23-1 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Chapter 23 Nuclear Reactions and Their Applications

23-2 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Nuclear Reactions and Their Applications 23.1 Radioactive Decay and Nuclear Stability 23.2 The Kinetics of Radioactive Decay 23.3 Nuclear Transmutation: Induced Changes in Nuclei 23.4 The Effects of Nuclear Radiation on Matter 23.5 Applications of Radioisotopes 23.6 The Interconversion of Mass and Energy 23.7 Applications of Fission and Fusion

23-3 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Table 23.1

23-4 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Figure 23.1 The behavior of three types of radioactive emissions in an electric field.

23-5 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Types of Radioactive Decay: Balancing Nuclear Equations Total A Total Z Reactants = Total A Total Z Products Alpha decay - A decreases by 4 and Z decreases by 2. Every element heavier than Pb undergoes  decay. Beta decay - ejection of a  particle from the nucleus from the conversion of a neutron into a proton and the expulsion of 0 -1 . The product nuclide will have the same Z but will be one atomic number higher. Positron decay - a positron ( 0 1  ) is the antiparticle of an electron. A proton in the nucleus is converted into a neutron with the expulsion of the positron. Z remains the same but the atomic number decreases. Electron capture - a nuclear proton is converted into a neutron by the capture of an electron. Z remains the same but the atomic number decreases. Gamma emission - energy release; no change in Z or A.

23-6 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Table 23.2

23-7 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sample Problem 23.1Writing Equations for Nuclear Reactions PLAN: SOLUTION: PROBLEM:Write balanced equations for the following nuclear reactions: (a) Naturally occurring thorium-232 undergoes  decay. (b) Chlorine-36 undergoes electron capture. Write a skeleton equation; balance the number of neutrons and charges; solve for the unknown nuclide. A = 228 and Z = Th Ra He (a) Th Ra He (b) Cl e A Z X A = 36 and Z = Cl e S

23-8 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Figure 23.2 A plot of neutrons vs. protons for the stable nuclides.

23-9 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Nuclear Stability and Mode of Decay Very few stable nuclides exist with N/Z < 1. The N/Z ratio of stable nuclides gradually increases a Z increases. All nuclides with Z > 83 are unstable. Elements with an even Z usually have a larger number of stable nuclides than elements with an odd Z. Well over half the stable nuclides have both even N and even Z. Predicting the Mode of Decay Neutron-rich nuclides undergo  decay. Neutron-poor nuclides undergo positron decay or electron capture. Heavy nuclides undergo  decay.

23-10 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Table 23.3

23-11 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sample Problem 23.2Predicting Nuclear Stability PLAN: SOLUTION: PROBLEM:Which of the following nuclides would you predcit to be stable and which radioactive? Explain. (a) Ne(b) S(c) Th(d) Ba Stability will depend upon the N/Z ratio, the value of Z, the value of stable N/Z nuclei, and whether N and Z are even or odd. (a) Radioactive. N/Z = 0.8; there are too few neutrons to be stable. (b) Stable. N/Z = 1.0; Z < 20 and N and Z are even. (c) Radioactive. Every nuclide with Z > 83 is radioactive. (d) Radioactive. N/Z = 1.20; the diagram on shows stability when N/Z ≥ 1.3.

23-12 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sample Problem 23.3Predicting the Mode of Nuclear Decay PLAN: SOLUTION: PROBLEM:Predict the nature of the nuclear change(s) each of the following radioactive nuclides is likely to undergo: (a) 12 5 B(b) U(c) As(d) La Find the N/Z ratio and compare it to the band stability. Then predict which of the modes of decay will give a ratio closer to the band. (a) N/Z = 1.4 which is high. The nuclide will probably undergo  decay altering Z to 6 and lowering the ratio. (b) The large number of neutrons makes this a good candidate for  decay. (c) N/Z = 1.24 which is in the band of stability. It will probably undergo  decay or positron emission. (d) N/Z = 1.23 which is too low for this area of the band. It can increase Z by positron emission or electron capture.

23-13 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Figure 23.3 The 238 U decay series.

23-14 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Decay rate (A) =  N/  t SI unit of decay is the becquerel (Bq) = 1d/s. curie (Ci) = number of nuclei disintegrating each second in 1g of radium-226 = 3.70x10 10 d/s Nuclear decay is a first-order rate process. Large k means a short half-life and vice versa.

23-15 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Figure 23.4 Decrease in the number of 14 C nuclei over time. Table 23.4

23-16 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sample Problem 23.4Finding the Number of Radioactive Nuclei PLAN: SOLUTION: PROBLEM:Strontium-90 is a radioactive by-product of nuclear reactors that behaves biologically like calcium, the element above it in Group 2A(2). When 90 Sr is ingested by mammals, it is found in their milk and eventually in the bones of those drinking the milk. If a sample of 90 Sr has an activity of 1.2x10 12 d/s, what are the activity and the fraction of nuclei that have decayed after 59 yr (t 1/2 of 90 Sr = 29 yr) The fraction of nuclei that have decayed is the change in the number of nuclei, expressed as a fraction of the starting number. The activity of the sample (A) is proportional to the number of nuclei (N). We are given the A 0 and can find A from the integrated form of the first-order rate equation. t 1/2 = ln2/k so k = 0.693/29 yr= yr -1 ln N 0 /N t = ln A 0 /A t = ktln A t = -kt + ln A 0 ln A t = -(0.024yr -1 )(59yr) + ln(1.2x10 12 d/s) ln A t = 26.4A t = 2.9x10 11 d/s Fraction decayed = (1.2x x10 11 ) (1.2x10 12 ) Fraction decayed = 0.76

23-17 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sample Problem 23.5Applying Radiocarbon Dating SOLUTION: PROBLEM:The charred bones of a sloth in a cave in Chile represent the earliest evidence of human presence in the southern tip of South America. A sample of the bone has a specific activity of 5.22 disintegrations per minute per gram of carbon (d/min*g). If the ratio of 12 C: 14 C in living organisms results in a specific activity of 15.3 d/min*g, how old are the bones? (t 1/2 of 14 C = 5730 yr) PLAN:Calculate the rate constant using the given half-life. Then use the first-order rate equation to find the age of the bones. k = ln 2/t 1/2 = 0.693/5730yr= 1.21x10 -4 yr -1 t = 1/k ln A 0 /A t =1/(1.21x10 -4 yr -1 ) ln (15.3/5.22)= 8.89x10 3 yr The bones are about 8900 years old.

23-18 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Figure 23.5 A linear accelerator. The linear accelerator operated by Standford University, California

23-19 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Figure 23.6 The cyclotron accelerator.

23-20 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Table 23.5

23-21 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Figure 23.7 Penetrating power of radioactive emissions. Penetrating power is inversely related to the mass and charge of the emission. Nuclear changes cause chemical changes in surrounding matter by excitation and ionization.

23-22 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Table 23.6

23-23 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Figure 24.9 RCOH O HOR'+ RCO O R' + HOH H + Which reactant contributes which group to the ester?

23-24 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Table 23.7

23-25 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Figure PET and brain activity. normal Alzheimer’s Figure 23.9 The use of radioisotopes to image the thyroid gland. asymmetric scan indicates disease normal

23-26 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Figure The increased shelf life of irradiated food.

23-27 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. The Interconversion of Mass and Energy E = mc 2  E =  mc 2  m =  E / c 2 The mass of the nucleus is less than the combined masses of its nucleons. The mass decrease that occurs when nucleons are united into a nucleus is called the mass defect. The mass defect (  m) can be used to calculate the nuclear binding energy in MeV. 1 amu = 931.5x10 6 eV = MeV

23-28 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Sample Problem 23.6Calculating the Binding Energy per Nucleon PLAN: SOLUTION: PROBLEM:Iron-56 is an extremely stable nuclide. Compute the binding energy per nucleon for 56 Fe and compare it with that for 12 C (mass of 56 Fe atom = amu; mass of 1 H atom = amu; mass of neutron = amu). Find the mass defect,  m; multiply that by the MeV equivalent and divide by the number of nucleons. Mass Defect = [(26 x amu) + (30 x amu)]  m = amu Binding energy == Mev/nucleon ( amu)(931.5 MeV/amu) 56 nucleons 12 C has a binding energy of MeV/nucleon, so 56 Fe is more stable.

23-29 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Figure The variation in binding energy per nucleon.

23-30 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Figure Induced fission of 235 U.

23-31 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Figure A chain reaction of 235 U.

23-32 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Figure Schematic of a light-water nuclear reactor.

23-33 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Figure The tokamak design for magnetic containment of a fusion plasma.