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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
27. IE •• (a) In an interaction using the virtual particle model, the range of the interaction (1) increases,(2) remains the same, (3) decreases as energy of the exchange particle increases. Why? (b) If the W particle has a rest energy on the order of 1.0 GeV, what is the approximate range (to
26. • (a) Assuming the range of the nuclear force to be 1.0 × 10−15 m, predict the mass (in kilograms) of the exchange particle related to this force. (b) Convert the answer into the particle’s rest energy (in MeV) and identify it.
25. ••• The expressions for the Q values associated with both β− and β+ decay are in Exercises 30.20 and 30.23.Assume that the daughter’s atomic mass MD is the same in both processes. (a) Use the β− expression to show that the requirement for β− decay to occur is simply that the
24. ••• The kinetic energy of a positron emitted from the β+ decay of a 13N nucleus into a 13C nucleus is 1.190 MeV. What is the energy of the accompanying neutrino? Neglect the recoil energy of the daughter nucleus. (See Exercise 23.)
23. ••• Show that the disintegration energy for β+ decay is Q = (mP − mD − me)c2 = (MP − MD − 2me)c2, where the ms represent the masses of the parent and daughter nuclei and the Ms represent the masses of the neutral atoms. [Hint: Count the number of electrons both before and after
22. •• The kinetic energy of an electron emitted from a 32P nucleus that beta decays into a 32S nucleus is 1.00 MeV.What is the energy of the accompanying neutrino?Neglect the recoil energy of the daughter nucleus. (See Exercise 20.)
21. •• What is the maximum kinetic energy of the electron emitted when a 12B nucleus beta decays into a 12C nucleus? (See Exercise 20.)
20. •• Show that the disintegration energy for β− decay is Q = (mP − mD − me)c2 = (MP − MD)c2 where the ms represent the masses of the parent and daughter nuclei and the Ms represent the masses of the neutral atoms.[Hint: The number of electrons before and after are the same. Why?]
19. IE • A neutrino created in a beta decay process has an energy of 2.65 MeV. What is the maximum possible kinetic energy of the beta particle if the disintegration energy is 5.35 MeV: (a) (1) zero, (2) less than 5.35 MeV but not zero, (3) 5.35 MeV, or (4) greater than 5.35 MeV?(b) Under these
18. • In a decay process the beta particle has a kinetic energy of 0.65 MeV, and the neutrino energy is 0.25 MeV. Neglecting daughter recoil, find the disintegration energy.
17. •• Fill in the blanks: (a) 1 21 22 H+ H→ 3He+___,(b) 1 21 3 0H+ H→___+ 1n. (c) Find the energy released in each.
16. •• Fill in the blanks: (a) 1 11 H+__→ 2H+γ,(b)___ + 2 32 41 1 He→ He+2( H). (c) Find the energy released in each.
15. •• (a) In power reactors, using water as a moderator(“neutron slower”) works well, because the proton and neutron have nearly the same mass. Explain why this is true. [Hint: Consider an elastic head-on collision of objects of equal mass.] (b) From your reasoning in part (a), it follows
14. • Find the approximate energy released in the following fission reactions: (a) 92 235 0U+ 1n→ fission products plus five neutrons, (b) 94 235 0Pu+ 1n→ fission products plus three neutrons.
13. IE ••• The same type of incident particle is used for two endoergic reactions. In one reaction, the mass of the target nucleus is 15 times that of the incident particle, and in the other reaction, it is 20 times the incident particle’s mass. The Q value of the first reaction is known to
12. •• 226Ra decays and emits a 4.706-MeV alpha particle.Find the kinetic energy of the recoiling daughter nucleus if the 226Ra was originally stationary.
11. •• What is the minimum kinetic energy a proton must have in order to initiate the reaction 1 3 H(p, d)1 2H?(“d” stands for a deuterium nucleus – the deuteron.)
10. •• Determine the Q value of the following reaction:4 92 46 12 01 9 012 183 4 002 603 12 000 000 1 Be He C n u u u+ → +( . ) ( . ) ( . ) ( .008 665u)
9. •• Is this reaction endoergic or exoergic? Prove your answer by finding the Q value.80 200 1 1 79 197 24 199 Hg H Au He mercury proton gold alpha particle+ → +( .968 321u) (1.007 825u) (196.966 56u) (4.002 603u)
8. •• Is this reaction endoergic or exoergic? Prove your answer by determining the Q value.3 71 1 24 24 7 016 005 1 007 825 4 002 603 4 Li H He He u u u+ → +( . ) ( . ) ( . ) ( .002 603u)
7. •• Find the threshold energy for the following reaction:2 30 11 21 23 016 029 1 008 665 2 014102 2 014 He n H H u u u+ → +( . ) ( . ) ( . ) ( . 102u)
6. •• Find the threshold energy for the following reaction:8 16 01 613 24 15 994 915 1 008 665 13 003 355 4 O n C He u u u+ → +( . ) ( . ) ( . ) ( .002 603u)
5. IE • 238U undergoes alpha decay as follows:92 238 90 234 24 238 050 786 234 043 583 4 002 603 U Th He u u u→ +( . ) ( . ) ( . )(a) Do you expect the Q value to be (1) positive,(2) negative, or (3) zero? Why? (b) Find the Q value.
4. • Find the Q value for 1 11 22 H+ H→ 3He+γ.
3. • Determine what the daughter nuclei are in each of the following decays. Can any of these decays occur spontaneously? Explain your reasoning in each case.(a) 10 22 1Ne→ + 0e. __ −(b) 88 226 2Ra→__+ 4He(c) 8 16 2O→__+ 4He
2. IE • (a) Consider the reaction 6 13 1 1 24 5C + H→ He+ 10B.Determine whether it is endoergic or exoergic. (b) If it is exoergic, find the amount of energy released; if it is endoergic, find the threshold energy.
1. • Complete the following nuclear reactions:(a) 0 118 n + 40Ar →____+α(b) 0 192 235 40 98 135 0n + U→ Zr + + (1 n) ___ __ __(c) 7 14N(α, p)___(d) 13C(___,α)10B
24. Successful unification of the electromagnetic force with the weak force led physicists to what surprising conclusion about the proton? Describe how you might experimentally detect and verify this prediction.
23. Theoretical physicists often assert that at the extremely high energies thought to have existed in the first moments of the universe, the W particle (known to have a mass several hundred times that of the proton)would behave, mass-wise, similarly to the (massless)photon. Explain this apparently
22. What are some of the important differences and distinctions between baryons and mesons?
21. With so many types of hadrons, why aren’t fractional electronic charges observed?
20. What is meant by quark flavor and color? Can these attributes be changed? Explain.
19. Which of the leptons are stable? Which of the hadrons are stable?
18. Explain how you can distinguish between a hadron and a lepton based on their interactions and exchange particles.
17. Compare the effective range of the strong nuclear force with that of the weak nuclear force. What does that tell you about the relative masses of the exchange particle(s) associated with these two forces? What should be the approximate (numerical) ratio of their masses (weak exchange particle
16. When a proton interacts with another proton, which of the four fundamental forces would be involved? How about when an electron interacts with another electron?
15. If virtual exchange particles are unobservable by themselves, how is their existence verified?
14. (a) In beta decay, if the daughter nucleus is stationary, what can you say about the directions of the beta particle and the neutrino? Explain. (b) In a β decay with a Q value of 1.5 MeV, suppose the β is emitted with very little kinetic energy. How would the momenta of the daughter nucleus
13. In beta decay, explain why the beta particle kinetic energy must be less than the Q value of the decay.
12. It is known that neutrinos have a very small mass. If they were massless (as previously assumed), neutrinos of all energies would travel at the same speed,c. Since they have mass, their speed must be less thanc. Is it still true that they would travel at the same speed regardless of their
11. A ve can interact with protons (very weakly but relatively strongly compared to other nuclei), usually the nucleus of the hydrogen atom in a water molecule in a target of water. The reaction is essentially the inverse of β− decay; that is, the proton is converted into a neutron. Neutrino
10. Does it take a higher temperature to fuse two protons or to fuse two 12C nuclei? Explain.
9. Explain why there are both density and temperature requirements to sustain a viable fusion energy plant.Why are these requirements at odds with one another?
8. As world oil prices generally rise there has been a call to move electric generation from fossil fuel plants to nuclear fission plants. Discuss some of the pros and cons involved in replacing fossil fuel plants with nuclear versions. Military, terrorism, global warming, and environmental
7. Countries entering the nuclear age by constructing nuclear power plants are of concern to the world community because these plants could supply material for nuclear weapons (fission bombs). Explain how this can happen. [Hint: Power reactors use 235U as the fissionable material, but it is only a
6. Used fuel rods from most U.S. reactors are currently stored on site in pools of water that contain a salt of boron (borated water). Why is the boron needed?
5. Explain clearly why the cooling water in a U.S. nuclear reactor helps keep the chain reaction from multiplying in addition to serving as a neutron moderator.
4. A 3He particle initiates a reaction when incident on a target nucleus. (a) Find a reaction scenario that would yield a product nucleus that is of the same species as the target nucleus. (b) Find a reaction scenario that would yield a product nucleus that has the same number of nucleons as the
3. To capture a slow neutron, which nucleus would have a larger capture cross-section: 24Mg or 25Mg? Explain.
2. For a given Q value and incident particle (labeled a), how does the threshold energy required to initiate a specific nuclear reaction vary as the mass of the target(labeled A) changes? Sketch a graph of threshold energy versus target mass ranging from target masses on the order of the incident
1. Using conservation of linear momentum, explain how a colliding beam reaction (in which both particles move toward a head-on collision) requires less incident kinetic energy than a reaction in which one particle is at rest.
24. A prediction of the grand unified theory is that(a) protons are unstable, (b) neutrons are unstable,(c) neutrinos are unstable.
23. The magnetic force is part of the (a) electroweak force,(b) weak force, (c) strong force, (d) superforce.
22. The grand unified theory would reduce the number of fundamental forces to (a) one, (b) two, (c) three,(d) four.
21. Individual free quarks may never be observed due to a phenomenon known as (a) quark invisibility,(b) quark cloaking, (c) quark confinement, (d) quark life sentences.
20. The virtual particle responsible for the color force between quarks is (a) the pion, (b) the muon,(c) the tauon, (d) the gluon.
19. Which of the following cannot be the charge on a quark: (a) (1/3)e, (b) −(2/3)e, (c) (2/3)e, or (d) zero?
18. Quarks are thought to make up which of the following particles: (a) hadrons, (b) muons, (c) electrons, or(d) neutrinos?
17. Which one of the following leptons has the least mass:(a) neutrino, (b) electron, (c) muon, or (d) tauon?
16. Which one of the following is not a hadron: (a) proton,(b) neutron, (c) pion, (d) electron, or (e) all are hadrons?
15. Particles that interact by the strong nuclear force are called (a) muons, (b) hadrons, (c) W particles,(d) leptons.
14. The exchange particle associated with the weak nuclear force is the (a) pion, (b) W particle, (c) muon,(d) positron.
13. The exchange particle associated with the strong nuclear force is the (a) pion, (b) W particle, (c) muon, (d) positron.
12. Virtual particles (a) form virtual images, (b) exist only in an amount of time permitted by the uncertainty principle, (c) make up positrons.
11. A beta decay of the unstable nuclide 28Al would produce what type of neutrino: (a) an antineutrino,(b) a neutrino.
10. β+ decay is associated with what type of neutrino:(a) an antineutrino, (b) a neutrino, or (c) no neutrino?
9. In β− decay, if the daughter nucleus is stationary, how do the moment a (magnitude) of the β− and the ve compare: (a) the β− has more momentum,(b) the ve has more momentum, or (c) they have the same momentum?
8. The net effect of the fusion cycle presently occurring in our Sun is to convert (a) hydrogen into helium,(b) helium into carbon, (c) helium into hydrogen.
7. A nuclear fusion reaction (a) has a positive Q value,(b) may occur in laboratories spontaneously, (c) is an example of “splitting” the atom.
6. A standard fission breeder reactor creates fissionable material by converting (a) 238U into 235U, (b) 238U into 239Pu, (c) 235U into 238U, (d) 239Pu into 235U.
5. A nuclear reactor (a) can operate on natural(unenriched) uranium, (b) has its chain reaction controlled by neutron-absorbing materials, (c) can be partially controlled by the amount of moderator,(d) all of the preceding.
4. Nuclear fission (a) is endoergic, (b) occurs only for 235U,(c) releases about 500 MeV per fission, (d) requires a critical mass for a sustained reaction.
3. A 27Mg nucleus and a free proton are the products of a nuclear reaction involving a target nucleus of 27Al.What was the incident particle that triggered this:(a) a neutron, (b) a proton, or (c) an alpha particle?
2. If an alpha particle is incident on a carbon-12 nucleus and the outgoing particle is a proton, what is the product nucleus: (a) 16O, (b) 16N, (c) 15N, or (d) 16C?
1. The absorption of a slow neutron by 235U temporarily results in the compound nucleus (a) 235U, (b) 235U*,(c) 236U*, (d) 236Np*.
53. ••• A cancer treatment called the gamma knife uses focused 60Co sources to treat tumors. Each 60Co nucleus emits two gamma rays, of energy 1.33 and 1.17 MeV, in quick succession. Assume that 50.0% of the total gamma-ray energy is absorbed by a tumor.Further assume that the total activity
52. •• Neutron activation analysis was performed on small pieces of hair that had been taken from the exiled Napoleon after he died on the island of St.Helena in 1821. This procedure involves exposing the samples to a source of neutrons. Some (stable)arsenic nuclei, if present in the sample,
51. • A person working with several nuclear isotope separation processes for a two-month period receives a 0.50-rad dose from a gamma source, a 0.30-rad dose from a slow-neutron source, and a 0.10-rad dose from an alpha source. Was the maximum permissible radiation dosage exceeded?
50. • A technician working at a nuclear reactor facility is exposed to a slow neutron radiation and receives a dose of 1.25 rad. (a) How much energy is absorbed by 200 g of the worker’s tissue? (b) Was the maximum permissible radiation dosage exceeded?
49. • In a diagnostic procedure, a patient in a hospital ingests 80 mCi of gold-198 (t1/2 = 2.7 days). What is the activity at the end of one month, assuming none of the gold is eliminated from the body by biological functions?
48. ••• The mass of 4 8 Be is 8.005 305 u. (a) Which is less, the total mass of two alpha particles or the mass of the 8Be nucleus? (b) Which is greater, the total binding energy of the 8Be nucleus or the total binding energy of two alpha particles? (c) On the basis of your answers to
47. •• The atomic mass of 92 236U is 235.043 925 u. Find the average binding energy per nucleon for this isotope.
46. •• On average, determine whether the nucleons are more tightly bound in a 27Al nucleus or in a 23Na nucleus.
45. •• Suppose an alpha particle could be removed intact from an aluminum-27 nucleus (m = 26.981 541 u).(a) Write the equation that represents this process and determine the daughter nuclide. (b) If the daughter nuclide has mass of 22.989 770 u, how much energy would be required to perform this
44. •• Calculate the binding energy of the last neutron in the 19 40K nucleus.
43. •• (a) How much energy (to four significant figures)would be required to completely separate all the nucleons of a nitrogen-14 nucleus, the atom of which has a mass of 14.003 074 u? (b) Compute the average binding energy per nucleon of this nuclide.
42. •• Near high-neutron areas, such as a nuclear reactor, neutrons will be absorbed by protons (the hydrogen nucleus in water molecules) and will give off a gamma ray of a characteristic energy in the process. (a) Write the equation for the neutron absorption process and the subsequent gamma
41. •• Which isotope of hydrogen has (a) the highest total binding energy and (b) the lowest average binding energy per nucleon, deuterium or tritium? Justify your answer mathematically.
40. •• The mass of the nuclide 8 16O is 15.994 915 u.(a) What is the total binding energy for this nucleus?(b) Determine its average binding energy per nucleon.
39. •• (a) What is the total binding energy of the 12C nucleus? (b) What is its average binding energy per nucleon?
38. • Use Avogadro’s number to show that 1 u = 1.66 × 10−27 kg. [Hint: Recall that a 12C atom has a mass of exactly 12 u.]
37. • The total binding energy of 1 2H is 2.224 MeV. Use this information to compute the mass (in u) of a 2H nucleus from the known mass of the proton and the neutron.
36. • Only two isotopes of Sb (antimony, Z = 51) are stable. Pick the two most likely stable isotopes from the following list and explain your rationale. (a) 120Sb,(b) 121Sb, (c) 122Sb, (d) 123Sb, (e) 124Sb.
35. • Which one of each of the following pairs of nuclei should it be easier to remove a neutron from? (a) 8 16 8Oor 17O, (b) 20 40 20 Ca or 42Ca, (c) 5 10 5B or 11B,(d) 82 208 83 Pb or 209Bi? State your reasoning in each case.
34. ••• Nitrogen-13, with a half-life of 10.0 min, decays by beta emission. (a) Write down the decay equation to determine the daughter product and whether the beta particle is a positron or electron. (b) If a sample of pure 13N has a mass of 1.50 g at a certain time, what is the activity min
33. ••• The recoverable U.S. reserves of high-grade uranium-238 ore (high-grade ore contains about 10 kg of 238U3O8 per ton) are estimated to be about 500 000 tons. Neglecting any geological changes, what mass of 238U existed in this high-grade ore when the Earth was formed, about 4.8 billion
32. •• An ancient artifact is found to contain 250 g of carbon and has an activity of 475 decays/min. (a) What is the approximate age of the artifact, to the nearest thousand years? (b) What would its initial activity have been?
31. •• In 1898, Pierre and Marie Curie isolated about 10 mg of radium-226 from eight tons of uranium ore. If this sample had been placed in a museum, (a) how much of the radium would remain in the year 2109? (b) How many radium nuclei would have decayed during this time?
30. •• A basement room containing radon gas(t1/2 = 3.82 days) is sealed to be airtight. (a) If 7.50 × 1010 radon atoms are trapped in the room, estimate how many radon atoms remain in the room after one week.(b) Radon undergoes alpha decay. After 30 days, is the number of its daughter nuclei
29. •• Francium-223 87(223Fr) has a half-life of 21.8 min.(a) How many nuclei are initially present in a 25.0-mg sample of 87 223Fr? (b) What is its initial activity? (c) How many nuclei will be present 1 h and 49 min later?(d) What will be the sample’s activity at this later time?
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