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# ch31 - CHAPTER 31 NUCLEAR PHYSICS AND RADIOACTIVITY...

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CHAPTER 31 NUCLEAR PHYSICS AND RADIOACTIVITY CONCEPTUAL QUESTIONS ____________________________________________________________________________________________ 1. REASONING AND SOLUTION Isotopes are nuclei that contain the same number of protons, but a different number of neutrons. A material is known to be an isotope of lead, although the particular isotope is not known. a. The atomic number Z of an atom is equal to the number of protons in its nucleus. It is different for different elements, and all isotopes of the same element have the same atomic number. Therefore, if we know that a material is an isotope of lead, we can specify its atomic number ( Z = 82). b. The various isotopes of the same element differ in the number of neutrons in the nucleus. Since we do not know which particular isotope of lead makes up the material, we cannot specify the neutron number. c. The atomic mass number is equal to the total number of protons and neutrons in the nucleus. Since we do not know which isotope of lead makes up the material, we do not know how many neutrons are in the nucleus. Therefore, we cannot specify the atomic mass number. ____________________________________________________________________________________________ 2. REASONING AND SOLUTION Two nuclei have different nucleon numbers A 1 and A 2 . The two nuclei may or may not be isotopes of the same element. Two isotopes of the same element have the same number of protons in the nucleus, but differ in the number of neutrons. The nucleon number is equal to the total number of protons and neutrons in the nucleus. If the nucleon numbers differ only because the neutron numbers differ, then the two nuclei are isotopes of the same element. However, if the nucleon numbers differ because the nuclei contain a different number of protons, then the two nuclei are not isotopes of the same element (regardless of their respective neutron numbers). Therefore, two nuclei with different nucleon numbers are not necessarily isotopes of the same element. ____________________________________________________________________________________________ 3. REASONING AND SOLUTION Two nuclei that contain different numbers of protons and different numbers of neutrons can have the same radius. According to Equation 31.2, the approximate radius of the nucleus depends on the atomic mass number A and is given by . The atomic mass number A is equal to the total number of protons and neutrons. Therefore, if two nuclei have different numbers of protons and different numbers of neutrons, but the sum of the protons and neutrons is the same for each nucleus, then the two nuclei have the same radius. r × ( . 1 2 10 –15 1/3 m) A ____________________________________________________________________________________________

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Chapter 31 Conceptual Questions 1547 4. REASONING AND SOLUTION Using Figure 31.5, the following nuclei have been ranked in ascending order (smallest first) according to the binding energy per nucleon: , 184 , 15 31 , 27 59 . 90 232 Th 74 W P Co ____________________________________________________________________________________________ 5. REASONING AND SOLUTION The general form for α decay is Z A Z A P D + He Parent nucleus Daughter nucleus particle helium nucleus 2 : 2 4 2 4 ±²³ α ( ) while the general form for the two types of beta decay are [ β decay] Z A Z A P D + Parent nucleus + Daughter nucleus –1 0 particle electron e 2 2 1 ±²³ β ( ) and [ β + decay] Z A Z A P D + Parent nucleus Daughter nucleus particle positron e + 2 0 1 1 0 ±²³ β ( ) According to Equation 31.2, the approximate radius of the nucleus depends on the atomic
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