3. Two atoms have the same nucleon number. Are both atoms necessarily the sameelement?
10.2. RADIOACTIVITY AND RADIOACTIVE DECAY 183
10.2 Radioactivity and Radioactive Decay
10.2.1 Activity: Types of Radioactive Decay
Activity:
1. Write out the decay process for each of the following isotopes:
(a) α decay of 21684 Po
(b) β− decay of 13755 Cs
(c) β+ decay of 2211Na
(d) γ decay of 15266 Dy
2. The chart below shows the masses of several nucleii and nuclear particles. Use thechart to answer the following questions:
Particle/Nucleus Mass (amu)proton 1.007825α 4.002603
20680 Hg 205.97749921082 Pb 209.98416321083 Bi 209.984120
23490 Th 234.04359323791 Pa 237.05114023892 U 238.050784
184 CHAPTER 10. NUCLEAR PHYSICS
(a) 23892 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 eachdecay process and then calculate the energy of the parent nucleus and productsfor each reation. Is emission of a single proton feasible? Why or why not?
3. 21082 Pb can decay either through α decay or β− decay. Write a reaction for each of theseprocesses and calculate the enrgy released upon transumtation of lead in each case.
10.2. RADIOACTIVITY AND RADIOACTIVE DECAY 185
10.2.2 Activity: Predicting the Half-Life of a Radioactive Isotope
Activity:Suppose you have a collection of 400 cubes in which each cube has 5 white sides and 1 blackside.
1. Assume that each cube represents a radioactive nucleus. If you rolled the cube sometime during a one minute period, what is the probability that a black side will comeup?
2. Suppose you roll a collection of N(0) = 420 cubes during a one minute period. In thisroll, 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 decayin 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 firstthirty 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 isthe 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 whena white side was rolled? How would this affect the decay rate and the half-life of theisotope?
10.2.3 Experiment: Measuring the Half-Life of a Radioactive Iso-tope
Equipment:420 cubes, each with one black side
Experiment:
1. Divide the cubes among your self and your classmates. Record N(0) = 420 in yourspreadsheet.
2. Roll all four hundred twenty cubes during the first minute. Remove the decayed cubesand 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. Doesit agree with your theoretical prediction? Calculate the percent error. Is there wayto 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 Activity: Radioactive Decay Series
Activity:In the figure below, fill in the missing information into the decay sequence.
232Th
14 billion years
! ?
6.7 years
" 228Ac
6.1 hours
228Th
1.9 years
!?
3.7 days
212Pb
11 hours
!
216At
164 µs
"
?220Rn
55 s
?
61 minutes
!
"
?
.16 s
?
? ! 208Tl
3.1 minutes
212Po
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
Activity:
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 23592 U nucleus.
Fire the neutron gun and observe the reaction. Describe your observations in thespace below.
3. Write a reaction for the process you observed assuming one of the daughter productsis 141
56 Ba.
4. Now change the number of 23592 U nuclei to 0 and the number of 238
92 U nucleii to 1. Firethe neutron gun at the 238
92 U nucleus (you may need to tilt the gun). Describe yourobservations 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 23592 U and 238
92 U nucleii. When do you get a chainreaction?
8. The natural abundance of 23592 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
Activity:
1. In the same simulation that you used in the last activity, click on the Nuclear Reactortab.
10.3. NUCLEAR FISSION AND NUCLEAR REACTORS 191
2. Begin with the control rods all the way in and fire the neutrons. What happens tothe reactor? Describe your observations of the temperature, energy output and poweroutput below. Reset the nucleii.
3. Now pull the control rods all the way out and fire the neutrons. What happens tothe reactor? Describe your observations of the temperature, energy output and poweroutput below. Reset the nucleii.
4. The goal of a nuclear power plant is to keep a fairly constant output power whilekeeping the temperature low enough not to damage the reactor. In this simulation youwant to keep the temeperature at or below the gray region. Run the simulation andattempt to keep the power constant and the temperature under control. In the spacebelow, 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
Activity:
Particle/Nucleus Mass (amu)10n 1.008721H 2.014131H 3.016142He 4.0026
14054 Xe 139.9229438 Sr 93.91523592 U 235.044
1. Calculate the amount of energy released for the following reaction using the values inthe table above:
10n+238
92 U→14054 Xe +94
38 Sr + 210n
10.4. NUCLEAR FUSION 193
2. Calculate the amount of energy released for the following reaction using the values inthe table above:
21H +3
1 H→42 He +1
0 n
3. Which reaction produces the most energy per reaction?
4. In a kilogram of hydrogen there are 6.0 × 1026 atoms while in a kilogram of uraniumthere are 2.6 × 1024 atoms. On a per kilogram of fuel basis, which reaction is moreefficient?
5. Which process would be the best for a nuclear power plant? Explain your reasoning.