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MasteringPhysics: Print View with Answers 1 of 20 https://session.masteringphysics.com/myct/assignmentPrintView?assign... Signed in as Weida Wu , Instructor Rutgers Analytical Physics 750:228, Spring 2016 My Courses Help Sign Out ( RUPHY228S16 ) Course Settings University Physics with Modern Physics, 14e Young/Freedman Instructor Resources Course Home eText Study Area Assignments Roster Gradebook Item Library 13. Nuclear Reactions (43.3-8) and Particle Physics (44) Overview Summary View Diagnostics View [ Edit ] Print View with Answers 13. Nuclear Reactions (43.3-8) and Particle Physics (44) Due: 11:59pm on Sunday, May 1, 2016 To understand how points are awarded, read the Grading Policy for this assignment. Exercise 43.14 Description: ^238 U decays spontaneously by alpha emission to ^234 (Th). The atomic masses are 238.050788 u for ^238 U and 234.043601 u for ^234 (Th). (a) Calculate the total energy released by this process. (b) Calculate the recoil velocity of the ^234... decays spontaneously by emission to . The atomic masses are 238.050788 for and 234.043601 for . Part A Calculate the total energy released by this process. Express your answer using four significant figures. ANSWER: = 4.270 Part B Calculate the recoil velocity of the nucleus. Express your answer using four significant figures. ANSWER: = 2.432×105 Exercise 43.16 Description: (a) What particle is emitted in the following radioactive decay? ^27_14(Si) rightarrow^27_13(Al). (b) What particle is emitted in the following radioactive decay? ^238_92U rightarrow^234_90(Th). (c) What particle is emitted in the following... Part A What particle is emitted in the following radioactive decay? . ANSWER: particle electron positron Part B What particle is emitted in the following radioactive decay? . ANSWER: 5/6/2016 4:35 PM MasteringPhysics: Print View with Answers 2 of 20 https://session.masteringphysics.com/myct/assignmentPrintView?assign... particle electron positron Part C What particle is emitted in the following radioactive decay? . ANSWER: particle electron positron Alternative Exercise 43.78 Description: Hydrogen atoms are placed in an external B-T magnetic field. (a) The protons can make transitions between states where the nuclear spin component is parallel and antiparallel to the field by absorbing or emitting a photon. Which state has lower... Hydrogen atoms are placed in an external 1.55- magnetic field. Part A The protons can make transitions between states where the nuclear spin component is parallel and antiparallel to the field by absorbing or emitting a photon. Which state has lower energy: the state with the nuclear spin component parallel or antiparallel to the field? ANSWER: Parallel Antiparallel Part B What is the frequency of the photon in part A? ANSWER: = = 6.59×107 Part C What is the wavelength of the photon in part A? ANSWER: = = 4.55 Part D In which region of the electromagnetic spectrum does it lie? ANSWER: radio wave microwave infrared visible light ultraviolet X-Rays Gamma Rays 5/6/2016 4:35 PM MasteringPhysics: Print View with Answers 3 of 20 https://session.masteringphysics.com/myct/assignmentPrintView?assign... Part E The electrons can make transitions between states where the electron spin component is parallel and antiparallel to the field by absorbing or emitting a photon. Which state has lower energy: the state with the electron spin component parallel or antiparallel to the field? ANSWER: Parallel Antiparallel Part F What is the frequency of the photon in part D? ANSWER: = 4.34×1010 = Part G What is the wavelength of the photon in part D? ANSWER: = = 6.91×10−3 Part H In which region of the electromagnetic spectrum does it lie? ANSWER: radio wavw microwave infrared visible light ultraviolet X-Rays Gamma Rays Alternative Exercise 43.80 Description: (a) What is the maximum wavelength of a gamma ray that could break a deuteron into a proton and a neutron? (This process is called photodisintegration.)... Part A What is the maximum wavelength of a ray that could break a deuteron into a proton and a neutron? (This process is called photodisintegration.) Express your answer using four significant figures. ANSWER: = 0.5575 Fusion and the Sun Description: The energy from a single fusion reaction is found and then compared to the power output of the sun . The sun, like all stars, releases energy through nuclear fusion. In this problem, you will find the total number of fusion reaction events that occur inside the sun every second. You will be considering the proton-proton chain, in which four hydrogen nuclei are converted into a helium nucleus and two positrons. The net reaction for the proton-proton chain is . To find the energy released by this reaction, you will need the following mass data: 5/6/2016 4:35 PM MasteringPhysics: Print View with Answers 4 of 20 https://session.masteringphysics.com/myct/assignmentPrintView?assign... mass of and mass of . Using the masses of the neutral atoms in your calculation accounts for the energy released by the annihilation of the positrons with electrons, so you can work this problem without reference to the positrons or their rest mass. Part A What is the total energy released in a single fusion reaction event for the equation given in the problem introduction? Use . Express your answer in joules to two significant figures. Hint 1. How to approach the question Find the mass defect of the reaction ( ); then use . ANSWER: = 4.30×10−12 Part B The power radiated by the sun is about . Using this number, find the number of proton-proton chain fusion reactions that must go on inside the sun in one second to release enough energy to balance the energy radiated away. (If this condition isn't met, the sun would cool off rapidly.) Express your answer to two significant figures. ANSWER: reactions in one second = 9.30×1037 Also accepted: 9.24×1037 The proton-proton chain is not the only sequence of fusion reactions that occurs inside of the sun, but the others account for such a small amount of the sun's total power output that we can ignore them in the rough calculations that we are doing. Part C What mass of hydrogen is converted into helium by the fusion reactions in one second? Use for the mass of one hydrogen nucleus. Express your answer in kilograms to two significant figures. ANSWER: hydrogen used up in one second = 6.20×1011 Part D The heat of combustion of hydrogen (the energy released by burning hydrogen with oxygen) is . What mass of hydrogen would have to be burned in the sun in one second to release the same amount of energy (i.e., generate the same power) as is released by fusion? Express your answer in kilograms to two significant figures. Hint 1. Relating mass of burned hydrogen and power Recall that one watt is equal to one joule per second. You are asked for the mass that must be burned in one second to generate the same energy as the sun generates in one second. Thus, the question is really asking what mass of hydrogen must be burned to generate . The heat of combustion gives the number of joules generated by burning one kilogram of hydrogen. Use this to find the number of kilograms of hydrogen that must be burned to generate . ANSWER: mass of hydrogen = 2.80×1018 5/6/2016 4:35 PM MasteringPhysics: Print View with Answers 5 of 20 https://session.masteringphysics.com/myct/assignmentPrintView?assign... At this rate, the sun would use up all of its hydrogen in only 17,000 years, instead of the roughly 5 billion years that solar physicists estimate for the sun's current fuel supply. (Of course, this is just an abstraction since there is no supply of oxygen available for such "burning" to take place.) Nineteenth-century physicists trying to determine the age of the sun based their calculations on how much energy the sun radiated. They immediately realized that chemical reactions could not produce nearly enough energy to account for the sun being more than a few thousand years old, an age directly contradicted by historical records. The largest energy source that they could imagine was the gravitational energy of all the matter that formed the sun. Even this source was far too weak: Calculations based on gravitational energy only allowed the sun to be around 30 million years old, though it is, in fact, over 4.5 billion years old! No nineteenthcentury physicist could have envisioned the incredible amounts of energy released by nuclear reactions. Antimatter Description: Conceptual questions about the nature of antimatter, as well as creation and annihilation of pairs, followed by simple calculations of energy and momentum in creation/annihilation processes. The first antiparticle, the positron or antielectron, was discovered in 1932. It had been predicted by Paul Dirac in 1928, though the nature of the prediction was not fully understood until the experimental discovery. Today, it is well accepted that all fundamental particles have antiparticles. Part A Which of the following are different for a particle and its antiparticle? ANSWER: charge only mass only spin only charge and mass charge and spin mass and spin charge and mass and spin Part B Which conservation law is violated by particle-antiparticle annihilation? ANSWER: conservation of energy conservation of momentum conservation of charge conservation of lepton number none of these Part C Suppose that an electron and a positron collide head-on. Both have kinetic energy of 4.00 and rest energy of 0.511 . They produce two photons, which by conservation of momentum must have equal energy and move in opposite directions. What is the energy of one of these photons? Express your answer in to three significant figures. ANSWER: = = 4.51 Part D Two protons, with equal kinetic energy, collide head-on. What is the minimum kinetic energy energy of a pion is . Express your answer in of one of these protons necessary to make a pion-antipion pair? The rest to three significant figures Hint 1. Connecting kinetic energy to mass In a sufficiently violent particle collision, kinetic energy may be converted into the rest energy of new particles. All that is necessary is for the amount of kinetic energy available to meet or exceed the rest energy of the pair that you wish to produce. Hint 2. Available kinetic energy Because the two protons collide head-on with equal kinetic energy, the net momentum before the collision is zero. Therefore, all of the kinetic energy could be 5/6/2016 4:35 PM MasteringPhysics: Print View with Answers 6 of 20 https://session.masteringphysics.com/myct/assignmentPrintView?assign... turned into rest energy of a particle-antiparticle pair. ANSWER: = 140 The Cyclotron Description: Several qualitative and quantitative questions: radius and frequency of revolution, energy of the particles. Focuses on classical model but last follow-up statement makes reference to relativistic model. Learning Goal: To learn the basic physics and applications of cyclotrons. Particle accelerators are used to create well-controlled beams of high-energy particles. Such beams have many uses, both in research and industry. One common type of accelerator is the cyclotron, as shown in the figure. In a cyclotron, a magnetic field confines charged particles to circular paths while an oscillating electric field accelerates them. It is useful to understand the details of this process. Consider a cyclotron in which a beam of particles of positive charge restricted by the magnetic field and mass is moving along a circular path (which is perpendicular to the velocity of the particles). Part A Before entering the cyclotron, the particles are accelerated by a potential difference Express your answer in terms of , . Find the speed with which the particles enter the cyclotron. , and . ANSWER: = Part B Find the radius of the circular path followed by the particles. The magnitude of the magnetic field is Express your answer in terms of , , . , and . Hint 1. Find the force Find the magnitude of the force acting on the particles. Express your answer in terms of , , , and . You may or may not use all these variables. ANSWER: = Hint 2. Find the acceleration Find the magnitude of the acceleration Express your answer in terms of of the particles. and the radius of revolution . ANSWER: = Hint 3. Solving for 5/6/2016 4:35 PM MasteringPhysics: Print View with Answers 7 of 20 https://session.masteringphysics.com/myct/assignmentPrintView?assign... Use Newton's second law to construct an equation to be solved for . ANSWER: = Part C Find the period of revolution for the particles. Express your answer in terms of Hint 1. Relationship between , , and . and The period is the amount of time it takes a particle to make one complete orbit. Since the speed of the particle is constant, the period will be equal to the distance the particle travels in one orbit divided by the particle's speed: . ANSWER: = Note that the period does not depend on the particle's speed (nor, therefore, on its kinetic energy). Part D Find the angular frequency of the particles. Express your answer in terms of , Hint 1. Relationship between , and . and Recall that the frequency of revolution is equal to ; it represents the number of revolutions a particle makes per second. The angular frequency ; it is the number of radians the particle traverses per second. is equal to ANSWER: = Part E Your goal is to accelerate the particles to kinetic energy Express your answer in terms of Hint 1. Find , , , and . What minimum radius of the cyclotron is required? . in terms of Find an expression for the speed Express your answer in terms of of a particle in terms of its kinetic energy and . . ANSWER: = You can now substitute this value for into your expression for from Part B. ANSWER: = Part F 5/6/2016 4:35 PM MasteringPhysics: Print View with Answers 8 of 20 https://session.masteringphysics.com/myct/assignmentPrintView?assign... If you can build a cyclotron with twice the radius, by what factor would the allowed maximum particle energy increase? Assume that the magnetic field remains the same. Hint 1. Find in terms of Using your result from Part E, solve for Express your answer in terms of , in terms of , , and . . ANSWER: = In other words, the kinetic energy is proportional to . ANSWER: 2 4 8 16 Part G If you can build a cyclotron with twice the radius and with the magnetic field twice as strong, by what factor would the allowed maximum particle energy increase? Hint 1. Find in terms of and Using your result from Part E, solve for Express your answer in terms of , in terms of , , and and . . ANSWER: = It's now clear that the kinetic energy is proportional to . ANSWER: 2 4 8 16 One limitation of the cyclotron has to do with the failure of the laws of classical mechanics to accurately predict the behavior of high-energy particles. When their speeds become comparable to the speed of light , the angular frequency is no longer what you determined in Part D. Using special relativity, one can show that the angular frequency is actually given by the formula . As you can see, the frequency drops as the energy (and speed) increases; the particles' motion falls out of phase with the pulsating voltage, restricting the cyclotron's ability to accelerate the particles further Designing a New Particle Accelerator Description: Find the available energy for two related particle collisions. A new particle accelerator facility is being built. The designers are considering two designs, one using stationary targets and the other using collisions of beams with the same energy. Part A Consider a beam of protons with energy 204.0 . If these protons collide with stationary protons, what is the available energy in a collision? Express your answer in billions of electron volts to three significant figures. 5/6/2016 4:35 PM MasteringPhysics: Print View with Answers 9 of 20 https://session.masteringphysics.com/myct/assignmentPrintView?assign... Hint 1. Formula for available energy Recall that the formula for available energy target particle, and is , where is the total energy of the moving particle. For cases where . is the mass of the moving particle, is the mass of the , such as this problem, the formula reduces to ANSWER: = 19.6 = Part B Now, consider two beams of protons, moving in opposite directions, each with energy 102 . What is the available energy when these beams collide? Express your answer in billions of electron volts to three significant figures. Hint 1. Considering the momentum In all particle collisions, momentum must be conserved. This is the reason that the available energy in collisions with a stationary target is less than the total energy of the collision: some of the energy must go into kinetic energy for the product to conserve momentum. If two beams of identical protons collide head-on, what is the total momentum of a pair of protons just before the collision? What is the minimum amount of energy that must go into kinetic energy to have the same total momentum after the collision? ANSWER: = = 204 Part C If the accelerator is intended to be a source of W bosons (mass of W boson = 80.4 ), which design should be chosen? ANSWER: Only the design from Part A can be chosen, because the W bosons will have low energy and will thus be easier to work with. Only the design from Part B can be chosen, because it is the only one with enough energy to make W bosons. Either design can be chosen, because the energy of the W bosons is not a concern. Neither design can be chosen, because neither has sufficient energy to make W bosons. Combining Quarks Description: In this problem the student determines the quark content of particles with specific charge, baryon number, and strangeness. Assume that each particle contains only combinations of the quarks , , and and the antiquarks , , and . Part A Deduce the quark content of a particle with charge +e, baryon number 0, and strangeness +1. 5/6/2016 4:35 PM MasteringPhysics: Print View with Answers 10 of 20 https://session.masteringphysics.com/myct/assignmentPrintView?assign... Hint 1. Charges of quarks The electric charges of the three quarks , , and are, respectively, , where is the magnitude of the electron charge. Note that the antiquarks will have the same charge magnitude, just with opposite sign to its corresponding quark. Hint 2. Baryons versus mesons Recall that hadrons are a general classification of particles that consist of quarks. They are divided into two subclasses: baryons, which consist of three quarks and have baryon number (as well as antibaryons with three antiquarks and baryon number ), and mesons, which consist of a quark-antiquark pair and have baryon number . Since in this problem, you are looking for a quark-antiquark pair. Hint 3. Definition of strangeness Strangeness is a quantum number that is used to track the number of strange particles in a hadron (both mesons and baryons). If a particle has a strange quark ( ), then it has strangeness . If the particle has an antistrange quark ( ), then it has strangeness . These numbers are additive; two strange quarks in combination means a strangeness of . ANSWER: Part B Deduce the quark content of a particle with charge +e, baryon number 1, and strangeness +1. Hint 1. Charges of quarks The electric charges of the three quarks , , and are, respectively, , where is the magnitude of the electron charge. Note that the antiquarks will have the same charge magnitude, just with opposite sign to its corresponding quark. Hint 2. Baryons versus mesons Recall that hadrons are a general classification of particles that consist of quarks. They are divided into two subclasses: baryons, which consist of three quarks and have baryon number (as well as antibaryons with three antiquarks and baryon number ), and mesons, which consist of a quark-antiquark pair and have baryon number . Hint 3. Definition of strangeness Strangeness is a quantum number that is used to track the number of strange particles in a hadron (both mesons and baryons). If a particle has a strange quark ( ), then it has strangeness . If the particle has an antistrange quark ( ), then it has strangeness . These numbers are additive; two strange quarks in combination means a strangeness of . ANSWER: Part C Deduce the quark content of a particle with charge 0, baryon number +1, and strangeness 2. Hint 1. Charges of quarks The electric charges of the three quarks , , and are, respectively, 5/6/2016 4:35 PM MasteringPhysics: Print View with Answers 11 of 20 https://session.masteringphysics.com/myct/assignmentPrintView?assign... , where is the magnitude of the electron charge. Note that the antiquarks will have the same charge magnitude, just with opposite sign to its corresponding quark. Hint 2. Baryons versus mesons Recall that hadrons are a general classification of particles that consist of quarks. They are divided into two subclasses: baryons, which consist of three quarks and have baryon number (as well as antibaryons with three antiquarks and baryon number ), and mesons, which consist of a quark-antiquark pair and have baryon number . Hint 3. Definition of strangeness Strangeness is a quantum number that is used to track the number of strange particles in a hadron (both mesons and baryons). If a particle has a strange quark ( ), then it has strangeness . If the particle has an antistrange quark ( ), then it has strangeness . These numbers are additive; two strange quarks in combination means a strangeness of . ANSWER: Exercise 43.44 Description: The United States uses 1.4*10^19 J of electrical energy per year. Assume, that all this energy came from the fission of ^235U, which releases 200 MeV per fission event. Assume that all fission energy is converted into electrical energy. (a) How ... The United States uses 1.4 10 of electrical energy per year. Assume, that all this energy came from the fission of Assume that all fission energy is converted into electrical energy. , which releases 200 per fission event. Part A How many kilograms of would be used per year? Express your answer to two significant figures and include the appropriate units. ANSWER: 5 = 1.7×10 Also accepted: 1.71×105 , 1.7×105 Part B How many kilograms of uranium would have to be mined per year to provide that much ? (Recall that only 0.70 of naturally occurring uranium is .) Express your answer to two significant figures and include the appropriate units. ANSWER: 7 = 2.4×10 Also accepted: 2.4×107 , 2.44×107 , 2.43×107 , 2.4×107 , 2.4×107 A Decay Chain Description: Find the daughter nucleus of, energy released by, and number of beta and alpha decays involved in the Th-232 decay chain. When the daughter nucleus produced in a radioactive decay is itself unstable, it will eventually decay and form its own daughter nucleus. If the newly formed daughter nucleus is also unstable, another decay will occur, and the process will continue until a nonradioactive nucleus is formed. Such a series of radioactive decays is called a decay chain. A good example of a decay chain is provided by , a naturally occurring isotope of thorium. Part A The first step in the decay chain of is an alpha decay. What is the daughter nucleus formed by this first decay? Hint 1. Alpha decay 5/6/2016 4:35 PM MasteringPhysics: Print View with Answers 12 of 20 https://session.masteringphysics.com/myct/assignmentPrintView?assign... In alpha-particle decay, a helium nucleus (consisting of two protons and two neutrons) is emitted from the parent atom, leaving it with four fewer nucleons and an atomic number reduced by two. Hint 2. Find the numbers of protons and neutrons in the daughter nucleus Recall that in radioactive decays the atomic number and mass number are conserved. How many protons and neutrons are there in the daughter nucleus when undergoes an alpha decay? ANSWER: 232 neutrons and 88 protons 88 neutrons and 232 protons 88 neutrons and 140 protons 140 neutrons and 88 protons ANSWER: Part B What is the energy 228.0301069 . released in the first step of the thorium-232 decay chain? The atomic mass of is 232.038054 and the atomic mass of is Express your answer numerically in megaelectron volts. Hint 1. How to approach the problem The energy released in a decay depends on the difference in mass, , of the system before and after the decay. It can be calculated using the relation . You need to take into account the mass of the particle emitted in the decay when calculating the mass of the system after the decay. Also, note that the number of electrons in the parent nucleus is the same as the number of electrons in the daughter nucleus plus the number of electrons in the alpha particle, so the electrons do not contribute to the total mass difference. Hint 2. Find the mass difference What is the difference in mass, , of the system before and after the alpha decay? Express your answer numerically in atomic mass units to four significant digits. Hint 1. Atomic mass of an alpha particle The atomic mass of an alpha particle is 4.002603 . ANSWER: = 0.005343 Now use the relation and remember to convert atomic mass units to electron volts. ANSWER: = 4.98 Part C then decays through a series of beta-minus decays; eventually, another isotope of thorium, chain process? , is formed. How many beta-minus decays will occur during this 5/6/2016 4:35 PM MasteringPhysics: Print View with Answers 13 of 20 https://session.masteringphysics.com/myct/assignmentPrintView?assign... Hint 1. Beta decay In a beta-minus decay, an electron (as well as an antineutrino with negligible mass) is emitted as a neutron is converted into a proton. Such a decay increases the atomic number by one without changing the number of nucleons. ANSWER: 1 2 4 6 Part D then decays by emitting alpha particles until is formed. How many alpha decays will occur during this chain process? Hint 1. Alpha decay In alpha-particle decay, a helium nucleus (consisting of two protons and two neutrons) is emitted from the parent atom, leaving it with four fewer nucleons and an atomic number reduced by two. ANSWER: 2 4 6 8 The chain continues with two more intermediate states until the stable isotope of lead is formed, after a total of 10 decays. ± Half-Life and Radioactive Dating Description: ± Includes Math Remediation. The equations for decay and half-life are derived, and then a simple problem in carbon-14 dating is solved. Learning Goal: To understand decay in terms of half-life and to solve radioactive dating problems. Particles in a nucleus are bound by the strong force. A reasonable model of this binding would be a barrier potential of finite energy. Quantum mechanics allows a small, nonzero probability for a particle to "tunnel" through a potential barrier. Working with this rough model, we can say that, for a given unstable nucleus, there is a constant probability of some particle, say an alpha particle, tunneling through the barrier and being emitted as radiation. Since this probability is constant, depending only on the particular nuclide involved, you would expect the number of decays per second to be proportional to the number of nuclei present. Since the number of decays is the same as the amount by which the total number of nuclei (of the particular type being considered) is reduced, you can construct the relationship , where is the number of nuclei at a time . The constant of proportionality is called the decay constant. Part A If , where is some constant, what is Express your answer in terms of ? , , and . ANSWER: = Notice that this expression is equal to . Thus, is the general solution to the differential equation for radioactive decay. Part B Given that at time there is a quantity of nuclei present Express your answer in terms of (in other words, ), find the value of the constant in the equation . and . Hint 1. Find 5/6/2016 4:35 PM MasteringPhysics: Print View with Answers 14 of 20 Since https://session.masteringphysics.com/myct/assignmentPrintView?assign... , simply plug zero into your equation Express your answer in terms of to find . and . ANSWER: = ANSWER: = Part C Combining your answers from Parts A and B gives the equation Express your answer in terms of . Find the time at which half of the original number of nuclei will remain. and . Hint 1. What values to use Which of the following correctly pairs the value of and the value of that should be entered into to find the value of ? ANSWER: 0 and and and and and ANSWER: = Part D How many nuclei are left after a time Express your answer in terms of ? and . ANSWER: = This is half the number of nuclei that were present at time , which was itself half the number present at time zero. The number is called the half-life of the nucleus. Frequently, the half-life is given instead of the decay constant when discussing the decay of radioactive nuclei. If you measure the number of nuclei at any time and then wait one half-life, of the nuclei will remain. If you wait two half-lives then will remain. If you wait three half-lives, will remain, and so on. The decay of radioactive nuclei can be used to measure the age of artifacts, fossils, and rocks. Dating an organic artifact entails looking at its carbon content. Carbon exists in three isotopic forms: , , and . Both and are stable whereas is radioactive. To find the age of an organic artifact, first, you measure how much is found within the artifact. Then, you estimate how much would have been in it when it was first made. You then plug these two values into the decay equation to find how old the artifact is. The quantity of originally in the artifact may be estimated fairly accurately because the percent of atmospheric carbon in the form of the isotope stays relatively constant with time. Since plants constantly take in new carbon from atmospheric carbon dioxide, the percent of in a plant should be the same as the percent in the atmosphere, until the plant dies and stops taking in new carbon. Therefore, you can use this percent and the present quantity of total carbon in the artifact to find how much was in it when it died. The half-life of is 5730 years. Part E 5/6/2016 4:35 PM MasteringPhysics: Print View with Answers 15 of 20 https://session.masteringphysics.com/myct/assignmentPrintView?assign... If a sample shows only one-fourth of its estimated original quantity of need to plug into it at all for this problem.) , how old is it? Think about half-lives; don't try to just plug into the decay equation. (You shouldn't Express your answer in years to three significant figures. Hint 1. Find the number of half-lives If the quantity is 1/4 of the original, how many half-lives must have passed? Express your answer as an integer. ANSWER: 2 half-lives Since you know that a half-life for is 5730 years, you can use the number of half-lives to find the total age of the sample. ANSWER: age = 1.15×104 years Part F The previous part could be done without using the decay equation, because the ratio of original to present so simple. To solve more general carbon dating problems, you must first find the value of the decay constant for Using the given half-life, 5730 years, find the value of the decay constant for . was an integer power of 1/2. Most problems are not , so that you can easily use the decay equation. Express your answer in inverse years to three significant figures. Hint 1. Relating and Recall that in Part C you found the relation . ANSWER: = 1.210×10−4 Part G Suppose that an Egyptian farmer claims to have discovered a linen burial cloth used during Egypt's Middle Kingdom some 4000 years ago. Careful analysis shows that the cloth contains 80% of the that it is estimated to have originally contained. How old is the cloth? Express your answer in years to two significant figures. ANSWER: age = 1800 years Although the cloth does seem to be rather old, it isn't close to 4000 years old. Radioactive dating is an important technique used by archaeologists to find the age of newly discovered items and to determine the authenticity of supposed artifacts. Exercise 43.35 Description: Food is often irradiated with either x rays or electron beams to help prevent spoilage. A low dose of 5-75 kilorads (krad) helps to reduce and kill inactive parasites, a medium dose of 100-400 krad kills microorganisms and pathogens such as... Food is often irradiated with either x rays or electron beams to help prevent spoilage. A low dose of 5-75 kilorads ( dose of 100-400 kills microorganisms and pathogens such as salmonella, and a high dose of 2300-5700 refrigeration. ) helps to reduce and kill inactive parasites, a medium sterilizes food so that it can be stored without Part A A dose of 175 kills spoilage microorganisms in fish. If x rays are used, what would be the dose in ? ANSWER: = = 1750 5/6/2016 4:35 PM MasteringPhysics: Print View with Answers 16 of 20 https://session.masteringphysics.com/myct/assignmentPrintView?assign... Part B What would be the dose in ? ANSWER: = 1750 = Part C What would be the dose in ? ANSWER: = = 1.75×105 Part D How much energy would a 160- portion of fish absorb? ANSWER: = = 280 Part E If electrons of RBE 1.50 are used instead of x rays, what would be the dose in ? ANSWER: = = 1750 Part F What would be the dose in ? ANSWER: = = 2630 Part G What would be the dose in ? ANSWER: = = 2.63×105 Part H How much energy would a 160- portion of fish absorb? ANSWER: = = 280 Alternative Exercise 43.81 Description: The isotope ^226(Ra) undergoes alpha decay with a half-life of 1620 years. (a) What is the activity of 1.00 g of ^226(Ra) in Bq? (b) What is the activity of 1.00 g of ^226(Ra) in Ci? The isotope undergoes decay with a half-life of 1620 . 5/6/2016 4:35 PM MasteringPhysics: Print View with Answers 17 of 20 https://session.masteringphysics.com/myct/assignmentPrintView?assign... Part A What is the activity of 1.00 of in ? of in ? ANSWER: = 3.61×1010 Part B What is the activity of 1.00 ANSWER: = 0.977 Alternative Exercise 43.88 Description: The isotope ^90(Sr) undergoes beta^- decay with a half-life of 28 years. (a) What nucleus is produced by this decay? (b) If a nuclear power plant is contaminated with ^90Sr, how long will it take for the radiation level to decrease to 1.0% of its... The isotope undergoes decay with a half-life of 28 years. Part A What nucleus is produced by this decay? ANSWER: Part B If a nuclear power plant is contaminated with Sr, how long will it take for the radiation level to decrease to 1.0% of its initial value? Express your answer using two significant figures. ANSWER: = 190 Exercise 43.20 Description: Radioactive isotopes used in cancer therapy have a "shelf-life," just like pharmaceuticals used in chemotherapy. Just after it has been manufactured in a nuclear reactor, the activity of a sample of ^60(Co) is 5000 Ci. When its activity falls below... Radioactive isotopes used in cancer therapy have a "shelf-life," just like pharmaceuticals used in chemotherapy. Just after it has been manufactured in a nuclear reactor, the activity of a sample of is 5000 . When its activity falls below 3500 , it is considered to be too weak a source to use in treatment. You work in the radiology department of a large hospital. One of these sources in your inventory was manufactured on October 6, 2011. It is now April 6, 2014. Part A Is the source still usable? The half-life of is 5.271 . ANSWER: yes no Exercise 43.36 Description: It has become popular for some people to have yearly whole-body scans (CT scans, formerly called CAT scans), using x rays, just to see if they detect anything suspicious. A number of medical people have recently questioned the advisability of such... It has become popular for some people to have yearly whole-body scans (CT scans, formerly called CAT scans), using x rays, just to see if they detect anything suspicious. A 5/6/2016 4:35 PM MasteringPhysics: Print View with Answers 18 of 20 https://session.masteringphysics.com/myct/assignmentPrintView?assign... number of medical people have recently questioned the advisability of such scans, due in part to the radiation they impart. Typically, one such scan gives a dose of 12 applied to the whole body. By contrast, a chest x ray typically administers 0.20 to only 5.0 of tissue. , Part A How many chest x rays would deliver the same total amount of energy to the body of a 75 person as one whole-body scan? Express your answer using two significant figures. ANSWER: = 900 ± Nuclear Power Description: ± Includes Math Remediation. The energy per reaction is calculated for fission of uranium-235. This is compared to the energy usage of the US in a year. Nuclear reactors generate power by harnessing the energy from nuclear fission. In a fission reaction, uranium-235 absorbs a neutron, bringing it into a highly unstable state as uranium-236. This state almost immediately breaks apart into two smaller fragments, releasing energy. One typical reaction is , where indicates a neutron. In this problem, assume that all fission reactions are of this kind. In fact, many different fission reactions go on inside a reactor, but all have similar reaction energies, so it is reasonable to calculate with just one. The products of this reaction are unstable and decay shortly after fission, releasing more energy. In this problem, you will ignore the extra energy contributed by these secondary decays. You will need the following mass data: mass of , mass of , mass of mass of , and . Part A What is the reaction energy of this reaction? Use . Express your answer in millions of electron volts to three significant figures. Hint 1. Formula for reaction energy . ANSWER: = 185 Part B Using fission, what mass of uranium-235 would be necessary to supply all of the energy that the United States uses in a year, roughly ? Express your answer in kilograms to two significant figures. Hint 1. Relating MeV and joules and . Hint 2. Find the mass of one uranium atom Find the mass of one atom of uranium-235. Recall that the mass in atomic mass units is equal to the mass in grams of one mole of atoms. Avagadro's number, , gives the number of atoms in one mole. Give your answer in kilograms to three significant figures. ANSWER: mass of one atom of = 3.900×10−25 Divide the mass per atom by the energy released per atom to get the mass of uranium used up per unit of energy released. ANSWER: = 1.30×105 5/6/2016 4:35 PM MasteringPhysics: Print View with Answers 19 of 20 https://session.masteringphysics.com/myct/assignmentPrintView?assign... As a comparison, a coal-burning plant would have to burn many times more coal than this to provide the energy needs of even one large city for just one day. It should be noted that nuclear power plants do not pose a substantial risk to surrounding communities, though this is a common misconception. Exercise 44.4 Description: A proton and an antiproton annihilate, producing two photons. (a) Find the energy of each photon if the p and bar p are initially at rest. Determine the values in the center-of-momentum reference frame. (b) Find the frequency of each photon if the... A proton and an antiproton annihilate, producing two photons. Part A Find the energy of each photon if the and are initially at rest. Determine the values in the center-of-momentum reference frame. Express your answers using three significant figures separated by a comma. ANSWER: , , = = 938, 938 Part B Find the frequency of each photon if the and are initially at rest. Determine the values in the center-of-momentum reference frame. Express your answers using three significant figures separated by a comma. ANSWER: , = 2.27×1023, 2.27×1023 , = Part C Find the wavelength of each photon if the and are initially at rest. Determine the values in the center-of-momentum reference frame. Express your answers using three significant figures separated by a comma. ANSWER: , = = 1.32×10−15, 1.32×10−15 , Part D Find the energy of each photon if the reference frame. and collide head-on, each with an initial kinetic energy of 670 . Determine the values in the center-of-momentum Express your answers using three significant figures separated by a comma. ANSWER: , = 1.61×103, 1.61×103 , = Part E Find the frequency of each photon if the reference frame. and collide head-on, each with an initial kinetic energy of 670 . Determine the values in the center-of-momentum Express your answers using three significant figures separated by a comma. ANSWER: , = , = 3.89×1023, 3.89×1023 Part F Find the wavelength of each photon if the and collide head-on, each with an initial kinetic energy of 670 . Determine the values in the center-of-momentum 5/6/2016 4:35 PM MasteringPhysics: Print View with Answers 20 of 20 https://session.masteringphysics.com/myct/assignmentPrintView?assign... reference frame. Express your answers using three significant figures separated by a comma. ANSWER: , = , = 7.71×10−16, 7.71×10−16 Exercise 44.24 Description: Which of the following reactions obey the conservation of baryon number? (a) p + p to p + e^+... (b) p + n to (2 e)^+ + e^-... (c) p to n + e^- ( + )bar nu_e... (d) p + (bar p) to2 gamma... Which of the following reactions obey the conservation of baryon number? Part A ANSWER: obeys does not obey Part B ANSWER: obeys does not obey Part C ANSWER: obeys does not obey Part D ANSWER: obeys does not obey Copyright © 2016 Pearson. All rights reserved. Legal Notice Privacy Policy Permissions Support 5/6/2016 4:35 PM