1cc. Which isotope X is needed to complete the reaction ...a) ...b) ...c) ...d) ...e) ... Get solution
1mcq. Radium-226 decays by emitting an alpha particle. What is the daughter nucleus?a) Rdb) Rnc) Bid) Pb Get solution
2cc. The isotopes ..., and ... have masses of 81.9134836 u, 81.9182086 u, and 81.91840164 u, respectively. For which of the β+ decays of ... and ... is positron emission possible?a) for neitherb) only for the ... decayc) only for the ... decayd) for both Get solution
2mcq. Which of the following decay modes involves a transition between states of the same nucleus?a) alpha decayb) beta decayc) gamma decayd) none of the above Get solution
3cc. Which of the following types of nuclear decays are possible for the isotope ...? (Hint: The mass of ... is 81.925 u, the mass of ... is 81.930 u, the mass of ... is 81.917 u, the mass of ... is 77.932 u, and the mass of ... is 4.0026u.)a) alpha decayb) beta decayc) positron emissiond) electron capturee) gamma decay Get solution
3mcq. In neutron stars, which are roughly 90% neutrons and are held together almost entirely by nuclear forces, which of the following terms become(s) relatively dominant for the binding energy, compared to that energy in an ordinary nucleus?a) the Coulomb termb) the asymmetry termc) the pairing termd) all of the abovee) none of the above Get solution
4cc. Which of the following isotopes has the largest fissionability?a) ...b) ...c) ...d) ... Get solution
4mcq. When a target nucleus is bombarded by a beam of the appropriate particles, it is possible to producea) a less massive nucleus, but not a more massive one.b) a more massive nucleus, but not a less massive one.c) a nucleus with a smaller charge number, but not one with a larger charge number.d) a nucleus with a larger charge number, but not one with a smaller charge number.e) a nucleus with either a larger or smaller charge number. Get solution
5cc. With that much hydrogen being converted into helium, how much longer can the Sun keep shining at the current burn rate? (Hint: The mass of the Sun is 1.99 · 1030 kg, the core contains approximately 10% of that mass, and approximately half of the core mass is currently still hydrogen.)a) 30,000 yearsb) 2 million yearsc) 100 million yearsd) 5 billion yearse) 3.3 · 1018 years Get solution
5mcq. The strong forcea) is only attractive.b) does not act on electrons.c) only acts over distances of a few femtometers.d) All of the above are true.e) None of the above are true. Get solution
6mcq. Cobalt has a stable isotope, ..., and 22 radioactive isotopes. The most stable radioactive isotope is .... What is the dominant decay mode of this isotope?a) β +b) β–c) proton emissiond) neutron emission Get solution
7mcq. The mass of an atom (atomic mass) is equal toa) the sum of the masses of the protons.b) the sum of the masses of protons and neutrons.c) the sum of the masses of protons, neutrons, and electrons.d) the sum of the masses of protons, neutrons, and electrons minus theatom’s binding energy. Get solution
9cq. Apart from fatigue, what is another reason the Federal Aviation Administration limits the number of hours that commercial jet pilots can fly each year? Get solution
10cq. Why are there magic numbers in the nuclear shell model? Get solution
11cq. The binding energy of ... is lower than that of .... Provide a plausible explanation, taking into consideration the Coulomb interaction between two protons in .... Get solution
12cq. Which of the following quantities is conserved during a nuclear reaction, and how?a) chargeb) the number of nucleons, Ac) mass-energyd) linear momentume) angular momentum Get solution
13cq. Some food is treated with gamma radiation to kill bacteria. Why is it not a concern that people who eat such food are ingesting gamma radiation? Get solution
14cq. The subsection “Terrestrial Fusion” in Section 40.4 discussed how achieving controlled fusion would be the solution to the world’s energy problems and how difficult it is to do this. Why is it so hard? The Sun does it all the time (see the subsection “Stellar Fusion”). Do we need to understand better how the Sun works to build a nuclear fusion reactor? Get solution
15cq. Why are atomic nuclei more or less limited in size and in neutron-proton ratio? That is, why are there no stable nuclei with 10 times as many neutrons as protons, and why are there no atomic nuclei the size of marbles? Get solution
16cq. A nuclear reaction of the kind ... is called a pick-up reaction.a) Why does it have this name, that is, what is picked up, what picked it up, and where did it come from?b) What is the resulting nucleus, X?c) What is the Q-value of this reaction?d) Is this reaction endothermic or exothermic? Get solution
17cq. Isospin, or isotopic spin, is a quantum variable describing the relationship between protons and neutrons in nuclear and particle physics. (Strictly, it describes the relationship between up and down quarks, as described in Chapter 39, but it was introduced before the advent of the quark model.) It has the same algebraic properties as quantum angular momentum: A proton and a neutron form an iso-doublet of states, with total isospin quantum number ...; the proton is in the tz = + ... state, and the neutron is in the tz = – ... state, where z refers to a direction in an abstract isospin space.a) What isospin states can be constructed from two nucleons, that is, two particles with t = ... ? To what nuclei do these states correspond?b) What isospin states can be constructed from three nucleons? To what nuclei do these correspond? Get solution
18cq. Before looking it up, predict intrinsic spin (i.e., actual angular momentum) of the deuteron, .... Explain your reasoning. (Hint: Nucleons are fermions.) Get solution
19cq. 18 39Ar is an isotope with a half-life of 269 yr. If it decays through β– decay, what isotope will result? Get solution
20cq. A neutron star is essentially a gigantic nucleus with mass 1.35 times that of the Sun, or a mass number of order 1057. It consists of approximately 99% neutrons, the rest being protons and an equal number of electrons. Explain the physics that determines these features. Get solution
21cq. What is the nuclear configuration of the daughter nucleus associated with the alpha decay of Hf (A = 157, Z = 72)? Get solution
22. Estimate the volume of the uranium-235 nucleus. Get solution
23. Calculate the binding energies of the following nuclei.a) ... b) ...c) ...d) ... Get solution
24. Give the numbers of protons, nucleons, neutrons, and electrons in an atom of .... Get solution
25. Using the Fermi function, determine the relative change in density, (dn(r)/dr)/n0, at the nuclear surface, r = R(A). Get solution
26. Calculate the binding energy for the following two uranium isotopes (where u = 1.66 · 10–27 kg):a) ..., which consists of 92 protons, 92 electrons, and 146 neutrons, with a total mass of 238.0507826 ub) ..., which consists of 92 protons, 92 electrons, and 143 neutrons, with a total mass of 235.0439299 uWhich isotope is more stable (or less unstable)? Get solution
27. Write equations for the β– decay of the following isotopes:a) ...b) ...c) ... Get solution
28. Write equations for the alpha decay of the following isotopes:a) ...b) ... Get solution
29. How much energy is released in the beta decay of ...? Get solution
30. A certain radioactive isotope decays to one-eighth of its original amount in 5.0 h.a) What is its half-life?b) What is its mean lifetime? Get solution
31. A certain radioactive isotope decays to one-eighth of its original amount in 5.00 h. How long would it take for 10.0% of it to decay? Get solution
32. Determine the decay constant of radium-226, which has a half-life of 1600 yr. Get solution
33. A 1.00-g sample of radioactive thorium-228 decays via β– decay, and 75 counts are recorded in one day by a detector that has 10.0% efficiency (that is, 10.0% of all events that occur are recorded by the detector). What is the lifetime of this isotope? Get solution
35. The specific activity of a radioactive material is the number of disintegrations per second per gram of radioactive atoms.a) Given the half-life of ... of 5730 yr, calculate the specific activity of .... Express your result in disintegrations per second per gram, becquerel per gram, and curie per gram.b) Calculate the initial activity of a 5.00-g piece of wood.c) How many ... disintegrations have occurred in a 5.00-g piece of wood that was cut from a tree on January 1, 1700? Get solution
36. During a trip to an excavation site, an archeologist found a piece of charcoal. Analysis of the charcoal found the activity of ... in the sample to be 0.42 Bq. If the mass of the charcoal is 7.2 g, estimate the approximate age of the site. Get solution
37. In 2008, crime scene investigators discover the bones of a person who appeared to have been the victim of a brutal attack that occurred a long time ago. They would like to know the year when the person was murdered. Using carbon dating, they determine that the rate of change of the ... is 0.268 Bq per gram of carbon. The rate of change of ... in the bones of a person who had just died is 0.270 Bq per gram of carbon. What year was the victim killed? The half-life of ... is 5.73 · 103 yr. Get solution
38. Physicists blow stuff up better than anyone else. The measure for gauging the usefulness of blowing something up is the fraction of initial rest mass converted into energy in the process. Looking up the necessary data, calculate this fraction for the following processes:a) chemical combustion of hydrogen: 2H2 + O2 → 2H2Ob) nuclear fission: ...c) thermonuclear fusion: ...d) decay of free neutron: ...e) decay of muon: ...f) electron-positron annihilation: e– + e+→ 2γ Get solution
39. An unstable nucleus A decays to an unstable nucleus B, which in turn decays to a stable nucleus. If at t = 0 s there are NA0 and NB0 nuclei present, derive an expression for NB, the number of B nuclei present, as a function of time. Get solution
40. In a simple case of chain radioactive decay, a parent radioactive nucleus, A, decays with a decay constant λ1 into a daughter radioactive nucleus, B, which then decays with a decay constant λ2 to a stable nucleus, C.a) Write the equations describing the number of nuclei of each of the three types as a function of time, and derive expressions for the number of daughter nuclei, N2, as a function of time and for the activity of the daughter nuclei, A2, as a function of time.b) Discuss the results in the case when λ2 > λ1 (λ2 ≈ 10 λ1) and when λ2 >> λ1 (λ2 ≈100 λ1). Get solution
41. Show that for the case of nuclei with odd mass number, A, the Bethe-Weizsäcker formula can be written as a quadratic in Z—and thus, for any given A, the binding energies of the isotopes having that A take a quadratic form, B = a + bZ + cZ2. Use your result to find the most strongly bound isotope (the most stable one) having A = 117. Get solution
42. The neutron drip line is defined to be the point at which the neutron separation energy for any isotope of an element is negative. That is, the neutron is unbound. Using the Bethe-Weizsäcker formula, find the neutron drip line for the element Sn. Find this value using Sn and S2n. Plot both Sn and S2n/2 as a function of neutron number. Get solution
43. A nuclear fission power plant produces about 1.50 GW of electrical power. Assume that the plant has an overall efficiency of 35.0% and that each fission event produces 200. MeV of energy. Calculate the mass of ... consumed each day. Get solution
44. a) What is the energy released in the fusion reaction ...?b) The Earth’s oceans have a total mass of water of 1.50 · 1016 kg, and 0.0300% of this quantity is deuterium, .... If all the deuterium in the oceans were fused by controlled fusion into ..., how many joules of energy would be released?c) World power consumption is about 1.00 · 1013 W. If consumption stayed constant and all problems arising from ocean water consumption (including those of political, meteorological, and ecological nature) could be avoided, how many years would the energy calculated in part (b) last? Get solution
45. The Sun radiates energy at the rate of 3.85 · 1026 W.a) At what rate, in kilograms per second, is the Sun’s mass converted into energy?b) Why is this result different from the rate calculated in Example 40.6: 6.02 · 1011 kg of protons being converted into helium each second?c) Assuming that the current mass of the Sun is 1.99 · 1030 kg and that it has radiated at the same rate for its entire lifetime of 4.50 · 109 yr, what percentage of the Sun’s mass has been converted into energy during its entire lifetime? Get solution
46. Consider the following fusion reaction, through which stars produce progressively heavier elements: .... The mass of ... is 3.016029 u, the mass of ... is 4.002603 u, and the mass of ... is 7.0169298 u. The atomic mass unit is 1 u = 1.66 · 10–27 kg. Assuming that the Be atom is at rest after the reaction and neglecting any potential energy between the atoms and the kinetic energy of the He nuclei, calculate the minimum possible energy and maximum possible wavelength of the photon, γ, that is emitted in this reaction. Get solution
47. Estimate the temperature that would be needed to initiate the fusion reaction ... Get solution
48. Consider a hypothetical fission process in which a ... nucleus splits into two identical ... nuclei without producing any other particles or radiation. The mass of ... is 119.904040 u, and the mass of ... is 59.934078 u. At the moment when the two iron nuclei form, but before they start moving away due to Coulomb repulsion, how far apart are the two nuclei? Get solution
49. The mass excess of a nucleus is defined as the difference between the atomic mass (in atomic mass units, u), and the mass number of the nucleus, A. Using the mass-energy conversion 1 u = 931.49 MeV/c2, this mass excess is usually expressed in kilo-electron-volts (keV). The table below presents the mass excess for several nuclei (from the Berkeley National Lab NuBase database):...a) Calculate the atomic mass (in atomic mass units) for each of the nuclei in the table. For reference, the atomic mass of the neutron is given.b) Using your results from part (a), determine the mass-energy difference between the initial and final states for the following possible fission reactions:...c) Will these reactions occur spontaneously? Get solution
50. Neutron stars are sometimes approximated to be nothing more than large atomic nuclei (but with many more neutrons). Assuming that a neutron star is as dense as an atomic nucleus, estimate the number of nucleons in a 10.0-km-diameter star. Get solution
51. What is the average kinetic energy of protons at the center of a star, where the temperature is 1.00 · 107 K? What is the average velocity of those protons? Get solution
52. Billions of years ago, the Solar System was created out of the remnants of a supernova explosion. Nuclear scientists believe that two isotopes of uranium, ... and ..., were created in equal amounts at that time. However, today 99.28% of uranium is in the form of ... and only 0.72% is in the form of .... Assuming a simplified model in which all of the matter in the Solar System originated in a single exploding star, estimate the approximate time of this explosion. Get solution
53. A drug containing ... (t1/2 = 6.05 h) with an activity of 1.50 μCi is to be injected into a patient at 9.30 a.m. You are to prepare the drug 2.50 h before the injection (at 7:00 a.m.). What activity should the drug have at the preparation time (7:00 a.m.)? Get solution
54. A 42.58-MHz photon is needed to produce nuclear magnetic resonance in free protons in a magnetic field of 1.000 T. What is the wavelength of the photon, its energy, and the region of the spectrum in which it lies? Could it be harmful to the human body? Get solution
55. The radon isotope ..., which has a half-life of 3.825 days, is used for medical purposes such as radiotherapy. How long does it take until ... decays to 10.00% of its initial quantity? Get solution
56. Radiation therapy is one of the techniques used for cancer treatment. Based on the approximate mass of a tumor, oncologists can calculate the radiation dose necessary to treat a patient. Suppose a patient has a 50.0-g tumor and needs to receive 0.180 J of energy to kill the cancer cells. What radiation absorbed dose should the patient receive? Get solution
57. The atom of sodium-22 ... has a mass of 21.994435 u. How much work would be needed to take this nucleus completely apart into its constituent pieces (protons, neutrons, and electrons)? Get solution
58. A Geiger counter initially records 7210 counts/s from a sample of radioactive material. After 45 min, it records 4585 counts/s. Ignore any uncertainty in the counts and find the half-life of the material. Get solution
59. How close can a 5.00-MeV alpha particle get to a uranium-238 nucleus, assuming that the only interaction is Coulomb? Get solution
60. ... decays with a half-life of 24,100 yr via emission of a 5.25-MeV alpha particle. If you have a 1.00 kg spherical sample of 2..., find the initial activity in becquerels. Get solution
62. Assuming that carbon makes up 14% of the mass of a human body, calculate the activity of a 75-kg person considering only the beta decays of carbon-14. Get solution
63. ... is an isotope that has a lifetime of less than a second. Its mass is 8.022485 u. Calculate its binding energy in MeV. Get solution
64. What is the total energy released in the decay ... Get solution
65. A gallon of regular gasoline (density of 737 kg/m3) contains about 131 MJ of chemical energy. How much energy is contained in the rest mass of this gallon? Get solution
66. If 1030 atoms of a radioactive sample remain after 10 half-lives, how many atoms remain after 20 half-lives? Get solution
67. Calculate the binding energy per nucleon ofa) ....b) ....c) ...d) ... Get solution
68. The mean lifetime for a radioactive nucleus is 4300 s. What is its half-life? Get solution
69. ... has a half-life of 26.8 min. How many minutes must elapse for 90.0% of a given sample of ... atoms to decay? Get solution
70. The most common isotope of uranium, ..., produces radon, ..., through the following sequence of decays:...A sample of ... will build up equilibrium concentrations of its daughter nuclei down to ...; the concentrations of each are such that each daughter is produced as fast as it decays. The ... decays to ..., which escapes as a gas. (The alpha particles also escape, as helium; this is a source of much of the helium found on Earth.) Radon is a health hazard when it occurs in high concentrations in buildings built on soil or foundations containing uranium ores, as it can be inhaled.a) Look up the necessary data, and calculate the rate at which 1.00 kg of an equilibrium mixture of ... and its first five daughters produces ... (mass per unit time).b) What activity (in curies per unit time) of radon does this represent? Get solution
71. After a tree has been chopped down and burned to ash, the carbon isotopes in the ash are found to have a ... to ... ratio of 1.300 · 10–12. Experimental tests on the ... atoms reveal that ... is a beta emitter with a half-life of 5730 yr. At an archeological excavation, a skeleton is found next to some wood ash from a campfire. If 50.0 g of carbon from the ash emits electrons at a rate of 20.0 per hour, how long ago did the campfire burn? Get solution
72. If your mass is 70.0 kg and you have a lifetime of 70.0 yr, how many proton decays will occur in your body during your life (assuming that your body is entirely composed of water)? Use a half-life of 1.00 · 1030 yr. Get solution
73. You have developed a grand unified theory that predicts the following things about the decay of protons: (1) protons never get any older, in the sense that their probability of decay per unit time never changes, and (2) half the protons in any given collection of protons will have decayed in 1.80 · 1029 yr. You are given experimental facilities to test your theory: a tank containing 1.00 · 104 metric tons of water and sensors to record proton decays. You will be allowed access to this facility for 2 years. How many proton decays will occur in this period if your theory is correct? Get solution
74. The precession frequency of the protons in a laboratory NMR spectrometer is 15.35850 MHz. The magnetic dipole moment of the proton is 1.410608 · 10–26 J/T, while its spin angular momentum is 0.5272863 · 10–34 J s. Calculate the magnitude of the magnetic field in which the protons are immersed. Get solution
75. Two species of radioactive nuclei, A and B, each with an initial population N0, start decaying. After a time of 100. s, it is observed that NA = 100NB. If ..., find the value of .... Get solution
76. A 12.43-g fragment of charcoal is to be carbon dated. Measurements show that it has an activity of 105 decays/ min. How many years ago did the tree from which the charcoal was produced die? (Hint: The half-life of ... is 5730 yr, and the ... ratio in living organic matter is 1.20 · 10–12.) Get solution
77. A fragment of charcoal has been determined by carbon dating to be 4384 years old. Measurements show that it has an activity of 107 decays/ min. What is the mass of the charcoal fragment? (Hint: The half-life of ... is 5730 yr, and the ... ratio in living organic matter is 1.20 · 10–12.) Get solution
78. A 13.83-g fragment of charcoal has been determined by carbon dating to be 4814 years old. How many decays per minute were measured in the carbon dating process? (Hint: The half-life of ... is 5730 yr, and the ... ratio in living organic matter is 1.20 · 10–12.) Get solution
1mcq. Radium-226 decays by emitting an alpha particle. What is the daughter nucleus?a) Rdb) Rnc) Bid) Pb Get solution
2cc. The isotopes ..., and ... have masses of 81.9134836 u, 81.9182086 u, and 81.91840164 u, respectively. For which of the β+ decays of ... and ... is positron emission possible?a) for neitherb) only for the ... decayc) only for the ... decayd) for both Get solution
2mcq. Which of the following decay modes involves a transition between states of the same nucleus?a) alpha decayb) beta decayc) gamma decayd) none of the above Get solution
3cc. Which of the following types of nuclear decays are possible for the isotope ...? (Hint: The mass of ... is 81.925 u, the mass of ... is 81.930 u, the mass of ... is 81.917 u, the mass of ... is 77.932 u, and the mass of ... is 4.0026u.)a) alpha decayb) beta decayc) positron emissiond) electron capturee) gamma decay Get solution
3mcq. In neutron stars, which are roughly 90% neutrons and are held together almost entirely by nuclear forces, which of the following terms become(s) relatively dominant for the binding energy, compared to that energy in an ordinary nucleus?a) the Coulomb termb) the asymmetry termc) the pairing termd) all of the abovee) none of the above Get solution
4cc. Which of the following isotopes has the largest fissionability?a) ...b) ...c) ...d) ... Get solution
4mcq. When a target nucleus is bombarded by a beam of the appropriate particles, it is possible to producea) a less massive nucleus, but not a more massive one.b) a more massive nucleus, but not a less massive one.c) a nucleus with a smaller charge number, but not one with a larger charge number.d) a nucleus with a larger charge number, but not one with a smaller charge number.e) a nucleus with either a larger or smaller charge number. Get solution
5cc. With that much hydrogen being converted into helium, how much longer can the Sun keep shining at the current burn rate? (Hint: The mass of the Sun is 1.99 · 1030 kg, the core contains approximately 10% of that mass, and approximately half of the core mass is currently still hydrogen.)a) 30,000 yearsb) 2 million yearsc) 100 million yearsd) 5 billion yearse) 3.3 · 1018 years Get solution
5mcq. The strong forcea) is only attractive.b) does not act on electrons.c) only acts over distances of a few femtometers.d) All of the above are true.e) None of the above are true. Get solution
6mcq. Cobalt has a stable isotope, ..., and 22 radioactive isotopes. The most stable radioactive isotope is .... What is the dominant decay mode of this isotope?a) β +b) β–c) proton emissiond) neutron emission Get solution
7mcq. The mass of an atom (atomic mass) is equal toa) the sum of the masses of the protons.b) the sum of the masses of protons and neutrons.c) the sum of the masses of protons, neutrons, and electrons.d) the sum of the masses of protons, neutrons, and electrons minus theatom’s binding energy. Get solution
9cq. Apart from fatigue, what is another reason the Federal Aviation Administration limits the number of hours that commercial jet pilots can fly each year? Get solution
10cq. Why are there magic numbers in the nuclear shell model? Get solution
11cq. The binding energy of ... is lower than that of .... Provide a plausible explanation, taking into consideration the Coulomb interaction between two protons in .... Get solution
12cq. Which of the following quantities is conserved during a nuclear reaction, and how?a) chargeb) the number of nucleons, Ac) mass-energyd) linear momentume) angular momentum Get solution
13cq. Some food is treated with gamma radiation to kill bacteria. Why is it not a concern that people who eat such food are ingesting gamma radiation? Get solution
14cq. The subsection “Terrestrial Fusion” in Section 40.4 discussed how achieving controlled fusion would be the solution to the world’s energy problems and how difficult it is to do this. Why is it so hard? The Sun does it all the time (see the subsection “Stellar Fusion”). Do we need to understand better how the Sun works to build a nuclear fusion reactor? Get solution
15cq. Why are atomic nuclei more or less limited in size and in neutron-proton ratio? That is, why are there no stable nuclei with 10 times as many neutrons as protons, and why are there no atomic nuclei the size of marbles? Get solution
16cq. A nuclear reaction of the kind ... is called a pick-up reaction.a) Why does it have this name, that is, what is picked up, what picked it up, and where did it come from?b) What is the resulting nucleus, X?c) What is the Q-value of this reaction?d) Is this reaction endothermic or exothermic? Get solution
17cq. Isospin, or isotopic spin, is a quantum variable describing the relationship between protons and neutrons in nuclear and particle physics. (Strictly, it describes the relationship between up and down quarks, as described in Chapter 39, but it was introduced before the advent of the quark model.) It has the same algebraic properties as quantum angular momentum: A proton and a neutron form an iso-doublet of states, with total isospin quantum number ...; the proton is in the tz = + ... state, and the neutron is in the tz = – ... state, where z refers to a direction in an abstract isospin space.a) What isospin states can be constructed from two nucleons, that is, two particles with t = ... ? To what nuclei do these states correspond?b) What isospin states can be constructed from three nucleons? To what nuclei do these correspond? Get solution
18cq. Before looking it up, predict intrinsic spin (i.e., actual angular momentum) of the deuteron, .... Explain your reasoning. (Hint: Nucleons are fermions.) Get solution
19cq. 18 39Ar is an isotope with a half-life of 269 yr. If it decays through β– decay, what isotope will result? Get solution
20cq. A neutron star is essentially a gigantic nucleus with mass 1.35 times that of the Sun, or a mass number of order 1057. It consists of approximately 99% neutrons, the rest being protons and an equal number of electrons. Explain the physics that determines these features. Get solution
21cq. What is the nuclear configuration of the daughter nucleus associated with the alpha decay of Hf (A = 157, Z = 72)? Get solution
22. Estimate the volume of the uranium-235 nucleus. Get solution
23. Calculate the binding energies of the following nuclei.a) ... b) ...c) ...d) ... Get solution
24. Give the numbers of protons, nucleons, neutrons, and electrons in an atom of .... Get solution
25. Using the Fermi function, determine the relative change in density, (dn(r)/dr)/n0, at the nuclear surface, r = R(A). Get solution
26. Calculate the binding energy for the following two uranium isotopes (where u = 1.66 · 10–27 kg):a) ..., which consists of 92 protons, 92 electrons, and 146 neutrons, with a total mass of 238.0507826 ub) ..., which consists of 92 protons, 92 electrons, and 143 neutrons, with a total mass of 235.0439299 uWhich isotope is more stable (or less unstable)? Get solution
27. Write equations for the β– decay of the following isotopes:a) ...b) ...c) ... Get solution
28. Write equations for the alpha decay of the following isotopes:a) ...b) ... Get solution
29. How much energy is released in the beta decay of ...? Get solution
30. A certain radioactive isotope decays to one-eighth of its original amount in 5.0 h.a) What is its half-life?b) What is its mean lifetime? Get solution
31. A certain radioactive isotope decays to one-eighth of its original amount in 5.00 h. How long would it take for 10.0% of it to decay? Get solution
32. Determine the decay constant of radium-226, which has a half-life of 1600 yr. Get solution
33. A 1.00-g sample of radioactive thorium-228 decays via β– decay, and 75 counts are recorded in one day by a detector that has 10.0% efficiency (that is, 10.0% of all events that occur are recorded by the detector). What is the lifetime of this isotope? Get solution
35. The specific activity of a radioactive material is the number of disintegrations per second per gram of radioactive atoms.a) Given the half-life of ... of 5730 yr, calculate the specific activity of .... Express your result in disintegrations per second per gram, becquerel per gram, and curie per gram.b) Calculate the initial activity of a 5.00-g piece of wood.c) How many ... disintegrations have occurred in a 5.00-g piece of wood that was cut from a tree on January 1, 1700? Get solution
36. During a trip to an excavation site, an archeologist found a piece of charcoal. Analysis of the charcoal found the activity of ... in the sample to be 0.42 Bq. If the mass of the charcoal is 7.2 g, estimate the approximate age of the site. Get solution
37. In 2008, crime scene investigators discover the bones of a person who appeared to have been the victim of a brutal attack that occurred a long time ago. They would like to know the year when the person was murdered. Using carbon dating, they determine that the rate of change of the ... is 0.268 Bq per gram of carbon. The rate of change of ... in the bones of a person who had just died is 0.270 Bq per gram of carbon. What year was the victim killed? The half-life of ... is 5.73 · 103 yr. Get solution
38. Physicists blow stuff up better than anyone else. The measure for gauging the usefulness of blowing something up is the fraction of initial rest mass converted into energy in the process. Looking up the necessary data, calculate this fraction for the following processes:a) chemical combustion of hydrogen: 2H2 + O2 → 2H2Ob) nuclear fission: ...c) thermonuclear fusion: ...d) decay of free neutron: ...e) decay of muon: ...f) electron-positron annihilation: e– + e+→ 2γ Get solution
39. An unstable nucleus A decays to an unstable nucleus B, which in turn decays to a stable nucleus. If at t = 0 s there are NA0 and NB0 nuclei present, derive an expression for NB, the number of B nuclei present, as a function of time. Get solution
40. In a simple case of chain radioactive decay, a parent radioactive nucleus, A, decays with a decay constant λ1 into a daughter radioactive nucleus, B, which then decays with a decay constant λ2 to a stable nucleus, C.a) Write the equations describing the number of nuclei of each of the three types as a function of time, and derive expressions for the number of daughter nuclei, N2, as a function of time and for the activity of the daughter nuclei, A2, as a function of time.b) Discuss the results in the case when λ2 > λ1 (λ2 ≈ 10 λ1) and when λ2 >> λ1 (λ2 ≈100 λ1). Get solution
41. Show that for the case of nuclei with odd mass number, A, the Bethe-Weizsäcker formula can be written as a quadratic in Z—and thus, for any given A, the binding energies of the isotopes having that A take a quadratic form, B = a + bZ + cZ2. Use your result to find the most strongly bound isotope (the most stable one) having A = 117. Get solution
42. The neutron drip line is defined to be the point at which the neutron separation energy for any isotope of an element is negative. That is, the neutron is unbound. Using the Bethe-Weizsäcker formula, find the neutron drip line for the element Sn. Find this value using Sn and S2n. Plot both Sn and S2n/2 as a function of neutron number. Get solution
43. A nuclear fission power plant produces about 1.50 GW of electrical power. Assume that the plant has an overall efficiency of 35.0% and that each fission event produces 200. MeV of energy. Calculate the mass of ... consumed each day. Get solution
44. a) What is the energy released in the fusion reaction ...?b) The Earth’s oceans have a total mass of water of 1.50 · 1016 kg, and 0.0300% of this quantity is deuterium, .... If all the deuterium in the oceans were fused by controlled fusion into ..., how many joules of energy would be released?c) World power consumption is about 1.00 · 1013 W. If consumption stayed constant and all problems arising from ocean water consumption (including those of political, meteorological, and ecological nature) could be avoided, how many years would the energy calculated in part (b) last? Get solution
45. The Sun radiates energy at the rate of 3.85 · 1026 W.a) At what rate, in kilograms per second, is the Sun’s mass converted into energy?b) Why is this result different from the rate calculated in Example 40.6: 6.02 · 1011 kg of protons being converted into helium each second?c) Assuming that the current mass of the Sun is 1.99 · 1030 kg and that it has radiated at the same rate for its entire lifetime of 4.50 · 109 yr, what percentage of the Sun’s mass has been converted into energy during its entire lifetime? Get solution
46. Consider the following fusion reaction, through which stars produce progressively heavier elements: .... The mass of ... is 3.016029 u, the mass of ... is 4.002603 u, and the mass of ... is 7.0169298 u. The atomic mass unit is 1 u = 1.66 · 10–27 kg. Assuming that the Be atom is at rest after the reaction and neglecting any potential energy between the atoms and the kinetic energy of the He nuclei, calculate the minimum possible energy and maximum possible wavelength of the photon, γ, that is emitted in this reaction. Get solution
47. Estimate the temperature that would be needed to initiate the fusion reaction ... Get solution
48. Consider a hypothetical fission process in which a ... nucleus splits into two identical ... nuclei without producing any other particles or radiation. The mass of ... is 119.904040 u, and the mass of ... is 59.934078 u. At the moment when the two iron nuclei form, but before they start moving away due to Coulomb repulsion, how far apart are the two nuclei? Get solution
49. The mass excess of a nucleus is defined as the difference between the atomic mass (in atomic mass units, u), and the mass number of the nucleus, A. Using the mass-energy conversion 1 u = 931.49 MeV/c2, this mass excess is usually expressed in kilo-electron-volts (keV). The table below presents the mass excess for several nuclei (from the Berkeley National Lab NuBase database):...a) Calculate the atomic mass (in atomic mass units) for each of the nuclei in the table. For reference, the atomic mass of the neutron is given.b) Using your results from part (a), determine the mass-energy difference between the initial and final states for the following possible fission reactions:...c) Will these reactions occur spontaneously? Get solution
50. Neutron stars are sometimes approximated to be nothing more than large atomic nuclei (but with many more neutrons). Assuming that a neutron star is as dense as an atomic nucleus, estimate the number of nucleons in a 10.0-km-diameter star. Get solution
51. What is the average kinetic energy of protons at the center of a star, where the temperature is 1.00 · 107 K? What is the average velocity of those protons? Get solution
52. Billions of years ago, the Solar System was created out of the remnants of a supernova explosion. Nuclear scientists believe that two isotopes of uranium, ... and ..., were created in equal amounts at that time. However, today 99.28% of uranium is in the form of ... and only 0.72% is in the form of .... Assuming a simplified model in which all of the matter in the Solar System originated in a single exploding star, estimate the approximate time of this explosion. Get solution
53. A drug containing ... (t1/2 = 6.05 h) with an activity of 1.50 μCi is to be injected into a patient at 9.30 a.m. You are to prepare the drug 2.50 h before the injection (at 7:00 a.m.). What activity should the drug have at the preparation time (7:00 a.m.)? Get solution
54. A 42.58-MHz photon is needed to produce nuclear magnetic resonance in free protons in a magnetic field of 1.000 T. What is the wavelength of the photon, its energy, and the region of the spectrum in which it lies? Could it be harmful to the human body? Get solution
55. The radon isotope ..., which has a half-life of 3.825 days, is used for medical purposes such as radiotherapy. How long does it take until ... decays to 10.00% of its initial quantity? Get solution
56. Radiation therapy is one of the techniques used for cancer treatment. Based on the approximate mass of a tumor, oncologists can calculate the radiation dose necessary to treat a patient. Suppose a patient has a 50.0-g tumor and needs to receive 0.180 J of energy to kill the cancer cells. What radiation absorbed dose should the patient receive? Get solution
57. The atom of sodium-22 ... has a mass of 21.994435 u. How much work would be needed to take this nucleus completely apart into its constituent pieces (protons, neutrons, and electrons)? Get solution
58. A Geiger counter initially records 7210 counts/s from a sample of radioactive material. After 45 min, it records 4585 counts/s. Ignore any uncertainty in the counts and find the half-life of the material. Get solution
59. How close can a 5.00-MeV alpha particle get to a uranium-238 nucleus, assuming that the only interaction is Coulomb? Get solution
60. ... decays with a half-life of 24,100 yr via emission of a 5.25-MeV alpha particle. If you have a 1.00 kg spherical sample of 2..., find the initial activity in becquerels. Get solution
62. Assuming that carbon makes up 14% of the mass of a human body, calculate the activity of a 75-kg person considering only the beta decays of carbon-14. Get solution
63. ... is an isotope that has a lifetime of less than a second. Its mass is 8.022485 u. Calculate its binding energy in MeV. Get solution
64. What is the total energy released in the decay ... Get solution
65. A gallon of regular gasoline (density of 737 kg/m3) contains about 131 MJ of chemical energy. How much energy is contained in the rest mass of this gallon? Get solution
66. If 1030 atoms of a radioactive sample remain after 10 half-lives, how many atoms remain after 20 half-lives? Get solution
67. Calculate the binding energy per nucleon ofa) ....b) ....c) ...d) ... Get solution
68. The mean lifetime for a radioactive nucleus is 4300 s. What is its half-life? Get solution
69. ... has a half-life of 26.8 min. How many minutes must elapse for 90.0% of a given sample of ... atoms to decay? Get solution
70. The most common isotope of uranium, ..., produces radon, ..., through the following sequence of decays:...A sample of ... will build up equilibrium concentrations of its daughter nuclei down to ...; the concentrations of each are such that each daughter is produced as fast as it decays. The ... decays to ..., which escapes as a gas. (The alpha particles also escape, as helium; this is a source of much of the helium found on Earth.) Radon is a health hazard when it occurs in high concentrations in buildings built on soil or foundations containing uranium ores, as it can be inhaled.a) Look up the necessary data, and calculate the rate at which 1.00 kg of an equilibrium mixture of ... and its first five daughters produces ... (mass per unit time).b) What activity (in curies per unit time) of radon does this represent? Get solution
71. After a tree has been chopped down and burned to ash, the carbon isotopes in the ash are found to have a ... to ... ratio of 1.300 · 10–12. Experimental tests on the ... atoms reveal that ... is a beta emitter with a half-life of 5730 yr. At an archeological excavation, a skeleton is found next to some wood ash from a campfire. If 50.0 g of carbon from the ash emits electrons at a rate of 20.0 per hour, how long ago did the campfire burn? Get solution
72. If your mass is 70.0 kg and you have a lifetime of 70.0 yr, how many proton decays will occur in your body during your life (assuming that your body is entirely composed of water)? Use a half-life of 1.00 · 1030 yr. Get solution
73. You have developed a grand unified theory that predicts the following things about the decay of protons: (1) protons never get any older, in the sense that their probability of decay per unit time never changes, and (2) half the protons in any given collection of protons will have decayed in 1.80 · 1029 yr. You are given experimental facilities to test your theory: a tank containing 1.00 · 104 metric tons of water and sensors to record proton decays. You will be allowed access to this facility for 2 years. How many proton decays will occur in this period if your theory is correct? Get solution
74. The precession frequency of the protons in a laboratory NMR spectrometer is 15.35850 MHz. The magnetic dipole moment of the proton is 1.410608 · 10–26 J/T, while its spin angular momentum is 0.5272863 · 10–34 J s. Calculate the magnitude of the magnetic field in which the protons are immersed. Get solution
75. Two species of radioactive nuclei, A and B, each with an initial population N0, start decaying. After a time of 100. s, it is observed that NA = 100NB. If ..., find the value of .... Get solution
76. A 12.43-g fragment of charcoal is to be carbon dated. Measurements show that it has an activity of 105 decays/ min. How many years ago did the tree from which the charcoal was produced die? (Hint: The half-life of ... is 5730 yr, and the ... ratio in living organic matter is 1.20 · 10–12.) Get solution
77. A fragment of charcoal has been determined by carbon dating to be 4384 years old. Measurements show that it has an activity of 107 decays/ min. What is the mass of the charcoal fragment? (Hint: The half-life of ... is 5730 yr, and the ... ratio in living organic matter is 1.20 · 10–12.) Get solution
78. A 13.83-g fragment of charcoal has been determined by carbon dating to be 4814 years old. How many decays per minute were measured in the carbon dating process? (Hint: The half-life of ... is 5730 yr, and the ... ratio in living organic matter is 1.20 · 10–12.) Get solution
