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physics
college physics a strategic approach 2nd
College Physics Essentials Electricity And Magnetism Optics Modern Physics Volume Two 8th Edition Jerry D. Wilson, Anthony J. Buffa, Bo Lou - Solutions
28. •• (a) What is the decay constant of fluorine-17 if its half-life is known to be 66.0 s? (b) How long will it take for the activity of a sample of 17F to decrease to 80% of its initial value? (c) Repeat part (b), but instead determine the time to decrease to an additional 20%to 60% of its
27. •• Suppose that some ancient writings on parchment are found sealed in a jar in a cave. If carbon-14 dating shows the parchment to be 28 650 years old, what percentage of the original carbon-14 atoms still remains in the sample?
26. •• Prove that the number N of radioactive nuclei remaining in a sample after an integer number (n) of half-lives has elapsed is given by N = (No/2n) = (1/2)nNo, where No is the initial number of nuclei present.
25. IE •• Carbon-14 dating is used to determine the age of some unearthed bones. (a) If the activity (in decays/min per gram of carbon) of bone A is higher than that of B, then A is (1) older than, (2) younger than, (3) the same age as B. Explain your reasoning. (b) A sample of A is found to
24. •• 131I is given to a patient for use in a diagnostic procedure on her thyroid. What percentage of the 131I sample remains after exactly one day, assuming that all of the 131I is retained in the patient’s thyroid gland?(Answer to three significant figures.)
23. •• Calculate the time required for a sample of radioactive tritium to lose 80.0% of its activity.(Tritium has a half-life of 12.3 years.)
22. •• A sample of technetium-104, which has a half-life of 18.0 min, has an initial activity of 10.0 mCi. Determine the activity of the sample after exactly 1 h has elapsed.
21. • A 1.25-μCi alpha source gives off alpha particles each with a kinetic energy of 2.78 MeV. At what rate(in watts) is kinetic energy being produced?
20. IE • The half-life of a radioactive isotope is known to be exactly 1 h. (a) What fraction of a sample would be left after exactly 3 h: (1) one-third, (2) one-eighth, or(3) one-ninth? (b) What fraction of a sample would be left after exactly 1 day?
19. • At present, a radioactive beta source with a long halflife has an activity of 20 mCi. (a) What is the present decay rate in decays per second? (b) Assuming that one beta particle is emitted per decay, how many are emitted per minute?
18. • A particular radioactive sample undergoes 2.50 × 106 decays/s. What is the activity of the sample in(a) curies and (b) becquerels?
16. •• Actinium-227 decays by alpha decay or beta decay and is part of a long decay sequence, shown in Figure 29.8. Write all the possible nuclear decays for the decay series from 227Ac to 215Po. Identify the daughter nucleus at the end of each decay.
15. •• Complete the following nuclear-decay equations by filling in the blanks:a. 92 238 90 ____→234 _____+____b. 19 40 20 K→40 Ca+___c. 92 236 53 131 01 39 U→ I+____( n)+ 102___d. 11 23Na*→γ +____e. 11C+____→____B
14. •• Complete the following nuclear decay equations by filling in the blanks:a. 4 82 Be→___ + 4Heb. 94 240 56 139 0Pu→____+ ____+2(1 n)c. ___→21 +47 Sc γd. 11 22 10 Na→____+ 22____
13. • A lead-209 nucleus results from both alpha–beta sequential decays and beta–alpha sequential decays.What was the grandparent nucleus? Show this result for both decay routes by writing the nuclear equations for both sequential decay processes.
12. IE • Polonium-214 can decay by alpha decay. (a) The product of its decay has how many fewer protons than polonium-214: (1) zero, (2) one, (3) two, or (4) four?(b) Write the nuclear equation for this decay and determine the daughter nucleus.
11. • Write the nuclear equations for (a) alpha decay of 237Np, (b) β− decay of 32P, (c) β+ decay of 56Co,(d) electron capture in 56Co, and (e) γ decay of 42K from an excited nuclear state to the ground state.
10. • Write the nuclear equations for (a) beta decay of 60Co and (b) alpha decay of 222Rn.
9. IE • Tritium is radioactive. (a) Would you expect it to(1) β +, (2) β−, or (3) alpha decay? Why? (b) Write the nuclear equation for the correct decay and identify the daughter nucleus. Is it stable?
8. IE ••• Assume Rutherford used alpha particles with a kinetic energy of 5.25 MeV. (a) To which of the following nuclei would the alpha particle come closest in a head-on collision: (1) aluminum, (2) iron, or (3) lead? (b) Determine the distance of closest approach for the three nuclei in
7. •• An experimental expression for the radius (R) of a nucleus is R = Ro A1/3, where Ro = 1.2 × 10−15 m and A is the mass number of the nucleus. (a) Find the nuclear radii of the noble gases: He, Ne, Ar, Kr, Xe, and Rn.(b) Determine the density of the nuclei associated with each of these
6. IE • (a) Isotopes of an element must have the same(1) atomic number, (2) neutron number, (3) mass number. (b) Write two possible isotopes for gold-197.
5. • One isotope of uranium has a mass number of 235, and another has a mass number of 238. What are the numbers of protons, neutrons, and electrons in a neutral atom of each?
4. •35Cl and 37Cl are two isotopes of chlorine. What are the numbers of protons, neutrons, and electrons in each if (a) the atom is electrically neutral, (b) the ion has a –2 charge, and (c) the ion has a +1 charge?
3. • An isotope of potassium has the same number of neutrons as argon-40. Write this potassium isotope in nuclear notation.
2. • Magnesium has three stable isotopes. Write these isotopes in nuclear notation including nucleon, proton, and neutron number on the elemental symbol.
1. • Determine the number of protons, neutrons, and electrons in a neutral atom with the following nuclei:(a) 90Zr and (b) 208Pb.
27. Theoretically, the tumor-killing efficiency of particle beams is much greater than that of a beam of X-rays or gamma rays. Explain why this is true.
26. A Geiger counter is not 100% efficient. That is, the number of events it records is smaller than the number of particles that enter it. Explain why the efficiency is not 100%.
25. PET scans require extremely fast computers coupled with gamma-ray detectors capable of accurate energy measurements. Explain why both energy accuracy and comparison of arrival times are crucial to the success of a PET scan. [Hint: In a PET scan, two opposing detectors pick up pair annihilation
24. If X-rays and slow neutrons give the same effective dose, how will their doses compare?
23. If X-rays and alpha particles give the same dose, how will their effective doses compare?
22. If one nucleus has a larger average binding energy than another, does this mean that it takes more total energy to break the former into its constituent nucleons? Explain.
21. Explain how fusing of light nuclei and splitting of heavy nuclei can both release energy.
20. Compared to 3He, the probability of absorbing a neutron is much less likely for 4He. Explain this using what you know about odd–even proton and neutron numbers.
19. Explain why, of the two main uranium isotopes, 238U is more abundant than 235U. [Hint: Although they both are unstable, 238U is closer to stability; why?]
18. Using the general guidelines for nuclear stability, explain why aluminum has only one stable isotope (27Al). Why aren’t other isotopes, such as 28Al or 26Al, stable?
17. What is the expression for the number of nuclei that have decayed, N, in a given time t in terms of the initial number of undecayed nuclei No, the time elapsed t, and the decay constant λ? [Hint: See Equation 29.3.]
16. Nuclide A has a half-life that is one-third that of nuclide B. The type A sample starts with twice the number of undecayed nuclei as in the sample of type B. Compare the initial sample activities expressed as a ratio of the activity of sample A to that of B.
15. What are the (a) half-life and (b) decay constant for a stable isotope?
14. Nuclide A has a decay constant that is half that of nuclide B. Samples of both types start with the same number of undecayed nuclei, N. In terms of N, after two of A’s half-lives have elapsed, (a) how many of A have decayed? (b) How many of B have decayed?
13. How do physical or chemical properties affect the decay rate, or half-life, of a radioactive isotope?
12. A basic assumption of radiocarbon dating is that the cosmic-ray intensity has been generally constant for the last 40 000 years or so. Suppose it were found that the intensity 100 000 years ago was much less than it is today. How would this finding affect the results (ages of samples) of
11. During a particular decay sequence in a decay chain, a nucleus first decays by alpha emission, followed by a β− emission, and last a gamma-ray emission.Compare the number of neutrons, protons, and nucleons in the final nucleus to that in the initial nucleus. How would your answer differ if
10. Suppose, in an alpha decay, the emitted alpha particle has a kinetic energy of 5.25 MeV. The total kinetic energy released (from mass energy) is actually 5.30 MeV. Explain where the difference went. [Hint:See the hint in Conceptual Question 9.]
9. When an excited nucleus decays to a lower energy level by gamma-ray emission, the actual energy of the gamma-ray photon is a bit less than the difference in energy between the two levels involved in the transition. Explain why this is true. [Hint: Think about conservation of linear momentum in a
8. 19F is the only stable isotope of fluorine. What two possible decay modes would you expect 18F to decay by?What would be the resulting nucleus in each case?
7. Neither neutron nor proton number is conserved in either type of beta decay. Is this a violation of the conservation of nucleons? Explain.
6. Nuclei with the same number of protons are called isotopes. List the stable nuclides that are isotopes of the most common form of nitrogen.
5. Nuclei with the same number of nucleons are called isobars. What nuclide of nitrogen is an isobar of carbon-13?
4. Nuclei with the same number of neutrons are called isotones. What nitrogen nucleus is an isotone of carbon-13?
3. A Rutherford scattering experiment is performed on a gold foil target with alpha beams of two different kinetic energies, one of 3.00 MeV, the second of 6.00 MeV. Qualitatively compare the distance of closest approach (rmin) for the two different energy alpha beams. Give a numerical answer as a
2. A Rutherford scattering experiment uses a beam of alpha particles of a known kinetic energy. Qualitatively compare the distance of closest approach (rmin) to a target consisting of lead atoms to that to a target of uranium atoms. Give a numerical answer as a ratio of the closest approach for
1. In the Rutherford scattering experiment, the minimum distance of approach for the alpha particle is given by Equation 29.1. Explain why this distance does not necessarily represent the nuclear radius. Is it larger or smaller than the nuclear radius?
24. The same radiation dose (in rads) is given by a source of fast neutrons and an alpha particle source. What is the ratio of the effective dose (in rems) from the neutrons to that from the alpha source: (a) 1:2, (b) 1:4,(c) 2:1, or (d) 4:1?
23. The same effective radiation dose (in rems) is given by a source of slow neutrons and an X-ray machine.What is the ratio of the dose (in rads) from the neutrons to that from the X-rays: (a) 1 : 2, (b) 1:4,(c) 2:1, or (d) 4:1?
22. A bubble chamber (in a magnetic field) shows two tracks of equal curvature but in opposite directions, emanating from a point in space with no apparent incoming particle. It is highly likely that this event is(a) alpha decay, (b) beta decay, (c) pair production.
21. Which type of detector records the trajectory of charged particles: (a) Geiger counter, (b) scintillation counter, or (c) spark chamber?
20. During which process is the average binding energy of the product nuclei less than the average binding energy of the initial nuclei: (a) fission, (b) fusion, (c) neither of these processes, or (d) both of these processes?
19. Isotopes of which of these elements would require more energy per nucleon to completely break them apart: (a) Fe, (b) Cd, or (c) Au?
18. From which nucleus is it easier to remove a neutron:(a) 26Mg, (b) 25Mg, or (c) they require the same amount of energy?
17. The average binding energy per nucleon of the daughter nucleus in a decay process is (a) greater than,(b) less than, or (c) equal to that of the parent nucleus.
16. For nuclei with A > 40, which of the following is correct: (a) the number of protons is approximately equal to the number of neutrons; (b) the number of protons exceeds the number of neutrons; (c) all such nuclei are stable up to Z = 92; or (d) none of these?
15. Radioactive element A has a decay constant three times greater than that of B. How do their half-lives compare:(a) A’s = 3 × B’s, (b) B’s = 3 × A’s, or (c) their relative half-lives can’t be determined from the data?
14. Radioactive element A has a half-life of 3.5 days and B’s half-life is 7.0 days. How do their decay constants compare: (a) λA = λB, (b) λA < λB, or (c) λA > λB?
13. A sample containing an alpha emitter gives off alpha particles of kinetic energy of 4.4 MeV. After three halflives, what is the energy of the alpha particles given off:(a) 2.2 MeV, (b) 1.1 MeV, (c) 8.8 MeV, or (d) 4.4 MeV?
12. In two half-lives, the activity of a radioactive sample will have decreased from its original value to what percent: (a) 25%, (b) 50%, (c) 75%, or (d) 87.5%?
11. After one half-life, a sample of a radioactive material(a) is half as massive, (b) has its half-life reduced by half, (c) is no longer radioactive, (d) has its activity reduced by half.
10. The gamma decay of 89Y* results in a nucleus containing how many neutrons: (a) 89, (b) 39, or (c) 50?
9. The alpha decay of 237Np144 results in a nucleus containing how many protons: (a) 233, (b) 91, or (c) 142?
8. Aluminum has only one stable isotope, 27Al. 26Al would be expected to decay by which decay mode:(a) β+, (b) β−, or (c) neither type of beta decay is an option for 26Al?
7. β− decay can occur only in nuclei with what Z values:(a) Z > 82, (b) Z ≤ 82, or (c) it can occur regardless of the Z value?
6. The conservation of nucleons and the conservation of charge apply to (a) only alpha decay, (b) only beta decay,(c) only gamma decay, (d) all nuclear decay processes.
5. The element X has a nucleus given by 7X4. This element is (a) nitrogen, (b) lithium, (c) beryllium, (d) none of these.
4. How many neutrons are there in the nuclide 25Mg:(a) 25, (b) 12, or (c) 13?
3. At a given distance, between which pair of particles is the nuclear force largest: (a) neutron–proton, (b)neutron–neutron, (c) proton–proton, or (d) the force is the same for all pairs?
2. The nuclei of oxygen-16 and oxygen-17 have the same number of (a) nucleons, (b) neutrons, (c) protons, or(d) none of the preceding.
1. In the Rutherford scattering experiment, which target nucleus would alpha particles of a given kinetic energy approach more closely: (a) carbon, (b) iron, or (c) lead?
35. IE •• (a) The minimum photon energy to create a proton–antiproton pair is (1) more than, (2) the same as, or (3) less than the minimum photon energy to create a neutron–antineutron pair. Explain. (b) Calculate minimum photon frequency to create the proton–antiproton pair and the
34. IE •• A muon, or μ meson, has the same charge as an electron, but is 207 times as massive. (a) Compared with electron–positron pair production, the pair production of a muon and an antimuon requires a photon of (1) more, (2) the same amount of, (3) less energy. Why? (b) What would be the
33. • What is the energy of the photons produced in proton–antiproton pair annihilation, assuming that both particles are essentially at rest initially?
32. •• The energy of a 2.00-keV electron is known to within ±3.00%. How accurately can its position be measured?
31. •• What is the minimum uncertainty in the position of a 0.50-kg ball that is known to have a speed uncertainty of 3.0 × 10−28 m/s?
30. •• What is the minimum uncertainty in the speed of an electron that is known to be somewhere between 0.050 nm and 0.10 nm on a horizontal axis?
29. IE • An electron and a proton each have a momentum of 3.28470 × 10−30 kg⋅m/s ± 0.00025 × 10−30 kg⋅m/s.(a) The minimum uncertainty in the position of the electron compared with that of the proton will be(1) larger, (2) the same, (3) smaller. Why? (b) Calculate the minimum
28. • A 1.0-kg ball has a position uncertainty of 0.20 m.What is its minimum momentum uncertainty?
27. ••• How would the electronic structure of lithium differ if electron spin were to have three possible orientations instead of just two?
26. IE ••• (a) If there were no electron spin, the 1s state would contain a maximum of (1) zero, (2) one, (3) two electrons. Why? (b) What would be the first two inert or noble gases if there were no electron spin?
25. •• Write the ground state electron configurations for each of the following atoms: (a) boron (B), (b) calcium(Ca), (c) zinc (Zn), and (d) tin (Sn).
24. •• Identify the atoms of each of the following ground state electron configurations: (a) 1s2 2s2; (b) 1s2 2s2 2p3;(c) 1s2 2s2 2p6; (d) 1s2 2s2 2p6 3s2 3p4.
23. •• Draw schematic diagrams for the electrons in the subshells of (a) sodium (Na) and (b) argon (Ar) atoms in the ground state.
22. •• Draw the ground state energy-level diagrams like those in Figure 28.8 for (a) nitrogen (N) and(b) potassium (K).
21. • An electron in an atom is in an orbit that has a magnetic quantum number of mℓ = 2. What are the minimum values that (a) ℓ and (b) n could be for that orbit?
20. IE • (a) Which has more possible sets of quantum numbers associated with it, n = 2 or ℓ = 2? (b) Prove your answer to part (a).
19. • How many possible sets of quantum numbers are there for the subshells with (a) ℓ = 2 and (b) ℓ = 3?
18. • (a) How many possible sets of quantum numbers are there for the n = 1 and n = 2 shells? (b) Write the explicit values of all the quantum numbers (n, ℓ, mℓ, ms) for these levels.
17. •• Let’s model a proton in a nucleus as a particle trapped in the one-dimensional box. Assume the particle is in a one-dimensional nucleus of length 7.11 fm(approximate diameter of a 208Pb nucleus). (a) Using the results of Exercise 28.16, find the energies of the proton in the ground
16. •• A particle in box is constrained to move in one dimension, like a bead on a wire, as illustrated in▼ Figure 28.14. Assume that no forces act on the particle in the interval 0 < x < L and that it hits a perfectly rigid wall. The particle will exist only in states of certain kinetic
15. • If you are twice as likely to find an electron at a distance of 0.0400 nm than 0.0500 nm from the nucleus, what is the ratio of the absolute value of its wave function at 0.0400 nm to that at 0.0500 nm?
14. • If the absolute value of the wave function of a proton is twice as large at location A than at location B, how many times is it more likely to find it at A than at B?
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