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Unformatted text preview: CHAPTER 31 NUCLEAR PHYSICS AND RADIOACTIVITY ANSWERS TO FOCUS ON CONCEPTS QUESTIONS 1. (e) In the notation In, A Z the symbol Z represents the number of protons, and the symbol A represents the number of protons plus the number of neutrons. 2. (c) Because the atomic number of the nucleus is 37, there are 37 protons in the nucleus. Thus, there must be 37 electrons in orbit about the electrically neutral atom. 3. r = 4.8 × 10- 15 m 4. (e) According to the discussion in Section 31.1, the nuclear density of all nuclei is approximately the same. 5. (c) The graph in Section 31.2 displays the nucleon number versus the proton number for the elements, and it shows that the number of neutrons in the nucleus is about equal to the number of protons for elements whose proton number is less than or equal to Z = 8. 6. (d) The mass defect depends is equal to the mass of the separated nucleons (63 u) minus the mass (62.5 u) of the stable nucleus (see Section 31.3). 7. (a) Both α and β- decays produce a daughter nucleus that has a different atomic number than the parent nucleus (see Section 31.4). Thus, each decay results in a new element. 8. (b) When a nucleus decays, electric charge is conserved. The number of protons in the 240 92 U daughter nucleus and the α particle (92 + 2) is the same as the number (94) of protons in the 244 94 Pu parent nucleus. Also, when a nucleus decays, the nucleon number is conserved. The number of nucleons in the 240 92 U daughter nucleus and the α particle (240 + 4) is the same as the number (244) of protons in the 244 94 Pu parent nucleus. 9. (d) The radius of a nucleus depends on the number of nucleons it contains (see Section 31.1). In α decay the number of nucleons in the daughter nucleus is four less than that in the parent nucleus, while in β- and γ decay the number of nucleons is the same as that in the parent nucleus (see Section 31.4). 48 NUCLEAR PHYSICS AND RADIOACTIVITY 10. (b) When a nucleus decays, electric charge is conserved. The combined charge (80 - 1) of the 198 80 Hg daughter nucleus and the β- particle is the same as the charge (79) in the 198 79 Au parent nucleus. Also, when a nucleus decays, the nucleon number is conserved. The number (198 + 0) of nucleons in the 198 80 Hg daughter nucleus and the β- particle is the same as the number (198) of nucleons in the 198 79 Au parent nucleus. 11. (c) The activity of a sample is directly proportional to the number of radioactive nuclei (see Equation 31.4). Therefore, if the mass of a substance increases, the number of nuclei increases. The decay constant λ depends on the specific type of radioactive nuclei in the sample, e.g., 14 6 C , but not on the mass of the radioactive material (See Equations 31.4 and 31.5). Since the half-life is inversely proportional to the decay constant (see Equation 31.6), the half-life also remains constant when the mass of the substance increases....
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