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Chapter 30: Nuclear Physics 1. (i) Consider the following three nuclei: 12C, 13N, 14O. What is the same for these three nuclei? (a) number of protons (b) number of neutrons (c) number of nucleons. (ii) Consider the following three nuclei: 12N, 13N, 14N. From the same list of choices, what is the same for these three nuclei? (iii) Consider the following three nuclei: 14C, 14N, 14O. From the same list of choices, what is the same for these three nuclei? Answer: (i), (b). The value of N = A − Z is the same for all three nuclei. (ii), (a). The value of Z is the same for all three nuclei because they are all nuclei of nitrogen. (iii), (c). The value of A is the same for all three nuclei, as seen by the unchanging preceding superscript. 2. Which do you expect to show very little variation among different isotopes of an element? (a) atomic mass (b) nuclear spin magnetic moment (c) chemical behavior Answer: (c). Isotopes of a given element correspond to nuclei with different numbers of neutrons. The result is different masses of the atom, and different magnetic moments because the neutron, despite being uncharged, has a magnetic moment. The chemical behavior, however, is governed by the electrons. All isotopes of a given element have the same number of electrons and therefore the same chemical behavior. 3. On your birthday, you measure the activity of a sample of 210Bi, which has a half-life of 5.01 days. The activity you measure is 1.000 μCi. What is the activity of this sample on your next birthday? (a) 1.000 μCi (b) 0 (c) ~0.2 μCi (d) ~0.01 μCi (e) ~10−22 μCi Answer: (e). A year of 365 days is equivalent to 365 d/5.01 d ≈ 73 half-lives. Therefore, the activity will be reduced after one year to approximately (1/2)73(1.000 μCi) ~ 10−22 μCi. 4. Suppose you have a pure radioactive material with a half-life of T1/2. You begin with N0 undecayed nuclei of the material at t = 0. At t = ½ T1/2, how many of the nuclei have decayed? (a) ¼ N0 (b) ½ N0 (c) ¾ N0 (d) 0.707N0 (e) 0.293N0 Answer: (e). The time we are interested in is half of a half-life. Therefore, the number of remaining nuclei is (½)1/2 N0 = ( 1 / 2 )N0 = 0.707N0. The number of nuclei that have decayed is N0 − 0.707N0 = 0.293N0. 5. Which of the following is the correct daughter nucleus associated with the alpha decay 153 153 157 of 157 72 Hf ? (a) 72 Hf (b) 70Yb (c) 70Yb Answer: (b). In alpha decay, the atomic number decreases by two and the atomic mass number decreases by four. 6. Which of the following is the correct daughter nucleus associated with the beta decay 183 183 184 of 184 72 Hf ? (a) 72 Hf (b) 73Ta (c) 73Ta Answer: (c). In e− decay, the atomic number increases by one and the atomic mass number stays fixed. None of the choices is consistent with e+ decay, so we assume that the decay must be by e−.