CHAPTER 18 NUCLEAR CHEMISTRY SOLUTIONS TO REVIEW QUESTIONS

Transcription

1 C18 1/9/1 11:5:6 Page 71 CHAPTER 18 NUCLEAR CHEMISTRY SOLUTIONS TO REVIEW QUESTIONS 1. Contributions to the early history of radioactivity include: (a) Henri Becquerel: He discovered radioactivity. Marie and Pierre Curie: They discovered the elements polonium and radium. (c) Wilhelm Roentgen: He discovered X rays and developed the technique of producing them. While this was not a radioactive phenomenon, it triggered Becquerel s discovery of radioactivity. (d) Ernest Rutherford: He discovered alpha and beta particles, established the link between radioactivity and transmutation, and produced the first successful man-made transmutation. (e) Otto Hahn and Fritz Strassmann: They were first to produce nuclear fission.. Chemical reactions are caused by atoms or ions coming together, so are greatly influenced by temperature and concentration, which affect the number of collisions. Radioactivity is a spontaneous reaction of an individual nucleus, and is independent of such influences. 3. The term isotope is used with reference to atoms of the same element that contains different masses. For example, 1 6 C and 14 6 C. The term nuclide is used in nuclear chemistry to infer any isotope of any atom. 4. ð half-life yearsþ 7:6 1 7 ¼ 7 half-lives year Even if plutonium-44 had been present in large quantities five billion years ago, no measureable amount would survive after 7 half-lives. 5. In living species, the ratio of carbon-14 to carbon-1 is constant due to the constant C-14=C-1 ratio in the atmosphere and food sources. When a species dies, life processes stop. The C-14=C-1 ratio decreases with time because C-14 is radioactive and decays according to its half-life, while the amount of C-1 in the species remains constant. Thus, the age of an archaeological artifact containing carbon can be calculated by comparing the C-14=C-1 ratio in the artifact with the C-14=C-1 ratio in the living species. 6. The half-life of carbon-14 is 573 years. ð half-life yearsþ ¼ 7 1 half-lives 573 years 7 half-lives would pass in 4 million years. Not enough C-14 would remain to allow detection with any degree of reliability. C-14 dating would not prove useful in this case. 7. (a) Gamma radiation requires the most shielding. Alpha radiation requires the least shielding. 8. Alpha particles are deflected less than beta particles while passing through a magnetic field, because they are much heavier (more than 7, times heavier) than beta particles

2 C18 1/9/1 11:5:6 Page 7 9. charge mass nature of particles penetrating power Alpha þ 4 amu He nucleus low Beta amu electron moderate Gamma electromagnetic radiation high 1. Decay of bismuth Bi! 4 7 He þ 81 Tl 7 81Tl! 1 e þ 7 8 Pb 11. Pairs of nuclides that would be found in the fission reaction of U-35. Any two nuclides, whose atomic numbers add up to 9 and mass numbers (in the range of 7-16) add up to Examples include: Sr and 54 Xe Ba and Kr 11 4 Mo and Sn 1. Natural radioactivity is the spontaneous disintegration of those radioactive nuclides found in nature. Artificial radioactivity is the spontaneous disintegration of radioactive isotopes produced synthetically, otherwise it is the same as natural radioactivity. 13. A radioactive disintegration series starts with a particular radionuclide and progresses stepwise by alpha and beta emissions to other radionuclides, ending at a stable nuclide. For example: 38 9 U! 14 steps 6 8 PbðstableÞ 14. Transmutation is the conversion of one element into another by natural or artificial means.the nucleus of an atom is bombarded by various particles (alpha, beta, protons, etc.). The fast moving particles are captured by the nucleus, forming an unstable nucleus, which decays to another kind of atom. For example: 9 4 Be þ 4 He! 1 6 C þ 1 n 15. a 8 3 9Th! b 8 89 Ra! b 8 9 Ac! a 4 a 1 8 Th! 16 84Po! a 86 b 1 83 Ra! Pb! Rn! a b 1 84 Bi! Po! a 8 8 Pb Np loses seven alpha particles and four beta particles. Determination of the final product: 9 83 Bi nuclear charge ¼ 93 7ðÞþ4ð1Þ ¼83 mass ¼ 37 7ð4Þ ¼9 17. Radioactivity could be used to locate a leak in an underground pipe by using a water soluble tracer element. Dissolve the tracer in water and pass the water through the pipe. Test the ground along the path of the pipe with a Geiger counter until radioactivity from the leak is detected. Then dig. 18. A scintillation counter is a radiation detector which contains molecules that emit light when they are struck by ionizing radiation. The number of light flashes are recorded as a numerical output of the radiation level

3 C18 1/9/1 11:5:6 Page The curie describes the amount of radioactivity produced by an element. One curie is equal to disintegrations/sec. REM stands for roentgen equivalent to man and measures the effective exposure to ionizing radiation. 1. Two Germans, Otto Hahn and Fritz Strassmann, were the first scientists to report nuclear fission. The fission resulted from bombarding uranium nuclei with neutrons.. Natural uranium is 99þ% U-38. Commercial nuclear reactors use U-35 enriched uranium as a fuel. Slow neutrons will cause the fission of U-35, but not U-38. Fast neutrons are capable of a nuclear reaction with U-38 to produce fissionable Pu-39. A breeder reactor converts nonfissionable U-38 to fissionable Pu-39, and in the process, manufactures more fuel than it consumes. 3. The fission reaction in a nuclear reactor and in an atomic bomb are essentially the same. The difference is that the fissioning is wild or uncontrolled in the bomb. In a nuclear reactor, the fissioning rate is controlled by means of moderators, such as graphite, to slow the neutrons and control rods of cadmium or boron to absorb some of the neutrons. 4. A certain amount of fissionable material (a critical mass) must be present before a self-sustaining chain reaction can occur. Without a critical mass, too many neutrons from fissions will escape, and the reaction cannot reach a chain reaction status, unless at least one neutron is captured for every fission that occurs. 5. The disadvantages of nuclear power include the danger of contamination from radioactive material and the radioactive waste products that accumulate, some having half-lives of thousands of years. 6. The hazards associated with an atomic bomb explosion include shock waves, heat and radiation from alpha particles, beta particles, gamma rays, and ultraviolet rays. Gamma rays and X-rays cause burns, sterilization, and gene mutation. If the bomb explodes close to the ground radioactive material is carried by dust particles and is spread over wide areas. 7. Heavy elements undergo fission and lighter elements undergo fusion. 8. In a nuclear power plant, a controlled nuclear fission reaction provides heat energy that is used to produce steam. The steam turns a turbine that generates electricity. 9. The mass defect is the difference between the mass of an atom and the sum of the masses of the number of protons, neutrons, and electrons in that atom. The energy equivalent of this mass defect is known as the nuclear binding energy. 3. When radioactive rays pass through normal matter, they cause that matter to become ionized (usually by knocking out electrons). Therefore, the radioactive rays are classified as ionizing radiation. 31. Some biological hazards associated with radioactivity are: (a) High levels of radiation can cause nausea, vomiting, diarrhea, and death. The radiation produces ionization in the cells, particularly in the nucleus of the cells. Long-term exposure to low levels of radiation can weaken the body and cause malignant tumors. (c) Radiation can damage DNA molecules in the body causing mutations, which by reproduction, can be passed on to succeeding generations

4 C18 1/9/1 11:5:6 Page Strontium-9 has two characteristics that create concern. Its half-life is 8 years, so it remains active for a long period of time (disintegrating by emitting b radiation). The other characteristic is that Sr-9 is chemically similar to calcium, so when it is present in milk Sr-9 is deposited in bone tissue along with calcium. Red blood cells are produced in the bone marrow. If the marrow is subjected to beta radiation from strontium-9, the red blood cells will be destroyed, increasing the incidence of leukemia and bone cancer. 33. A radioactive tracer is a radioactive material, whose presence is traced by a Geiger counter or some other detecting device. Tracers are often injected into the human body, animals, and plants to determine chemical pathways, rates of circulation, etc. For example, use of a tracer could determine the length of time for material to travel from the root system to the leaves in a tree

5 C18 1/9/1 11:5:6 Page 75 SOLUTIONS TO EXERCISES 1. Protons Neutrons Nucleons (a) 7 8 Pb Ga Protons Neutrons Nucleons (a) 18 5Te S When a nucleus loses an alpha particle, its atomic number decreases by two, and its mass number decreases by four. 4. When a nucleus loses a beta particle, its atomic number increases by one, and its mass number remains unchanged. 5. Equations for alpha decay: (a) 1 83 Bi!4 6 He þ 81 Ra 38 9 U! 4 34 He þ 9 Th 6. Equations for alpha decay: 38 (a) 9 Th!4 34 He þ Pu!4 35 He þ 9 U Ra 7. Equations for beta decay: 13 (a) 7 N! 1 e þ 13 8 O 34 9Th! 1 e þ Pa 8. Equations for beta decay: (a) Al! 1 e þ Si Np! 1 e þ Pu 9. (a) alpha-emission beta-emission then gamma-emission (c) beta-emission 1. (a) gamma-emission alpha-emission then beta-emission (c) alpha-emission then gamma-emission Al! þ1 e þ 6 1 Mg P! 1 e þ 3 16 S

6 C18 1/9/1 11:5:6 Page (a) 66 9Cu!66 3 Zn þ 1 e 1 e þ 7 4 Be!7 3 Li 7 (c) 13 Al þ 4 3 He! 14 Si þ 1 1 H 85 (d) 37 Rb þ 1 n!8 35 Br þ 4 He (a) 13 Al þ 4 3 He! 15 P þ 1 n 7 14Si! þ1 e þ 7 13 Al (c) 1 6 C þ 1 H!13 7 N þ 1 n (d) 8 35Br!8 36 Kr þ 1 e 15. ð11 yearsþ 1 half-life ¼ 4 half-lives 8 years In 4 half-lives 1=16th or ( 1 = ) 4 of the starting amount would remain. 1: mg Sr-9 16 ¼ :65 mg Sr-9 remains after 11 years: Cts=min ¼ 1 Cts=min; 1 Cts=min ¼ 6 Cts=min; 6 Cts=min ¼ 3 Cts=min; 3 half-lives are required to reduce the count from 4 to 3 counts=min. 198 þ (3 8) ¼ 64. After 1 half-life, 1/ of the sample remains, after half-lives 1/4 of the sample remains, and after 3 half-lives 1/8 of the sample remains. 17. Loss of mass: 33 5 ¼ 8, equivalent to alpha particles. Loss in atomic number: ¼, equivalent to 1 alpha particle. With a loss of alpha particles the loss of atomic number should be 4. Therefore, there must also be a loss of beta particles to increase the atomic number by. So one possible series is: 33 91Pa! b 33 9 U! a 9 9 a 5 Th! Ra! b 5 89 Ac 18. Loss of mass: 8 1 ¼ 16, which is equivalent to 4 alpha particles. Loss in atomic number 9 8 ¼ 8, which is equivalent to 4 alpha particles. This looks like a total loss of 4 alpha particles. Therefore the series is: a 4 8 9Th! a 86 Ra! a Rn! Po! a 1 8 Pb

7 C18 1/9/1 11:5:6 Page (a) 35 9 U þ 1 n! Sr þ 54 Xe þ 3 1 n þ energy Mass loss ¼ mass of reactants mass of products Mass of reactants ¼ amu þ 1.87 amu ¼ amu Mass of products ¼ amu þ amu þ 3(1.87 amu) ¼ 35,8594 amu (c) Mass lost ¼ amu amu ¼.193 amu 1: g 9: 1 13 J ð:193 amuþ 6: 1 3 ¼ : J=atom U-35 amu 1: g : J atom 6: 1 3 atoms ¼ 1: J=mol mol :193 amu ð1þ ¼:8185% mass loss 36:56 amu. 1 (a) 1 H þ 1 H! 3 He þ energy Mass loss ¼ mass of reactants mass of products Mass of reactants ¼ g=mol þ.141 g=mol ¼ 3.4 g=mol Mass of products ¼ g=mol Mass lost ¼ 3.4 g=mol g=mol ¼.61 g=mol :61 g 9: 1 13 J ¼ 5: J=mol mol g :61 g ð1þ ¼:199% mass loss 3:4 g 1. (a) Chromium-51: 4 protons; 7 neutrons; 4 electrons Holmium-166: 67 protons; 99 neutrons; 67 electrons (c) Palladium-13: 46 protons; 57 neutrons; 46 electrons (d) Strontium-89: 38 protons; 51 neutrons; 38 electrons Th! 8 Pb a 8 3 9Th! a 16 84! Po! b 8 89 Ra! b At! b 8 9 Th! a 1 83 Bi! a 4 Ac! b 1 84 Ra! a 86 Rn Po! a 8 8 Pb : ¼ 1:5 g left after one half of the sample disintegrates. ð1 half-lifeþð1: mo yearsþ ¼ 1:5 1 1 months: 1yr

8 C18 1/9/1 11:5:7 Page Cf þ 15 7 N!þ41 n þ 6 15 Db Ra contains 138 neutrons and electrons mass of neutron ¼ 1.87 amu mass of electron ¼.55 amu ð138þð1:87 amuþ ð1þ ¼61:59% neutrons by mass 6 amu ðþð:55 amuþ ð1þ ¼:1% electrons by mass 6 amu 6:gRa $9, 6. ð:1 g RaCl Þ ¼ $685 96:9 g RaCl 1gRa % to 5% requires half-lives. The half-life of C-14 is 573 years. The specimen will be the age of two half-lives: ()(573 years) ¼ 11,46 years old g! 8. g! 4. g!. g! 1. g!.5 g 16. g to.5 g requires five half-lives. 9 minutes ¼ 18 minutes=half-life 5 half-lives 9. 7 (a) 3 Li is made up of 3 protons, 4 neutrons, and 3 electrons. Calculated mass 3 protons 3(1.73 g) ¼ 3.19 g 4 neutrons 4(1.87 g) ¼ g 3 electrons 3(.55 g) ¼.17 g calculated mass g Mass defect ¼ calculated mass actual mass Mass defect ¼ g 7.16 g ¼.44 g=mol Binding energy :44 g 9: 1 13 J ¼ 3:8 1 1 J=mol mol g U! 8 Pb Mass loss: 35 7 ¼ 8 Net proton loss (atomic number): 9 p 8 p ¼ 1 p The mass loss is equivalent to 7 alpha particles (8=4). A loss of 7 alpha particles gives a loss of 14 protons. A decrease in the atomic number to 78 (14 protons) is due to the loss of 7 alpha particles (9 14 ¼ 78). Therefore, a loss of 4 beta particles is required to increase the atomic number from 78 to 8. The total loss ¼ 7 alpha particles and 4 beta particles

9 C18 1/9/1 11:5:7 Page (a) Geiger counter: Radiation passes through a thin glass window into a chamber filled with argon gas and containing two electrodes. Some of the argon ionizes, sending a momentary electrical impulse between the electrodes to the detector. This signal is amplified electronically and read out on a counter or as a series of clicks. Scintillation counter: Radiation strikes a scintillator, which is composed of molecules that emit light in the presence of ionizing radiation. A light sensitive detector counts the flashes and converts them into a digital readout. (c) Film badge: Radiation penetrates a film holder. The silver grains in the film darken when exposed to radiation. The film is developed at regular intervals. 3. (3 days)(4 hours=day) ¼ 7 hours 7 hr þ 6hr¼78 hr 78 hr 13 hr t1 ¼ 6 half-lives 1 6 ð1 mgþ ¼:16 mg remaining 33. First change micrograms to nanograms. 15: mg ð1 ng/mgþ ¼15; ng 15; ng! 7;5 ng! 3;75 ng! 1;875 ng! 937 ng! 468 ng! 34 ng! 117 ng! 59 ng! 9 ng! 15 ng! 7ng! 4ng!< ng!< 1ng Each arrow represents 1 half-life. There are 14 half-lives for a total of 11 days, (14 half-lives)(8 days/ half-life) ¼ 11 days, for the iodine 131 to decay to less than a nanogram. 34. If you were to start with a 1 mg sample more than 99% would decay after 7 half-lives. This would take 5 ½ hours for the bismuth-13, 8 days for the rhenium-186, and 35 years for the cobalt-6. The best choice is the rhenium-186 because it will be detectable long enough for the termites to move the sample, but not so long that it becomes a hazard Am! 4 a þ Np 36. Fission is the splitting of a heavy nuclide into two or more intermediate-sized fragments with the conversion of some mass into energy. Fission occurs in nuclear reactors, or atomic bombs. Example: 35 9 U þ 1 n! Xe þ 38 Sr þ 3 1 n Fusion is the process of combining two relatively small nuclei to form a single larger nucleus. Fusion occurs on the sun, or in a hydrogen bomb. Example: 3 1 H þ 1 H!4 He þ 1 n þ energy

10 C18 1/9/1 11:5:7 Page Grams of material remaining Time (days) The graph produces a curve for radioactive decay which never actually crosses the x-axis (where mass ¼ ), it simply approaches that point. 38. (a) 35 9 U þ 1 n! Xe þ 3 1 n þ 9 38 Sr 35 9 U þ 1 1 n! 39 Y þ 3 1 n þ I (c) 14 7 N þ 1 n! 1 1 H þ 14 6 C 39. (a) H O(l)! H O(g) Energy : Weakest bond changes requires the least energy. H (g) þ O (g)! H O(g) Energy 1 : medium-sized value involved in interatomic bonds. (c) 1 H þ 1 H!3 1 H þ 1 1 H Energy 3 : Nuclear process; greatest amount of energy involved U! 38 Sr þ 3 1 n þ Xe 41. (a) beta emission: 9 1Mg! 1 e þ 9 13 Al alpha emission: 15 6 Nd!4 146 He þ 58 Ce (c) positron emission: 7 33As! þ1 e þ 7 3 Ge 4. ð7 yearsþ 1 half-life ¼ 9 half-lives 3 years Work down from 7 years: t1, years Amount, g There would have been 768 g originally or 15. g ( 9 ) ¼ 768 g - 8 -

11 C18 1/9/1 11:5:7 Page Curie ¼ disintegrations=sec 1 becquerel ¼ 1 disintegration=sec Therefore there are becquerels=l Curie 3:7 1 1 becquerel ð1:4 CuriesÞ ¼4:6 1 1 becquerels 1 Curie g Co-6 (a) one half-life: 1: g ¼ :5 g left two half-lives: :5 g ¼ :5 g left (c) four half-lives: 4 1 ¼ 16; 16 left 1: g ¼ :65 g left 16 (d) ten half-lives: 1 1 ¼ 14; 14 left 1: g 14 ¼ 9: g left 45. (a) 11 5 B! 4 He þ 7 3 Li 38Sr! 1 e þ 39 Y (c) Ag þ 1 18 n! 47 Ag (d) K!1 1 H þ 4 18 Ar 116 (e) 51 Sb þ 1 e 5 Sn 46. C-14 content is 1=16 of that in living plants. This means that four half-lives have passed. 14 C half-life is 573 years. 573 years ð4 half-livesþ ¼,9 years ð:9 1 4 yearsþ half-life 47. Ionizing radiation can change the genetic material (DNA). These changes can then be passed on to future generations. 48. Long-term exposure to low-level ionizing radiation can cause tumors, cancer, and damage to blood producing cells. 49. Scientists can feed a plant with radiophosphorus labeled phosphates and by recording the rate of increase of radiation emitted from the plant can gauge the rate of uptake of these phosphates by the plant (a) 37Rb! 1 e þ Sr 87 38Sr! þ1 e þ Rb

12 C18 1/9/1 11:5:7 Page t1, hours Amount, mg Fraction of K-4 remaining: :65 mg 15:4mg ¼ :393ðor :393%Þ No. After an additional eight half-lives there would be less than one microgram (.1 g) remaining. ð hrsþ 1 half-life ¼ 16 half-lives 1:5 hrs Amount remaining ¼ 1 16 ð15:4mgþ 13 mg ¼ :35 mg after 16 half-lives mg - 8 -