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All Textbook Solutions for College Physics
How many Gy of exposure is needed to give a cancerous tumor a dose of 40 Sv if it is exposed to acfivity?What is the dose in Sv in a cancer treatment that exposes the patient to 200 Gy of rays?One half the rays from 99mTc are absorbed by a 0.170mmthick lead shielding. Half of the rays that pass through the first layer of lead are absorbed in a second layer of equal thickness. What thickness of lead will absorb all but one in 1000 of these rays?A plumber at a nuclear power plant receives a whole—body dose of 30 mSv in 15 minutes while repairing a crucial valve. Find the radiation—induced yearly risk of death from cancer and the chance of genetic defect from this maximum allowable exposure.In the 1980s, the term picowave was used to describe food irradiation in order to overcome public resistance by playing on the well—known safety of microwave radiation. Find the energy in MeV of a photon having a wavelength of a picometer.Find the mass of 239Pu mat has an activity of 1.00 Ci.A beam of 168MeV nitrogen nuclei is used for cancer therapy. If this beam is directed onto a 0.200kg tumor and gives it a 2.00Sv dose, how many nitrogen nuclei were stopped? (Use an RBE of 20 for heavy ions.)(a) If the average molecular mass of compounds in food is 50.0 g, how many molecules are mere in 1.00 kg at food? (b) How many ion pairs are created in 1.00 kg of food, if it is exposed to 1000 Sv and it takes 32.0 eV to create an ion pair? (c) Find the ratio of ion pairs to molecules. (d) If these ion pairs recombine into a distribution of 2000 new compounds, how many parts per billion is each?Calculate the dose in Sv to the chest at a patient given an xray under the following conditions. The xray beam intensity is 1.50 W/m2, the area of the chest exposed is 0.0750 m2 35.0% of the xrays are absorbed in 20.0 kg of tissue, and the exposure time is 0.250 s.(a) A cancer patient is exposed to rays from a 5000Ci 60Co transillumination unit for 32.0 s. The rays are collimated in such a manner that only 1.00% of them strike the patient. Of those, 20.0% are absorbed in a tumor having a mass of 1.50 kg. What is the dose in rem to the tumor, it the average energy per decay is 1.25 MeV? None of the s from the decay reach the patient. (b) Is the dose consistent with stated therapeutic doses?What is the mass of 60Co in a cancer therapy transillumination unit containing 5.00 kCi of 60Co?Large amounts of 65Zn are produced in copper exposed to accelerator beams. While machining contaminated copper, a physicist ingests 50.0 Ci of 65Zn. Each 65Zn decay emits an average ray energy of 0.550 MeV, 40.0% of which is absorbed in the scientist’s 75.0kg body. What dose in mSv is caused by this in one day?Naturally occurring 40K is listed as responsible for 16 mrem/y of background radiation. Calculate the mass of 40K that must be inside the 55kg body of a woman to produce this dose. Each 40K decay emits a 1.32MeV , and 50% of the energy is absorbed inside the body.(a) Background radiation due to 226Ra averages only 0.01 mSv/y, but it can range upward depending on where a 226Ra in the 80.0kg body of a man who receives a dose of 2.50mSv/y from it, noting that each 226Ra decay emits a 4.80MeV particle. You may person lives. Find the mass of neglect dose due to daughters and assume a constant amount, evenly distributed due to balanced ingestion and handily elimination. (b) Is it surprising that such a small mass could cause a measurable radiation dose? Explain.The annual radiation dose from 14C in our bodies is 0.01 mSv/y. Each 14C decay emits a averaging 0.0750 MeV. Taking the fraction of 14C to be 1.31012N of normal 12C, and assuming the body is 13% carbon, estimate the fraction of the decay energy absorbed. (The rest escapes, exposing those close to you.)If everyone in Australia received an extra 0.05 mSv per year of radiation, what would be the increase in the number of cancer deaths per year? (Assume that time had elapsed for the effects to become apparent.) Assume that there are 200104 deaths per Sv of radiation per year. What percent at the actual number of cancer deaths recorded is this?Verify that the total number at nucleons, total charge, and electron family number are conserved for each of the fusion reactions in the proton—proton cycle in 1H+1H2H+e++ve,1H+2H3He+, and 2H+3He4He++1H+1H. (List the value of each of the conserved quantities before and after each of the reactions.)Calculate the energy output in each of the fusion reactions in the protonproton cycle, and verify the values given in the above summary.Show that the total energy released in the proton—proton cycle is 26.7 MeV, considering the overall effect in 1H+1H2H+e++ve,1H+2H3He+, and 3H+3He4He+1H+1H and being certain to include the annihilation energy.Verify by listing the number of nucleons, total charge, and electron family number before and after the cycle that these quanti?es are conserved in the overall proton—proton cycle in 2e+41H4He+2ve+6.The energy produced by the fusion of a 1.00—kg mixture of deuterium and tritium was found in Example Calculating Energy and Power from Fusion. Approximately how many kilograms would be required to supply the annual energy use in the United States?Tritium is naturally rare, but can be produced by the reaction n+2H3H+. How much energy in MeV is released in this neutron capture?Two fusion reactions mentioned in the text are n+3H4He+ and n+1H2H+. But reactions release energy, but the second also creates more fuel. Confirm that the energies produced in the reactions are 20.53 and 2.22 MeV, respectively. Comment on which product nuclide is most tightly bound, 4He or 2H.(a) Calculate the number of grams of deuterium in an 80.000L swimming pool, given deuterium is 0.0150% of natural hydrogen. (b) Find the energy released in joules if this deuterium is fused via the reaction 2H+2H3He+n. (c) Could the neutrons be used to create more energy? (d) Discuss the amount of this type of energy in a swimming pool as compared to that in, say, a gallon of gasoline, also taking into consideration that water is far more abundant.How many kilograms of water are needed to obtain the 198.8 mol of deuterium, assuming that deuterium is 0.01500% (by number) of natural hydrogen?The power output of the Sun is 41026W. (a) If 90% of this is supplied by the protonproton cycle, how many protons are consumed per second? (b) How many neutrinos per second should there be per square meter at the Earth from this process? This huge number is indicative of how rarely a neutrino interacts, since large detectors observe very few per day.Another set of reactions that result in the fusing of hydrogen into helium in the Sun and especially in hotter stars is called the carbon cycle. It is 12C+1H13N+, 13N13C+e++ve, 13C+1H14N+, 14N+1H15O+, 15O15N+e++ve, 15N+1H12C+4He. Write down the overall effect at the carbon cycle (as was done for the protonproton cycle in 2e+41H+4He+2ve+6. Note the number of protons (lH) required and assume that the positrons (e+) annihilate electrons to form more (rays.(a) Find the total energy released in MeV in each carbon cycle (elaborated in the above problem) including the annihilation energy. (b) How does this compare with the protonproton cycle output?Verify that the total number of nucleons, total charge, and electron family number are conserved for each of the fusion reactions in the carbon cycle given in the above problem. (List the value of each of the conserved quantifies before and after each of the reactions.)Integrated Concepts The laser system tested for inertial con?nement can produce a 100kJ pulse only 1.000 ns in duration. (a) What is the power output of the laser system during the brief pulse? (b) How many photons are in the pulse, given their wavelength is 1.06 (m? (c) What is the total momentum of all these photons? (d) How does the total photon momentum compare with that of a single 1.00 MeV deuterium nucleus?Integrated Concepts Find the amount of energy given to the 4He nucleus and to the ray in the reaction n+3He4He+, using the conservation of momentum principle and taking the reactants to be initially at rest. This should confirm the contention that must of the energy goes to the ray.Integrated Concepts: (a) What temperature gas would have atoms moving fast enough to bring two 3He nuclei into contact? Note that, because both are moving, the average kinetic energy only needs to be half the electric potential energy of these doubly charged nuclei when just in contact with one another. (b) Does this high temperature imply practical difficulties for doing this in controlled fusion?Integrated Concepts (a) Estimate the years 1hat1he deuterium fuel in the oceans could supply the energy' needs of the world. Assume world energy consumption to be ten times that of the United States which is 81019J/y and the deuterium in the oceans could be converted to energy with an efficiency of 32%. You must estimate or look up the amount of water in the oceans and take the deuterium content to be 0.015% of natural hydrogen to find the mass of deuterium available. Note that approximate energy yield at deuterium is 3.371014J/kg. (b) Comment on how much time this is by any human measure. (It is not an unreasonable result, only an impressive one.)(a) Calculate the energy released in the neutroninduced fission (similar to the spontaneous fission in Example 32.3) n+238U96Sr+140Xe+3n, given m(96Sr)=95.921750u and m(140Xe)=139.92164. (b) This result is about 6 MeV greater than the result for spontaneous fission. Why? (c) Con?rm that the total number at nucleons and total charge are conserved in this reaction.(a) Calculate the energy released in the neutroninduced fission reaction n+235U92Kr+142Ba+2n, given m(92Kr)=91.926269 and m(142Ba)=141.916361u. (b) Confirm that the total number at nucleons and total charge are conserved in this reaction.(a) Calculate the energy released in the neutroninduced fission reaction n+239Pu96Sr+140Ba+4n, given m(96Sr)=95.921750u and m(140Ba)=139.910581u. (b) Confirm that the total number of nucleons and total charge are conserved in this reaction.Confirm that each at the reactions listed for plutonium breeding just following Example 32.4 conserves the total number of nucleons, the total charge, and electron family number.Breeding plutonium produces energy even before any plutonium is fissioned. (The primary purpose of the four nuclear reactors at Chernobyl was breeding plutonium for weapons. Electrical power was a byproduct used by the civilian population.) Calculate the energy produced in each of the reactions listed for plutonium breeding just following Example 32.4. The pertinent masses are m(239U)=239.054289u,m(239Np)=239.052932u, and m(239Pu)=239.052157u.The naturally occurring radioactive isotope 232Th does not make good fission fuel, because it has an even number of neurons; however, it can be bred into a suitable fuel (much as 238U is bred into 239P). (a) What are Z and N for 232Th? (b) Write the reaction equation for neutron captured by 232Th and identify the nuclide AX produced in n+232ThAX+. (c) The product nucleus β decays, as does its daughter. Write me decay equations for each, and identify the final nucleus. (d) Conform that the final nucleus has an odd number of neutrons, making it a better fission fuel. (e) Look up the halflife of the final nucleus to see if it lives long enough to be a useful fuel.The electrical power output of a large nuclear reactor facility is 900 MW. It has a 35.0% efficiency in converting nuclear power to electrical. (a) What is the thermal nuclear power output in megawatts? (b) How many 235U nuclei fission each second, assuming the average fission produces 200 MeV? (c) What mass of 235U is fissioned in one year of fullpower operation?A large power reactor that has been in operation for some months is turned off, but residual activity in the core still produces 150 MW of power. If the average energy per decay of the fission products is 1.00 MeV, what is the core activity in curies?Find the mass converted into energy by a 12.0kT bomb.What mass is converted into energy by a 1.00MT bomb?Fusion bombs use neutrons from their fission trigger to create tritium fuel in the reaction n+6Li3H+4He. What is the energy released by this reaction in MeV?It is estimated that the total explosive yield of all the nuclear bombs in existence currently is about 4.000 MT. (a) Convert this amount of energy to kilowatthours, noting that 1kWh=3.60106J. (b) What would the monetary value of this energy be if it could be converted to electricity costing 10 cents per kW.h?A radiationenhanced nuclear weapon (or neutron bomb) can have a smaller total yield and still produce more prompt radiation than a conventional nuclear bomb. This allows the use of neutron bombs to kill nearby advancing enemy forces with radiation without blowing up your own forces with the blast. For a 0.500kT radiationenhanced weapon and a 1.00kT conventional nuclear bomb: (a) Compare the blast yields. (b) Compare the prompt radiation yields.(a) How many 239Pu nuclei must fission to produce a 20.0kT yield, assuming 200 MeV per fission? (b) What is the mass of this much 239Pu?Assume onefourth of the yield of a typical 320kT strategic bomb comes from fission reactions averaging 200 MeV and the remainder from fusion reactions averaging 20 MeV. (a) Calculate the number of fissions and the approximate mass of uranium and plutonium fissioned, taking the average atomic mass to be 238. (b) Find the number of fusions and calculate the approximate mass of fusion fuel, assuming an average total atomic mass of the two nuclei in each reaction to be 5. (c) Considering the masses found, does it seem reasonable that some missiles could carry 10 warheads? Discuss, noting that the nuclear fuel is only a part of the mass of a warhead.This problem gives some idea of the magnitude of the energy yield of a small tactical bomb. Assume that half the energy of a 1.00kT nuclear depth charge set off under an aircraft carrier goes into lifting it out of the water—that is, into gravitational potential energy. How high is the carrier lifted if its mass is 90,000 tons?It is estimated that weapons tests in the atmosphere have deposited approximately 9 MCi of 90Sr on the surface of the earth. Find the mass of this amount of 90Sr.A 1.00MT bomb exploded a few kilometers above the ground deposits 25.0% of its energy into radiant heat. (a) Find the calories per cm2 at a distance of 10.0 km by assuming a uniform distribution over a spherical surface at that radius. (b) If this heat falls on a person’s body, what temperature increase does it cause in the affected tissue, assuming it is absorbed in a layer 1.00cm deep?Integrated Concepts One scheme to put nuclear weapons to nonmilitary use is to explode them underground in a geologically stable region and extract the geothermal energy for electricity production. There was a total yield of about 4,000 MT in the combined arsenals in 2006. If 1.00 MT per day could be converted to electricity with an ef?ciency of 10.0%: (a) What would the average electrical power output be? (b) How many years would the arsenal last at this rate?The total energy in the beam of an accelerator is far greater than the energy of the individual beam particles. Why isn't this total energy available to create a single extremely massive particle?Synchrotron radiation takes energy from an accelerator beam and is related to acceleration. Why would you expect the problem to be more severe for electron accelerators than proton accelerators?What two major limitations prevent us from building highenergy accelerators that are physically small?What are the advantages of collidingbeam accelerators? What are the disadvantages?Large quanti?es of antimatter isolated from normal matter should behave exactly like normal matter. An antiatom for example, composed of positrons. antiprotons, and antineutrons should have the same atomic spectrum as its matter counterpart. Would you be able to tell it is antimatter by its emission of antiphotons? Explain briefly.Massless particles are not only neutral, they are chargeless (unlike the neutron). Why is this so?Massless particles must travel at the speed of light, while others cannot reach this speed. Why are all massless particles stable? If evidence is found that neutrinos spontaneously decay into other particles, would this imply they have mass?When a stat erupts in a supernova explosion, huge numbers of electron neutrinos are formed in nuclear reactions. Such neutrinos from the 1987A supernova in the relatively nearby Magellanic Cloud were observed within hours of the initial brightening, indicating they traveled to earth at approximately the speed of light. Explain how this date can be used to set an upper limit on the mass of the neutrino, noting that the mass is small the neutrinos could travel very close to the speed at light and have a reasonable energy (on the order of MeV).Theorists have had spectacular success in predicting previously unknown particles. Considering past theoretical triumphs, why should we bother to perform experiments?What lifetime do you expect for an antineutron isolated from normal matter?Why does the meson have such a short lifetime compared to most other mesons?(a) Is a hadron always a baryon? (b) Is a baryon always a hadron? (c) Can an unstable baryon decay into a meson, leaving no other baryon?Explain how conservation of baryon number is responsible for conservation of total atomic mass (total number at nucleons) in nuclear decay and reactions.The quark ?avor change it takes place in decay. Does this mean that the reverse quark ?avor change takes place in decay? Justify your response by writing the decay in terms of the quark constituents, noting that it looks as if a proton is converted into a neutron in decay.Explain how the weak force can change strangeness by changing quark ?avor.Beta decay is caused by the weak force, as are all reactions in which strangeness changes. Does this imply that the weak force can change quark ?avor? Explain.Why is it easier to see the properties of the c, b, and t quarks in mesons having composition W or rather than in baryons having a mixture of quarks, such as udb?How can quarks, which are fermions, combine to form bosons? Why must an even number combine to form a boson? Give one example by stating the quark substructure of a boson.What evidence is cited is support the contention that the gluon force between quarks is greater than the strong nuclear force between hadrons? How is this related to color? Is it also related to quark confinement?Discuss how we know that (mesons are not fundamental particles and are not the basic earners of the strong force.An antibaryon has three antiquarks with colors What is its color?Suppose leptons are created in a reaction. Does this imply the weak force is acting? (for example, consider (decay.)How can the lifetime of a particle indicate that its decay is caused by the strong nuclear force? How can a change in strangeness imply which force is responsible for a reaction? What does a change in quark ?avor imply about the force that is responsible?(a) Do all particles having strangeness also have at least one strange quark in them? (b) Do all hadrons with a strange quark also have nonzero strangeness?The sigmazero particle decays mostly via the reaction Explain how this decay and the respective quark compositions imply that the is an excited state of theWhat do the quark compositions and other quantum numbers imply about the relationships between the and the proton? The and the neutron?Discuss the similarities and differences between the photon and the Z0 in terms of particle properties, including forces felt.Identity evidence for electroweak unification.The quarks in a particle are con?ned, meaning individual quarks cannot be directly observed. Are gluons con?ned as well? ExplainIf a GUT is proven, and the four forces are unified, it will still be correct to say that the orbit of the moon is determined by the gravitational force. Explain why.If the Higgs boson is discovered and found to have mass, will it be considered the ultimate carrier of the weak force? Explain your response.Gluons and the photon are massless. Does this imply that the W+, W-, and Z0 are the ultimate carriers of the weak force?A virtual particle having an approximate mass of may be associated with the uni?cation of the strong and electroweak forces. For what length of time could this virtual particle exist (in temporary violation of the conservation of mass-energy as allowed by the Heisenberg uncertainty principle)?Calculate the mass in of a virtual carrier particle that has a range limited to by the Heisenberg uncertainty principle. Such a particle might be involved in the unification of the strong and electroweak forces.Another component of the strong nuclear force is transmitted by the exchange of virtual Kmesons. Taking Kmesons to have an average mass of what is the approximate range at this component of the strong force?(a) Find the ratio of the strengths the weak and electromagnetic forces under ordinary circumstances. (b) What does that ratio become under circumstances in which the forces are unified?We ratio of the strong to the weak force and the ratio of the strong force to the electromagnetic force become 1 under circumstances where they are unified. What are the ratios of the strong force to wage two forces under normal circumstances?At full energy, protons in the 2.00kmdiameter Fermilab synchrotron travel at nearly the speed of light, since their energy is about 1000 times their rest mass energy. (a) How long does it take for a proton to complete one trip around? (b) How many times per second will it pass through the target area?Suppose a W created in a bubble chamber lives for What distance does it move in this time if it is traveling at 0.900 c? Since this distance is too short to make a track, the presence of the W must be inferred from its decay products. Note that the time is longer than the given W lifetime, which can be due to the statistical nature of decay or time dilation.What length track does a (+ traveling at 0.100 c leave in a bubble chamber if it is created there and lives for (Those moving faster or living longer may escape the detector before decaying.)The 3.20kmlong SLAC produces a beam of 50.0GeV electrons. If there are 15,000 accelerating tubes, what average un?age must be across the gaps between them to achieve this energy?Because of energy loss due to synchrotron radiation in the LHC at CERN, only 5.00 MeV is added to the energy of each proton during each revolution around the main ring. How many revolutions are needed to produce 7.00TeV (7000 GeV) protons, if they are injected with an initial energy of 8.00 GeV?A proton and an antiproton collide headon, with each having a kinetic energy of 7.00 TeV (such as in the LHC at CERN). How much collision energy is available, taking into account the annihilation of the two masses? (Note that this is not significantly greater than the extremely relativistic kinetic energy.)When an electron and positron collide at the SLAC facility, they each have 50.0 GeV kinetic energies. What is the total collision energy available, taking into account the annihilation energy? Note that the annihilation energy is insignificant, because the electrons are highly relativistic.The is its own antiparticle and decays in the following manner: What is the energy of each (ray if the is at rest when it decays?The primary decay mode for the negative pion is What is the energy release in MeV in this decay?The mass of a theoretical particle that may be associated with the uni?cation of the electroweak and strong forces is (a) How many proton masses is this? (b) How many electron masses is this? (This indicates how extremely relativistic the accelerator would have to be in order to make the particle, and how large the relativistic quantity (would have to be.)The decay mode of the negative muon is (a) Find the energy released in MeV. (b) Verify that charge and lepton family numbers are conserved.The decay mode of the positive tau is (a) What energy is released? (b) Verify that charge and lepton family numbers are conserved. (c) The is the antiparticle of the Verify that all the decay products of the are the antiparticles of those in the decay of the given in the text.The principal decay mode at the sigma zero is (a) What energy is released? (b) Considering the quark structure of the two baryons, does it appear that the is an excited state of the (c) Verify that strangeness, charge, and baryon number are conserved in the decay. (d) Considering the preceding and the short lifetime, can the weak force be responsible? State why or why not.(a) What is the uncertainty in the energy released in the decay of a due to its short lifetime? (b) What traction of the decay energy is this, noting that the decay mode is (so that all the mass is destroyed)?(a) What is the uncertainty in the energy released in the decay of a due to its short lifetime? (b) Is the uncertainty in 1his energy greater than or lees than the uncertainty in the mass of the tau neutrino? Discuss the source of the uncertainty.(a) Verify from its quark composition that the particle could be an excited state of the proton. (b) There is a spread of about 100 MeV in the decay energy of the interpreted as uncertainty due to its short lifetime. What is its approximate lifetime? (c) Does its decay proceed via the strong or weak force?Accelerators such as the Triangle Universities Meson Facility (TRIUMF) in British Columbia produce secondary beams of pions by having an intense primary proton beam strike a target. Such “meson factories“ have been used for many years to study the interaction of pions with nuclei and, hence, the strong nuclear force. One reaction that occurs is where the is every shortlived particle. The graph in Figure 33.26 shows the probability of this reaction as a function of energy. The width of the bump is the uncertainty in energy due to the short lifetime at the (a) Find this lifetime. (b) Verify from the quark composition of the particles that this reaction annihilates and then recreates a d quark and a antiquark by writing the reaction and decay in terms of quarks. (c) Draw a Feynman diagram of the production and decay of the showing the individual quarks involved. Figure 33.26 This graph shows the probability of an interaction between a and a proton as a function of energy. The bump is interpreted as a very short lived particle called a The approximately 100MeV width of the bump is due to the short lifetime of theThe reaction (described in the preceding problem) takes place via the strong force. (a) What is the baryon number of the particle? (b) Draw a Feynman diagram of the reaction showing the individual quarks involved.One of the decay modes of the omega minus is (a) What is the change in strangeness? (b) Verify that baryon number and charge are conserved, while lepton numbers are unaffected. (c) Write the equation in terms of the constituent quarks, indicating that the weak force is responsible.Repeat the previous problem for the decay modeOne decay mode for the etazero meson is (a) Find the energy released. (b) What is the uncertainty in the energy due to the short lifetime? (c) Write the decay in terms at the constituent quarks. (d) Verify that baryon number, lepton numbers, and charge are conserved.One decay mode for the etazero meson is (a) Write the decay in terms at the quark constituents. (b) How much energy is released? (c) What is the ultimate release of energy, given the decay mode for the pi zero isIs the decay possible considering the appropriate conservation laws? State why or why not.Is the decay possible considering the appropriate conservation laws? State why or why not.(a) Is the decay possible considering the appropriate conservation laws? State why or why not. (b) Write the decay in terms of the quark constituents of the particles.(a) Is the decay possible considering the appropriate conservation laws? Stale why or why not. (b) Write the decay in terms of the quark constituents of the particles.The only combination of quark colors that produces a white baryon is RGB. Identify all the color combinations that can produce a white meson.(a) Three quarks form a baryon. How many combinations of the six known quarks are there if all combinations are possible? (b) This number is less than the number of known baryons. Explain why.(a) Show that the conjectured decay of the proton, violates conservation of baryon number and conservation of lepton number. (b) What is the analogous decay process for the antiproton?Verify the quantum numbers given for the + in Table 33.2 by adding the quantum numbers for its quark constituents as inferred from Table 33.4.Verify the quantum numbers given for the proton and neutron in Table 33.2 by adding the quantum numbers for their quark constituents as given in Table 33.4.(a) How much energy would be released if the proton did decay 1uria the conjectured reaction (b) Given that the decays to two (s and that the will find an electron to annihilate, what total energy is ultimately produced in proton decay? (c) Why is this energy greater than the proton's total mass (converted to energy)?(a) Find the charge, baryon number, strangeness, charm, and bottomness of the particle from its quark composition. (b) Do the same for the particle.There are particles called Dmesons. One of them is the D+ meson, which has a single positive charge and a baryon number of zero, also the value of its strangeness, topness, and bottomness. It has a charm of +1. What is its quark configuration?There are particles called bottom mesons or Bmesons. One of item is the B meson, which has a single negative charge; its baryon number is zero, as are its strangeness, charm, and topness. It has a bottomness of l. What is its quark configuration?(a) What particle has the quark composition u-u-d? (b) What should its decay made be?(a) Show than all combinations of three quarks produce integral changes. Thus baryons must have integral charge. (b) Show than all combinations at a quark and an antiquark produce only integral charges. Thus mesons must have integral change.Integrated Concepts The intensity of cosmic ray radiation decreases rapidly with increasing energy, but there are occasionally extremely energetic cosmic rays that create a shower of radiation from all the particles they create by striking a nucleus in the atmosphere as seen in the figure given below. Suppose a cosmic ray particle having an energy of converts its energy into particles with masses averaging (a) How many particles are created? (b) If the particles rain down an a 1.00km2 area, how many particles are there per square meter? Figure 33.27 An extremely energetic cosmic ray creates a shower of particles on earth. The energy of these rare cosmic rays can approach a joule (about and, after multiple collisions, huge numbers of panicles are created from this energy. Cosmic ray showers have been observed to extend over many square kilometers.Integrated Concepts Assuming conservation of momentum, what is the energy of each (ray produced in the decay of a neutral at rest pion, in the reaction +?Integrated Concepts What is the wavelength of a 50GeV electron, which is produced at SLAC? This provides an idea of the limit to the detail it can probe.Integrated Concepts Calculate the relativistic quantity for 1.00TeV protons produced at Fermilab. (b) If such a proton created a having the same speed, how long would its life be in the laboratory? (c) How far could it travel in this time?Integrated Concepts The primary decay mode for the negative pion is (a) What is the energy release in MeV in this decay? (b) Using conservation of momentum, how much energy does each of the decay products receive, given the is at rest when it decays? You may assume the muon antineutrino is massless and has momentum just like a photon.Integrated Concepts Plans for an accelerator that produces a secondary beam of Kmesons to scatter from nuclei, for the purpose of studying the strong force, call for them to have a kinetic energy of 500 MeV. (a) What would the relativistic quantity be for these particles? (b) How long would their average lifetime be in the laboratory? (c) How far could they travel in this time?Integrated Concepts Suppose you are designing a proton decay experiment and you can detect 50 percent of the proton decays in a tank of water. (a) How many kilograms of water would you need to see one decay per month, assuming a lifetime of 1031 y? (b) How many cubic meters of water is this? (c) If the actual lifetime is 1033 y, how long would you have to wait on an average to see a single proton decay?Integrated Concepts In supernovas, neutrinos are produced in huge amounts. They were detected from the 1987A supernova in the Magellanic Cloud, which is about 120,000 light years away from the Earth (relatively close to our Milky Way galaxy). If neutrinos have a mass, they cannot travel at the speed of light, but it their mass is small, they can get close. (a) Suppose a neutrino with a mass has a kinetic energy of 700 keV. Find the relativistic quantity for it (b) If the neutrino leaves the 1987A supernova at the same time as a photon and both travel to Earth, how much sooner does the photon arrive? This is not a large time difference, given that it is impossible to know which neutrino left with which photon and the peer ef?ciency of the neutrino detectors. Thus, the fact that neutrinos were observed within hours of the brightening of the supernova only places an upper limit on the neutrino’s mass. (Hint: You may need to use a series expansion to find if for the neutrino, since its (is so large.)Construct Your Own Problem Consider an ultrahighenergy cosmic ray entering the Earth’s atmosphere (some have energies approaching a joule). Construct a problem in which you calculate the energy of the particle based on the number of particles in an observed cosmic ray shower. Among the things to consider are the average mass of the shower particles, the average number per square meter, and the extent (number of square meters covered) of the shower. Express the energy in eV and joules.Construct Your Own Problem Consider a detector needed to observe the proposed, but extremely rare, decay of an electron. Construct a problem in which you calculate the amount of matter needed in the detector to be able to observe the decay, assuming that it has a signature that is clearly identi?able. Among the things to consider are the estimated half life (long for rare events), and the number of decays per unit time that you wish to observe, as well as the number of electrons in the detector substance.Explain why it only appears that we are at the center of expansion of the universe and why an observer in another galaxy would see the same relative motion of all but the closest galaxies away from her.If there is no observable edge to the universe, can we determine where its center of expansion is? Explain.If the universe is infinite, does it have a center? Discuss.Another known cause of red shift in light is the source being in a high gravitational field. Discuss how this can be eliminated as the source of galactic red shifts, given that the shifts are proportional to distance and not to the size of the galaxy.If some unknown cause of red shiftsuch as light becoming "?red" from traveling long distances through empty spaceis discovered, what effect would there be on cosmology?Olbers’s paradox poses an interesting question: If the universe is infinite, then any line of sight should eventually fall on a stars surface. Why then is the sky dark at night? Discuss the commonly accepted evolution of the universe as a solution to this paradox.If the cosmic microwave background radiation (CMBR) is the remnant of the Big Bang’s ?reball, we expect to see hot and cold regions in it. What are two causes of these wrinkles in the CMBR? Are the observed temperature variations greater or less than originally expected?The decay of one type of Kmeson is cited as evidence that nature favors matter over antimatter. Since mesons are composed of a quark and an antiquark, is it surprising that they would preferentially decay to one type over another? Is this an asymmetry in nature? Is the predominance of matter over antimatter an asymmetry?Distances to local galaxies are determined by measuring the brightness of stats, called Cepheid variables, that can be observed individually and that have absolute brightnesses at a standard distance that are well known. Explain how the measured brightness would vary with distance as compared with the absolute brightness.Distances to very remote galaxies are estimated based on their apparent type, which indicate the number of stars in the galaxy, and their measured brightness. Explain how the measured brightness would vary with distance. Would there be any correction necessary to compensate for the red shift of the galaxy (all distant galaxies have signi?cant ted shifts)? Discuss possible causes of uncertainties in these measurements.If the smallest meaningful time interval is greater than zero, will the lines in Figure 34.9 ever meet?Quantum gravity, if developed, would be an improvement on both general relativity and quantum mechanics, but more mathematically difficult. Under what circumstances would it be necessary to use quantum gravity? Similarly, under what circumstances could general relativity be used? When could special relativity, quantum mechanics, or classical physics be used?Does observed gravitational lensing correspond to a converging or diverging lens? Explain briefly.Suppose you measure the red shifts of all the images produced by gravitational lensing, such as in Figure 34.12. You find that the central image has a red shill less than the outer images, and those all have the same red shift. Discuss how this not only shows that the images are of the same object, but also implies than the red shift is not affected by taking different paths through space. Does it imply that cosmological red shifts are not caused by traveling through space (light getting tired, perhaps)?What are gravitational waves, and have they yet been observed either directly or indirectly?Is the event horizon of a black hole the actual physical surface of the object?Suppose black holes radiate their mass away and the lifetime of a black hole created by a supernova is about 1067 years. How does this lifetime compare with the accepted age of the universe? Is it surprising that we do not observe the predicted characteristic radiation?Discuss the possibility that star velocities at the edges of galaxies being greater than expected is due to unknown properties of gravity rather than to the existence of dark matter. Would this mean, for example, that gravity is greater or smaller than expected at large distances? Are there other tests that could he made of gravity at large distances, such as observing the motions of neighboring galaxies?How does relativistic time dilation prohibit neutrino oscillations it they are massless?If neutrino oscillations do occur, will they violate conservation of the various lepton family numbers and Will neutrino oscillations violate conservation of the total number of leptons?Lacking direct evidence of WIMPs as dark matter, why must we eliminate all other possible explanations based on the known forms of mailer before we invoke their existence?Must a complex system be adaptive to be of interest in the field of complexity? Give an example to support your answer.State a necessary condition for a System to be chaotic.What is critical temperature Tc? Do all materials have a critical temperature? Explain why or why not.Explain how good thermal contact with liquid nitrogen can keep object at a temperature of 77 K (liquid nitrogen's boiling point at atmospheric pressure).Not only is liquid nitrogen a cheaper coolant than liquid helium, its boiling point is higher (77 K vs. 4.2 K). How does higher temperature help lower the cost of cooling a material? Explain in terms of the rate of heat transfer being related to the temperature difference between the sample and its surroundings.For experimental evidence particularly of previously unobserved phenomena, to be taken seriously it must be reproducible or of sufficiently high quality that a single observation is meaningful. Supernova 1987A is not reproducible. How do we know observations of it were valid? The fifth force is not broadly accepted. Is this due to lack of reproducibility or poorquality experiments (or both)? Discuss why forefront experiments are more subject to observational problems than those involving established phenomena.Discuss whether you think there are limits to what humans can understand about the laws of physics. Support your arguments.Find the approximate mass of the luminous matter in the Milky Way galaxy, given it has approximately 1011 stars at average mass 1.5 times than of our Sun.Find the approximate mass of the dark and luminous matter in the Milky Way galaxy. Assume the luminous matter is due to approximately 1011 stars of average mass 1.5 times that of our Sun. and take the dark matter to be 10 times as massive as the luminous matter.(a) Estimate the mass of the luminous matter in the known universe, given there are 1011 galaxies, each containing 1011 stars of average mass 1.5 times that of our Sun. (b) How many protons (the most abundant nuclide) are there in this mates? (c) Estimate the total number of particles in the observable universe by multiplying the answer to (b) by two, since there is an electron for each proton, and then by 109, since there are far more particles (such as photons and neutrinos) in space than in luminous matter.If a galaxy is 500 Mly away from us, how fast do we expect it to be moving and in what direction?On average, how far away are galaxies mat are moving away from us at 2.0% of the speed of light?Our solar system orbits the center of the Milky Way galaxy. Assuming a circular orbit 30,000 ly in radius and an orbital speed of 250 km/s, how many years does it take for one revolution? Note than this is approximate, assuming constant speed and circular orbit, but it is representative of the time for our system and local stars to make one revolution around the galaxy.(a) What is the approximate speed relative to us of a galaxy near the edge of the known universe, some 10 Gly away? (b) What traction of the speed of light is this? Note that we have observed galaxies moving away from us at greater than 0.9c.(a) Calculate The approximate age of the universe from the average value of the Hubble constant, To do this, calculate the time it would take to travel 1 Mly at a constant expansion rate of 20 km/s. (b) If deceleration is taken into account, would the actual age of the universe be greater or less than that found here? Explain.Assuming a circular orbit for the Sun about the center of the Milky Way galaxy, calculate its orbital Speed using the following information: The mass of the galaxy is equivalent to a single mass times that at the Sun (or located 30,000 ly away.(a) What is the approximate force of gravity on a 70kg person due to the Andromeda galaxy, assuming its total mass is 1013 than of our Sun and acts like a single mass 2 Mly away? (b) What is the ratio of this force to the person's weight? Note that Andromeda is the closest large galaxy.Andromeda galaxy is the closest large galaxy and is visible to the naked eye. Estimate its brightness relative to the Sun, assuming it has luminosity l012 times that of the Sun and lies 2 Mly away.(a) A particle and its antiparticle are at rest relative to an observer and annihilate (completely destroying both masses), creating two (rays of equal energy. What is the characteristic (ray energy you would look for if searching for evidence of protonantiproton annihilation? (The fact that such radiation is rarely observed is evidence that here is very little antimatter in the universe.) (b) How does this compare with the 0.511MeV energy associated with electronpositron annihilation?The average particle energy needed to observe uni?cation of forces is estimated to be 1019 GeV. (a) What is the rest mass in kilograms of a particle that has a rest mass of (b) How many times the mass of a hydrogen atom is this?The peak intensity of the CMBR occurs at a wavelength of 1.1 mm. (a) What is the energy in eV at a 1.1mm photon? (b) There are approximately 109 photons for each massive particle in deep space. Calculate the energy of 109 such photons. (c) If the average massive particle in space has a mass half that of a proton, what energy would be created by convening its mass to enemy? (d) Does this imply that space is “matter dominated”? Explain briefly.(a) What Hubble constant corresponds to an approximate age of the universe of 1010 y? To get an approximate value, assume the expansion rate is constant and calculate the speed at which two galaxies must move apart to be separated by 1 Mly (present average galactic separation) in a time of 1010 y. (b) Similarly, what Hubble constant corresponding to a universe approximately old?Show that the velocity of a star orbiting its galaxy in a circular orbit is inversely proportional to the square root of its orbital radius, assuming the mass of the stars inside its orbit acts like a single mass at the center of the galaxy. You may use an equation from a previous chapter to support your conclusion, but you must justify its use and define all terms used.The core of a star collapses during a supernova, forming a neutron star. Angular momentum of the core is conserved, and so the neutron star spins rapidly. If the initial core radius is and it collapses to 10.0 km, find the neutron star’s angular velocity in revolutions per second, given the Core’s angular velocity was originally 1 revolution per 30.0 days.Using data from the previous problem, find the increase in rotational kinetic energy, given the core’s mass is 1.3 times that of our Sun. Where does this increase in kinetic energy come from?Distances to the nearest stars (up to 500 by away) can be measured by a technique called parallax, as shown in Figure 34.26. What are the angles 1 and 2 relative to the plane of the Earth’s orbit for a star 4.0 by directly above the Sun?(a) Use the Heisenberg uncertainty principle to calculate the uncertainty in energy for a corresponding time interval of (b) Compare this energy with the unificationofforces energy and discuss why they are similar.Construct Your Own Problem Consider a star moving in a circular orbit at the edge at a galaxy. Construct a problem in which you calculate the mass of that galaxy in kg and in multiples of the solar mass based on the velocity of the star and its distance from the center of the galaxy. Figure 34.26 Distances to nearby stars are measured using triangulation, also called the parallax method. The angle of line of sight to the star is measured at intervals six momma apart, and the distance is calculated by using the known diameter of the Earth's orbit. This can be done for stars up to about 500 ly away.What is the Schwarzschild radius of a blank hole that has a mass eight times that of our Sun? Note that stars must be more massive than the Sun to form black holes as a result of a supernova.Black holes with masses smaller than muse formed in supernovas may have been created in the Big Bang. Calculate the radius of one that has a mass equal to the Earth’s.Supermassive black holes are thought to exist at the center of many galaxies. (a) What is the radius of such an object if it has a mass of 109 Suns? (b) What is this radius in light years?Construct Your Own Problem Consider a supermassive black hole near the center of a galaxy. Calculate the radius of such an object based on its mass. You must consider how much mass is reasonable for these large objects, and which is now nearly directly observed. (Information on black holes posted on the Web by NASA and other agencies is reliable, for example.)The characteristic length of entities in Superstring theory is approximately (a) Find the energy in GeV of a photon of this wavelength. (b) Compare this with the average particle energy of 1019 GeV needed for uni?cation of forces.If the dark matter in the Milky Way were composed entirely of MACHOs (evidence shows it is not), approximately how many would there have to be? Assume the average mass of a MACHO is 1/1000 that of the Sun, and that dark matter has a mass 10 times that of the luminous Milky Way galaxy with its 1011 stars of average mass 1.5 times the Sun’s mass.The critical mass density needed to just halt the expansion of the universe is approximately (a) Convert this to (b) Find the number of neutrinos per cubic meter needed to close the universe if their average mass is and they have negligible kinetic energies.Assume the average density of the universe is 0.1 of the critical density needed for closure. What is the average number of protons per cubic meter, assuming the universe is composed mostly of hydrogen?To get an idea of how empty deep spam is on the average, perform the following calculations: (a) Find the volume our Sun would occupy if it had an average density equal to the critical density of thought necessary to halt the expansion of the universe. (b) Find the radius of a sphere of this volume in light years. (c) What would this radius be if the density were that of luminous matter, which is approximately 5% that of the critical density? (d) Compare the radius found in part (c) with me 4-ly average separation of stars in the aims of the Milky Way.A section of superconducting wire carries a current of 100 A and requires 1.00 L of liquid nitrogen per hour to keep it below its critical temperature. For it to be economically advantageous to use a superconducting wire, the cost at cooling the wire must be less than the cost of energy lost to heat in the wire. Assume that the cost of liquid nitrogen is $0.30 per liter, and that electric energy costs What is the resistance of a normal wire that costs as much in wasted electric energy as the cost of liquid nitrogen for the superconductor?