Nuclear Chemistry Chapter 23 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. • In chemical reactions, only the outer electrons of the atoms are disturbed. • In nuclear reactions, the nuclear changes that occur are independent of the chemical environment of the atom. 20 | 2 Radioactive decay is the process in which a nucleus spontaneously disintegrates, giving off radiation. A nuclear bombardment reaction is a nuclear reaction in which a nucleus is bombarded, or struck, by another nucleus or by a nuclear particle. 20 | 3 We write nuclear equations using nuclide symbols. Nuclear equations are balanced when the total mass number and the atomic number on both reactant and product sides are equal. • Let’s look at the decay of uranium-238. 20 | 4 Symbols for other particles are given below: Proton 1 1 H or 11P Neutron 1 0 Electron 0 -1 Positron 0 1 Gamma photon 0 0 n e or -01β e or 01β 20 | 5 γ Atomic number (Z) = number of protons in nucleus Mass number (A) = number of protons + number of neutrons = atomic number (Z) + number of neutrons Mass Number Atomic Number A ZX Element Symbol proton 1p 1H or 1 1 neutron 1n 0 electron 0b 0e or -1 -1 positron 0b 0e or +1 +1 a particle 4He 4a or 2 2 A 1 1 0 0 4 Z 1 0 -1 +1 2 23.1 Balancing Nuclear Equations 1. Conserve mass number (A). The sum of protons plus neutrons in the products must equal the sum of protons plus neutrons in the reactants. 235 92 U + 10n 138 55 Cs + 96 37 Rb + 2 10n 235 + 1 = 138 + 96 + 2x1 2. Conserve atomic number (Z) or nuclear charge. The sum of nuclear charges in the products must equal the sum of nuclear charges in the reactants. 235 92 U + 10n 138 55 Cs + 96 37 Rb 92 + 0 = 55 + 37 + 2x0 + 2 10n 23.1 212Po decays by alpha emission. Write the balanced nuclear equation for the decay of 212Po. 4 alpha particle - 42He or 2a 212Po 84 4He 2 + AZX 212 = 4 + A A = 208 84 = 2 + Z Z = 82 212Po 84 4He 2 + 208 82Pb 23.1 Radon-222 is a radioactive noble gas that is sometimes present as an air pollutant in homes built over soil with high uranium content (uranium-238 decays to radium-226, which in turn decays to radon-222). A radon-222 nucleus decays to polonium-218 by emitting an alpha particle. Write the nuclear equation for this decay process. 20 | 9 From the periodic table, we can see that the atomic number of radon is 86 and the atomic number of polonium is 84. For the alpha particle symbol, both He and a are correct. 222 86 222 86 Rn 42 α Rn 42 He 218 84 Po 218 84 Po To check, total the mass numbers and atomic numbers on each side of the reaction. Mass numbers: 222 = 4 + 218 Atomic numbers: 86 = 2 + 84 20 | 10 Iodine-131 is used in the diagnosis and treatment of thyroid cancer. This isotope decays by beta emission. What is the product nucleus? 20 | 11 From the periodic table, we find that the atomic number of iodine is 53. The beta particle symbol is correct as either e or b. 131 0 A I e 53 -1 ZX 131 53 I -01β AZ X Now find the atomic and mass number of the product: 131 = 0 + A 53 = –1 + Z A = 131 Z = 54 Next, use the atomic number to find the symbol: Xe. 131 53 I -01e 131 54 131 53 Xe 20 | 12 I -01β 131 54 Xe 23.1 n/p too large beta decay X Y n/p too small positron decay or electron capture 23.2 Nuclear Stability It is reasonable to wonder how a nucleus with positively charged protons is held together, given that positively charged particles repel each other. The stability of the nucleus is due to the strong nuclear force. The nuclear force acts only at very short distances, about 10-13 m. At this distance it is stronger than the electric repulsion. 20 | 15 The shell model of the nucleus is a nuclear model in which protons and neutrons exist in levels, or shells, analogous to the shell structure that exists for electrons. 20 | 16 Just as certain very stable numbers of electrons (2, 10, 28, and so on) occur when a shell is filled, so there are magic numbers for nucleons. A magic number is the number of nuclear particles in a completed shell of protons and neutrons. For protons, the magic numbers are 2, 8, 20, 28, 50, and 82. For neutrons, the magic numbers also include 114. 20 | 17 • 20 | 18 For stable nuclides with Z ≤ 20, the ratio of neutrons to protons is between 1 and 1.1. For stable nuclides with Z > 20, the ratio of neutrons to protons increases to about 1.5. This is believed to be due to the increasing repulsion between protons, which requires more neutrons to increase the strong nuclear force. No stable nuclide exists for Z > 83, perhaps because the proton repulsion becomes too great. 20 | 19 Nuclear Stability • Certain numbers of neutrons and protons are extra stable • n or p = 2, 8, 20, 50, 82 and 126 • Like extra stable numbers of electrons in noble gases (e- = 2, 10, 18, 36, 54 and 86) • Nuclei with even numbers of both protons and neutrons are more stable than those with odd numbers of neutron and protons • All isotopes of the elements with atomic numbers higher than 83 are radioactive • All isotopes of Tc and Pm are radioactive 23.2 • Predict which nucleus in each pair should be more stable and explain why. • a. astatine-210 and lead-207 b. molybdenum-91 and molybdenum-92 c. calcium-37 and calcium-42 20 | 21 a. Astatine-210 has 85 protons and 125 neutrons. Lead-207 has 82 protons and 125 neutrons. Lead-207 is more stable because it has a magic number of protons. Also, At has > 83 protons. b. Molybdenum-91 has 42 protons and 49 neutrons. Molybdenum-92 has 42 protons and 50 neutrons. Molybdenum-92 is more stable because it has a magic number of neutrons. 20 | 22 c. Calcium-37 has 20 protons and 17 neutrons. Calcium-42 has 20 protons and 22 neutrons. Calcium-42 is more stable because it has an even number of neutrons. (Both have a magic number of protons.) 20 | 23 • There are six common types of radioactive decay. 1. Alpha emission Emission of an alpha particle from an unstable nucleus. 20 | 24 2. Beta emission Emission of a beta particle from an unstable nucleus. Beta emission is equivalent to a neutron converting to a proton. 20 | 25 3. Positron emission Emission of a positron particle from an unstable nucleus. Positron emission is equivalent to a proton converting to a neutron. 20 | 26 4. Electron capture The decay of an unstable nucleus by capture of an electron from an inner orbital of the atom. Electron capture is equivalent to a proton converting to a neutron. 20 | 27 5. Gamma emission Emission from an excited nucleus of a gamma photon, corresponding to radiation with a wavelength of approximately 10-12 m. Technetium-99m is an example of a metastable nucleus; it is in an excited state and has a lifetime of ≥ 10-9 s. Copyright © C 20 | 28 6. Spontaneous fission The spontaneous decay of an unstable nucleus in which a heavy nucleus of mass number greater than 89 splits into lighter nuclei and energy is released. 20 | 29 Nuclides to the left of the band of stability have a neutron-to-proton ratio, N/Z, that is too large. They decay by beta emission, which reduces the N/Z ratio by converting a neutron to a proton. Nuclides to the right of the band of stability have an N/Z ratio that is too small. These nuclides decay by either positron emission or electron capture. Either process increases the N/Z ratio by converting a proton to a neutron. 20 | 30 • 20 | 31 Thallium-201 is a radioactive isotope used in the diagnosis of circulatory impairment and heart disease. How do you expect it to decay? Thallium-201 has 81 protons and 120 neutrons. N/Z < 1.5 (too small). Thallium-201 will decay by either electron capture or positron emission—probably electron capture, given that it is a heavy element. 20 | 32 Radioactive Decay Series A sequence in which one radioactive nucleus decays to a second, which then decays to a third, and so forth, until a stable nucleus of lead is formed. Three radioactive decay series are found naturally: uranium-238, uranium-235, and thorium-232. 20 | 33 The radioactive decay series for uranium-238 ends with lead-206 Copyright © Cengage Learning. All rights res 20 | 34 You have two samples of water, each made up of different isotopes of hydrogen: one contains hydrogen-1 and the other contains hydrogen-3. a. Would you expect these two water samples to be chemically similar? b. Would you expect these two water samples to be physically the same? c. Which one of these water samples would you expect to be radioactive? 20 | 35 a. Yes, isotopes have similar chemical properties. b. No, the hydrogen-3 water has more mass than the hydrogen-1 water. c. The hydrogen-3 (tritium) water should be radioactive. 20 | 36 Nuclear Bombardment Reactions Nuclear bombardment reactions are not spontaneous. They involve the collision of a nucleus with another particle. Transmutation is the change of one element into another by bombarding the nucleus of the element with nuclear particles or nuclei. 20 | 37 When Rutherford allowed alpha particles to collide with nitrogen nuclei, he found that a proton was ejected and oxygen was formed. 20 | 38 James Chadwick proposed the existence of the neutron based on the result of bombarding beryllium-9 with alpha particles. The product included neutral radiation we now know as neutrons. 9 Be 4 He 12C 1 n 4 2 6 0 The first radioactive nucleus produced in the laboratory was phosphorus-30. 27 13 Al 2 He 15P 0n 4 30 1 Phosphorus-30 decays by positron emission. 30 15 P Si e 30 14 20 | 39 0 1 In the abbreviated notation for nuclear bombardment reactions, the starting nucleus is written first. It is followed by, within parentheses, the bombarding particle, a comma, and then the ejected particle. Finally, the product nucleus is written. 20 | 40 For example, for the bombardment of nitrogen14 with an alpha particle, which leads to the ejection of a proton, the reaction is written as follows: 4 17 1 N He O H 7 2 8 1 14 The abbreviated notation is 14 7 4 2 1 1 17 N He, p 8 O 20 | 41 The following symbols are used for nuclide particles when writing them using the abbreviated notation for a nuclear bombardment reaction. Neutron, n Proton, p Deuteron (hydrogen-2), d Alpha (helium-4), a 20 | 42 Sodium-22 is made by the bombardment of magnesium-24 (the most abundant isotope of magnesium) with deuterons. An alpha particle is the other product. Write the abbreviated notation for the nuclear reaction. Reaction : 24 12 Mg H 2 1 Abbreviate d notation : 20 | 43 24 12 Na He 22 11 4 2 22 Mg d, a 11Na A neutron is produced when lithium-7 is bombarded with a proton. What product nucleus is obtained in this reaction? Reaction : 73 Li 11H 74 Be 01n The product is 74 Be. 20 | 44 Energy of Nuclear Reactions Nuclear reactions involve changes of energy on a much larger scale than occur in chemical reactions. This energy is used in nuclear power reactors and to provide the energy for nuclear weapons. 20 | 45 Mass–Energy Calculations When nuclei decay, they form products of lower energy. The change of energy is related to changes of mass, according to the equation derived by Einstein, E = mc2. 20 | 46 DE = (Dm)c2 We can compute the change in energy for a nuclear reaction by calculating the change in mass. The change in mass must be given in kilograms to satisfy Einstein’s equation. The masses of some elements and other particles are given in Table 20.3. 20 | 47 Consider the following nuclear reaction, in which a lithium-7 nucleus is bombarded with a hydrogen nucleus to produce two alpha particles: 7 1 4 Li H 2 3 1 2 He What is the energy change of this reaction per gram of lithium? Nuclear masses: 7 3 Li, 7.01436 amu 1 1 H, 1.00728 amu 4 2 He, 4.00150 amu 20 | 48 • First we find the change in mass for one mole of lithium-7. • Mass of products: • 2(4.00150 × 10-3 kg) = 8.00300 × 10-3 kg • Mass of reactants: • 7.01436 × 10-3 kg + 1.00728 × 10-3 kg • = 8.02164 × 10-3 kg Dm = –1.864 × 10-5 kg 20 | 49 DE = (–1.864 × 10-5 kg)(2.998 × 108 m/s)2 DE = –1.675 × 1012 J ΔE – 1.675 1012 J 7 g 3 Li 7.01436 g 73 Li ΔE 11 7 – 2.388 10 J/g 3 Li 7 g 3 Li 20 | 50 Nuclear binding energy (BE) is the energy required to break up a nucleus into its component protons and neutrons. BE + 199F 911p + 1010n E = mc2 BE = 9 x (p mass) + 10 x (n mass) – 19F mass BE (amu) = 9 x 1.007825 + 10 x 1.008665 – 18.9984 BE = 0.1587 amu 1 amu = 1.49 x 10-10 J BE = 2.37 x 10-11J binding energy binding energy per nucleon = number of nucleons 2.37 x 10-11 J = 1.25 x 10-12 J = 19 nucleons 23.2 Nuclear binding energy per nucleon vs Mass number nuclear binding energy nucleon nuclear stability 23.2 Nuclear Binding Energy • The equivalence of mass and energy explains the mass defect—that is, the difference between the total mass of the nucleons that make up an atom and the mass of the atom. The difference in mass is the energy holding the nucleus together. • The binding energy of a nucleus is the energy needed to break a nucleus into its individual protons and neutrons. 20 | 53 Both the binding energy and the mass defect are indications of the stability of the nucleus. 20 | 54 Rate of Radioactive Decay The rate of radioactive decay is the number of nuclei disintegrating per unit time. It is proportional to the number of nuclei in the sample. Rate = kNt Nt = the number of radioactive nuclei at time, t. k = the radioactive decay constant or rate constant for radioactive decay; it is characteristic of the nuclide. 20 | 55 The thorium-234 isotope decays by emitting a beta particle. A 50.0-mg sample of thorium-234 has an activity of 1.16 Ci. What is the decay constant for thorium-234? 20 | 56 • First, we find the number of nuclei of thorium-234. 23 1 mol 6.022 10 nuclei -6 Nt 50.0 10 g 232.04 g 1mol Nt 1.298 10 nuclei 17 Next, we convert the activity from curies to disintegrations per second. disintegra tions 3.700 x 10 s Rate 1.16 Ci 1 Ci 10 disintegra tions Rate 4.292 10 s 10 20 | 57 Finally, we use the rate equation, understanding that 1 disintegration = 1 nuclei. rate k Nt disintegra tions 4.292 10 s k 1.298 1017 nuclei 10 k 3.31 10 -7 /s 20 | 58 • Half-life is the time it takes for one-half of the nuclei in a sample to decay. • Half-life is related to the decay constant by the following equation: t1 2 0.693 k 20 | 59 • After one half-life, half of the sample (0.5) remains. • After two half-lives, one-fourth of the sample (0.25) remains. • After three half-lives, one-eighth of the sample remains. • This relationship is summarized in the following equation and in the graph on the next slide. n 1 Fraction remaining , 2 where n number of half - lives 20 | 60 • 20 | 61 Thallium-201 is used in the diagnosis of heart disease. This isotope decays by electron capture; the decay constant is 2.63 × 10-6/s. What is the half-life of thallium-201 in days? 20 | 62 t1 2 0.693 t1 2 k 0.693 t1 -6 2 2.63 10 s 1 min 1h 1 day 5 2.63 10 s 60 s 60 min 24 h t 1 3.05 days 2 Iodine-131 is used in the diagnosis and treatment of thyroid disorders. The halflife for the beta decay of iodine-131 is 8.07 days. a. What is the decay constant (in units per second)? b. What is the activity (in curies) of a 1.0-mg sample of iodine? 20 | 64 a. k 0.693 t1 2 0.693 k 24 h 60 min 60 s 8.07 days 1 day 1h 1min k 9.94 10 -7 /s 20 | 65 23 1 mol 6.022 10 nuclei -6 Nt 1.0 10 g b. 126.90 g 1mol Nt 4.745 1015 nuclei Rate kNt 9.94 10-7 15 Rate 4.745 10 nuclei s 9 nuclei Rate 4.72 10 s 20 | 66 The rate constant is related to the fraction of nuclei remaining by the following equation: Nt - kt ln N0 N0 is the original number of nuclei. Nt is the number of nuclei at time t. Nt is the fraction of nuclei remaining at time t. N0 Nt 4.745 x 10 nuclei 15 20 | 67 A 0.500-g sample of iodine-131 is obtained by a hospital. How much will remain after a period of one week? The half-life of this isotope is 8.07 days. 20 | 68 First, we find the value of k. 0.693 k t1 2 0.693 k 1 week 8.07 days 7 day 0.601 k week 20 | 69 Next, we find the fraction of nuclei remaining. Nt - kt ln N0 Nt 0.601 ln 1 week week N0 Nt ln - 0.601 N0 Nt 0.548 N0 54.8% of nuclei remain. 20 | 70 Radioactive Dating Because the rate of radioactive decay is constant, this rate can serve as a sort of clock for dating objects. Carbon-14 is part of all living material. While a plant or animal is living, the fraction of carbon-14 in it remains constant due to exchange with the atmosphere. Once dead, the fraction of carbon-14 and, therefore, the rate of decay decrease. In this way, the fraction of carbon-14 present in the remains becomes a clock measuring the time since the plant’s or animal’s death. 20 | 71 The half-life of carbon-14 is 5730 years. Living organisms have a carbon-14 decay rate of 15.3 disintegrations per minute per gram of total carbon. The ratio of disintegrations at time t to time 0 is equal to the ratio of nuclei at time t to time 0. 20 | 72 A sample of wheat recovered from a cave was analyzed and gave 12.8 disintegrations of carbon-14 per minute per gram of carbon. What is the age of the grain? Carbon from living material decays at a rate of 15.3 disintegrations per minute per gram of carbon. The half-life of carbon-14 is 5730 years. 20 | 73 Ratet = 12.8 disintegrations/min/g Rate0 = 15.3 disintegrations/min/g t1/2 = 5730 y Nt rate t 12.8 disintegra tions/min/ g 0.8366 N0 rate 0 15.3 disintegra tions/min/ g Nt Nt ln ln N0 N0 ln 0.8366 t 0.693 0.693 t1 2 k 5730 y 3 t 1.48 10 y 20 | 74 Kinetics of Radioactive Decay N daughter DN rate = Dt rate = lN DN = lN Dt N = N0exp(-lt) lnN = lnN0 - lt N = the number of atoms at time t N0 = the number of atoms at time t = 0 l is the decay constant ln2 l = t½ 23.3 Kinetics of Radioactive Decay ln[N] = ln[N]0 - lt ln [N] [N] [N] = [N]0exp(-lt) 23.3 Radiocarbon Dating 14N 7 + 01n 14C 6 14C 6 14N 7 + 11H + -10b + n t½ = 5730 years Uranium-238 Dating 238U 92 206Pb 82 + 8 24a + 6-10b t½ = 4.51 x 109 years 23.3 Nuclear Transmutation 14N 7 27Al 13 14N 7 + 24a + 24a + 11p 17O 8 + 11p 30P 15 + 01n 11C 6 + 42a Cyclotron Particle Accelerator 23.4 Nuclear Transmutation 23.4 Nuclear Fission 235U 92 + 01n 90Sr 38 1n + Energy + 143 Xe + 3 0 54 Energy = [mass 235U + mass n – (mass 90Sr + mass 143Xe + 3 x mass n )] x c2 Energy = 3.3 x 10-11J per 235U = 2.0 x 1013 J per mole 235U Combustion of 1 ton of coal = 5 x 107 J 23.5 Nuclear Fission Representative fission reaction 235U 92 + 01n 90Sr 38 1n + Energy + 143 Xe + 3 0 54 23.5 Nuclear Fission Nuclear chain reaction is a self-sustaining sequence of nuclear fission reactions. The minimum mass of fissionable material required to generate a self-sustaining nuclear chain reaction is the critical mass. Non-critical Critical 23.5 Schematic Diagram of a Nuclear Reactor 23.5 Nuclear Fission Annual Waste Production 35,000 tons SO2 4.5 x 106 tons CO2 3.5 x 106 ft3 ash 1,000 MW coal-fired power plant 70 ft3 vitrified waste 1,000 MW nuclear power plant 23.5 Nuclear Fission Hazards of the radioactivities in spent fuel compared to uranium ore From “Science, Society and America’s Nuclear Waste,” DOE/RW-0361 TG 23.5 Chemistry In Action: Nature’s Own Fission Reactor Natural Uranium 0.7202 % U-235 99.2798% U-238 Measured at Oklo 0.7171 % U-235 Nuclear Fusion Fusion Reaction 2 2 3 1 1 H + 1H 1 H + 1H 2H 1 + 13H 6Li 3 + 12H 4He 2 2 + 10n 4He 2 Energy Released 6.3 x 10-13 J 2.8 x 10-12 J 3.6 x 10-12 J Tokamak magnetic plasma confinement 23.6 Radioisotopes in Medicine • 1 out of every 3 hospital patients will undergo a nuclear medicine procedure • 24Na, • 131I, t½ = 14.8 hr, b emitter, thyroid gland activity • 123I, t½ = 13.3 hr, gray emitter, brain imaging • 18F, t½ = 1.8 hr, b emitter, positron emission tomography • 99mTc, t½ = 14.8 hr, b emitter, blood-flow tracer t½ = 6 hr, gray emitter, imaging agent Brain images with 123I-labeled compound 23.7 Radioisotopes in Medicine Research production of 99Mo 98Mo 42 + 10n 99Mo 42 Commercial production of 99Mo 235U 92 99Mo 42 99mTc 43 + 10n 99Mo 42 99mTc 43 99Tc 43 + other fission products + -10b + n + g-ray Bone Scan with 99mTc t½ = 66 hours t½ = 6 hours 23.7 Radiation Counters There are two types of devices: ionization counters and scintillation counters. 20 | 90 The Geiger counter is an ionization counter used to count particles emitted by radioactive nuclei. It consists of a metal tube filled with gas, such as argon. 20 | 91 A scintillation counter detects nuclear radiation based on flashes of light generated in a material by the radiation. A phosphor is a substance that emits flashes of light when struck by radiation. In the scintillation counter, the flashes of light are detected by a photomultiplier tube. 20 | 92 • The activity of a radioactive source is the number of nuclear disintegrations per unit time occurring in a radioactive material. • The curie (Ci) is a unit of activity equal to 3.700 × 1010 disintegrations per second. 20 | 93 Biological Effects and Radiation Dosage The rad (from radiation affected dose) is the dosage of radiation that deposits 1 × 10-2 J of energy per kilogram of tissue. 20 | 94 The rem is a unit of radiation dosage that is used to relate various kinds of radiation in terms of biological destruction. It equals the rad times a factor for the type of radiation, called the relative biological effectiveness (RBE). • rem = rad × RBE Beta and gamma radiation have an RBE of about 1, neutron radiation has an RBE of about 5, and alpha radiation has an RBE of about 10. 20 | 95 The effect of radiation on a person depends on the dosage and the length of time of the exposure. A series of small doses have less overall effect than a large dose given all at once. A single dose of 500 rems is fatal to most people. Detectable effects are seen at dosages as low as 30 rems. Background radiation averages about 0.1 rem per year but varies dramatically by location. 20 | 96 If you are internally exposed to 10 rads of a, b, and g radiation, which form of radiation will cause the greatest damage? The a radiation has the highest RBE, so it will cause the greatest damage. 20 | 97 Biological Effects of Radiation Radiation absorbed dose (rad) 1 rad = 1 x 10-5 J/g of material Roentgen equivalent for man (rem) 1 rem = 1 rad x Q Quality Factor g-ray = 1 b=1 a = 20 23.8 Chemistry In Action: Food Irradiation Dosage Effect Up to 100 kilorad Inhibits sprouting of potatoes, onions, garlics. Inactivates trichinae in pork. Kills or prevents insects from reproducing in grains, fruits, and vegetables. 100 – 1000 kilorads Delays spoilage of meat poultry and fish. Reduces salmonella. Extends shelf life of some fruit. 1000 to 10,000 kilorads Sterilizes meat, poultry and fish. Kills insects and microorganisms in spices and seasoning.