Ch.20 - Nuclear Chemistry
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Problem 36c
Write balanced nuclear equations for the following processes. (c) Beta emission of 188W
Problem 37a
Write balanced nuclear equations for the following processes. (a) Beta emission of 157Eu
Problem 37b
Write balanced nuclear equations for the following processes. (b) Electron capture of 126Ba
Problem 37c
Write balanced nuclear equations for the following processes. (c) Alpha emission of 146Sm
- Radioactive 100Tc decays to form 100Mo. There are two possible pathways for this decay. Write the balanced equations for both pathways.
Problem 38
- 226Ac can decay by any of three different nuclear processes: a emission, b emission, or electron capture. Write a balanced nuclear equation for the decay of 226Ac by each process.
Problem 39
- Of the two isotopes of tungsten, 160W and 185W, one decays by b emission and one decays by a emission. Which does which? Explain.
Problem 40
- Of the two isotopes of iodine, 136I and 122I, one decays by b emission and one decays by positron emission. Which does which? Explain.
Problem 41
- Of the two isotopes of iodine, 196Pb and 206Pb, one is nonra-dioactive and one decays by positron emission. Which does which? Explain.
Problem 42
- Why do nuclei that are neutron-rich emit b particles? Why do nuclei that are neutron-poor emit a particles or positrons or undergo electron capture?
Problem 43
- Americium-241, a radioisotope used in smoke detectors, decays by a series of 12 reactions involving sequential loss of a, a, b, a, a, b, a, a, a, b, a, and b particles. Identify each intermediate nucleus and the final stable product nucleus.
Problem 44
- Radon-222 decays by a series of three a emissions and two b emissions. What is the final stable nucleus?
Problem 45
- Thorium-232 decays by a 10-step series, ultimately yielding lead-208. How many alpha particles and how many beta particles are emitted?
Problem 46
- How many a particles and how many b particles are emitted in the 11-step decay of 235U into 207Pb?
Problem 47
- Neptunium-237 decays by a series of steps to bismuth-209. How many α and β particles are produced by this decay process?
Problem 48
- Naturally occurring uranium-238 undergoes a radioactive decay series and emits 8 a particles and 6 b particles. What is the stable nucleus at the end of the series?
Problem 49
- The half-life of indium-111, a radioisotope used in studying the distribution of white blood cells, is t1/2 = 2.805 days. What is the decay constant of 111In?
Problem 50
- The decay constant of plutonium-239, a waste product from nuclear reactors, is 2.88 * 10-5 year - 1. What is the half-life of 239Pu?
Problem 51
- Polonium-209, an a emitter, has a half-life of 102 years. How many alpha particles are emitted in 1.0 s from a 1.0 ng sample of 209Po?
Problem 54
- A sample of 37Ar undergoes 8540 disintegrations/min initially but undergoes 6990 disintegrations/min after 10.0 days. What is the half-life of 37Ar in days?
Problem 58
- Radioactive decay exhibits a first-order rate law, rate = -∆N/∆t = kN, where N denotes the number of radio-active nuclei present at time t. The half-life of strontium-90, a dangerous nuclear fission product, is 29 years. (a) What fraction of the strontium-90 remains after three half-lives?
Problem 60
- Potassium ion, K+, is present in most foods and is an essen-tial nutrient in the human body. Potassium-40, however, which has a natural abundance of 0.0117%, is radioactive with t1/2 = 1.25 x 10^9 years. What is the decay constant of 40K? How many 40K+ ions are present in 1.00 g of KCl? How many disintegration/s does 1.00 g of KCl undergo?
Problem 61
- The electronic systems on the New Horizons spacecraft, which launched on January 19, 2006, and reached its closest approach to Pluto on July 14, 2015, were powered by elec-tricity generated by heat. The heat came from the radioac-tive decay of 238Pu in the 11 kg of 238PuO2 fuel onboard. The generator provided 240 W when the spacecraft was launched. If the power output is directly proportional to the amount of 238Pu in the generator, what was the power output when the spacecraft reached Pluto? The half-life of 238Pu is 87.7 y.
Problem 62
- The radioisotope 226Ac can decay by any of three different nuclear processes: alpha emission, beta emission, or electron capture. (a) Write a balanced nuclear equation for the decay of 226Ac by each decay mode.
Problem 63
- What is the 14C activity in decay events per minute of 1.0 g of a 3000-year-old wooden object? All living organisms contain an equilibrium concentration of radioactive 14C that gives rise to an average of 15.3 nuclear decay events per minute per gram of carbon. (14C, t1/2 = 5715 years)
Problem 65
- Uranium-238 has a half-life of 4.47 * 109 years and decays through a series of events to yield lead-206. Estimate the age of a rock that contains 105 mmol of 238U and 33 mmol of 206Pb. Assume all the 206Pb is from the decay of 238U.
Problem 70
- The age of an igneous rock that has solidified from magma can be found by analyzing the amount of 40K and 40Ar. Potassium-40 emits a positron to produce argon-40 and the half-life of 40K is 1.25 * 109 years. What is the age of a rock whose 40Ar/40K ratio is 1.42?
Problem 73
- Why does a given nucleus have less mass than the sum of its constituent protons and neutrons?
Problem 74
- In an endothermic chemical reaction, do the products have more mass, less mass, or the same mass as the reactants? Explain.
Problem 75
- Calculate the mass defect (in g/mol) and the binding energy (in MeV/nucleon) for the following nuclei. Which of the two is more stable? (a) 50Cr (atomic mass = 49.94605) (b) 64Zn (atomic mass = 63.92915)
Problem 78