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21 Nuclear Chemistry Solutions to Exercises (d) A reduction of 12.5% in amount or concentration of a radionuclide amounts to three half-lives. If the total decay time is 1 hour, 1/3 of this time is 20 min. The radionuclide with a half-life of 20 min is 21.6 Analyze/Plan. Express the particles in the diagram as a nuclear reaction. Determine the mass number and atomic number of the unknown particle by balancing these quantities in the nuclear reaction. Solve. (a) 239 94 95 40 + ? + 2 The unidentified particle has an atomic number of (94-40) = 54; it is Xe. The mass number of the nuclide is [(239 + 1) - (95 + 2)] = 143. The unknown particle is (b) 40 p, 55 n is stable. ¹⁴³Xe: 54 p, 89 n is above the belt of stability and is not stable; it will probably undergo Radioactivity (section 21.1) 21.7 Analyze/Plan. Given various nuclide descriptions, determine the number of protons and neutrons in each nuclide. The left superscript is the mass number, protons plus neutrons. If there is a left subscript, it is the atomic number, the number of protons. Protons can always be determined from chemical symbol; all isotopes of the same element have the same number of protons. A number following the element name, as in part (c) is the mass number. Solve. p = protons, n = neutrons, e = electrons; number of protons = atomic number; number of neutrons = mass number - atomic number (a) 55 Mn : 25p, 30n (b) 80p, 121n (c) 19p, 20n 21.8 p = protons, n = neutrons, e = electrons; number of protons = atomic number; number of neutrons = mass number - atomic number (a) (b) 37 Cl: 17p, 20n (c) 232 Th: 90p, 142n 21.9 Analyze/Plan. See definitions in Section 21.1. In each case, the left superscript is mass number, the left subscript is related to atomic number. Solve. (b) 4 (a) 2 Heora (c) or Y 21.10 (a) 1 or (b) -1 0 or (c) ie 21.11 Analyze/Plan. Follow the logic in Sample Exercises 21.1 and 21.2. Pay attention to definitions of decay particles and conservation of mass and charge. Solve. (a) 90 37 Rb 38 + (b) 72 34 Se + (orbital electron) (c) 76 Kr 76 Br 36 35 + ie (d) 226 88 Ra 222 86 + 21.12 (a) 213 83 Bi 81 (b) 13 7 N+ (orbital electron) (c) 98 43 Tc + (orbital electron) (d) 188 + ie 21.13 Analyze/Plan. Using definitions of the decay processes and conservation of mass number and atomic number, work backwards to the reactants in the nuclear reactions. 649