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21 Nuclear Chemistry Solutions to Exercises Bi: 83 p, 128 n; 81 p, 126 n. 129 128 127 126 125 80 81 82 83 84 Check. An α-particle has 2 p and 2 n. The diagram shows a decrease in 2 p and 2 n for the reaction. 21.4 Analyze/Plan. Write the balanced equation for the decay. Nuclear decay is a first-order process; use appropriate relationships for first-order processes to determine k and remaining after 12 minutes. Solve. (a) is the time required for half of the original nuclide to decay. Relative to the graph, this is the time when the amount of is reduced from 1.0 to 0.5. This time is 7 minutes. (b) For a first-order process, = 0.693/k or k = k = 0.693/7 min = 0.0990 = 0.1 min⁻¹ (c) From the graph, the fraction of remaining after 12 min is 0.3/1.0 = 0.3 Check. = -kt = -(0.099)(12) = -1.188; = 1.188 = 0.30. (d) 21.5 Analyze/Plan. Atomic number is number of protons, mass number is (protons + neutrons). Chemical symbol is determined by atomic number. Beta decay increases the number of protons while mass number stays constant. Positron emission decreases the number of protons while mass number stays constant. Half-life, is the time required to reduce the amount of radioactive material by half. Solve. (a) (b) On the diagram, is the only radioactive nuclide above and left of the band of stable red nuclides. will reduce its neutron-to-proton ratio by ß-decay. + (c) On the diagram, radioactive nuclides right and below the band of stable red nuclides are likely to increase their neutron-to-proton ratio via positron emission. In order to be useful for positron emission tomography, the nuclides must have a half-life on the order of minutes. (Nuclides with very fast decay disappear before they can be imaged. Those with longer half-lives linger in the patient.) Four radioactive nuclides fit these criteria: 648