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21 Nuclear Chemistry Solutions to Exercises Solve. (a) Pb (b) 50 + 25 Mn (c) (d) 21.14 (a) Na + a particle is produced (b) 188 79 Au + a positron is produced (c) + a particle is produced (d) 238 92 + an α particle is produced 21.15 Analyze/Plan. Given the starting and ending nuclides in a nuclear decay sequence, we are asked to determine the number of alpha and beta emissions. Use the total change in A and Z, along with definitions of alpha and beta decay, to answer the question. Solve. The total mass number change is (235-207) = 28. Since each α particle emission decreases the mass number by four, whereas emission of a particle does not correspond to a mass change, there are 7 α particle emissions. The change in atomic number in the series is 10. Each α particle results in an atomic number lower by two. The 7 α particle emissions alone would cause a decrease of 14 in atomic number. Each particle emission raises the atomic number by one. To obtain the observed lowering of 10 in the series, there must be 4 ß emissions. 21.16 This decay series represents a change of (232-208 =) 24 mass units. Since only alpha emissions change the nuclear mass, and each changes the mass by four, there must be a total of 6 α emissions. Each alpha emission causes a decrease of two in atomic number. Therefore, the 6 alpha emissions, by themselves, would cause a decrease in atomic number of 12. The series as a whole involves a decrease of 8 in atomic number. Thus, there must be a total of 4 emissions, each of which increases atomic number by one. Overall, there are 6 α emissions and 4 emissions. Nuclear Stability (section 21.2) 21.17 Analyze/Plan. Follow the logic in Sample Exercise 21.3, paying attention to the guidelines for neutron-to-proton ratio. Solve. (a) - low neutron/proton ratio, positron emission (for low atomic numbers, positron emission is more common than orbital electron capture) (b) 68 29 Cu - high neutron/proton ratio, beta emission (c) P - slightly high neutron/proton ratio, beta emission (d) 39 17 - high neutron/proton ratio, beta emission 21.18 (a) 1 3 - high neutron/proton ratio, beta emission (b) 89 38 Sr - (slightly) high neutron/proton ratio, beta emission 650