(c) If energy is worth 12.0 cents per \(\displaystyle kW⋅h\), what is the monetary value of the energy emitted? Solution 76. Solution 64. If you have difficulties you should discuss them with the Course Lecturer. Solution The detail observable using a probe is limited by its wavelength. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Chapter 14. Calculate the energy released in the \(\displaystyle β^+\) decay of \(\displaystyle ^{22}Na\), the equation for which is given in the text. (b) If all of this energy is converted to thermal energy in the gas, what is its temperature increase, assuming \(\displaystyle 50.0 cm^3\) of ideal gas at 0.250-atm pressure? The mass of the daughter nuclide is 231.036298 u. What is the half-life in years? (c) 5.67 kW. (Consider the binding energy per nucleon.). You will find the difference is equal to the electron’s mass to three digits, implying the binding energy is small in comparison. 7. Depleted uranium has been erroneously called non-radioactive. Estimate the minimum age of the charcoal, noting that \(\displaystyle 2^{10}=1024\). (b) Only part of the emitted radiation goes in the direction of the detector. (b) What is the velocity of the \(\displaystyle γ\) ray relative to the \(\displaystyle β\) ray? Solution (c) Explain why the two \(\displaystyle γ\) rays travel in exactly opposite directions if the center of mass of the electron-positron system is initially at rest. Calculate how much power must cross each square meter of the Earth’s surface if the power is dissipated at the same rate as it is generated. 71. \(\displaystyle ^{209}Bi\) is the heaviest stable nuclide, and its \(\displaystyle BE/A\) is low compared with medium-mass nuclides. 24. 85. Note that you must use four-digit or better values for \(\displaystyle c\) and \(\displaystyle ∣q_e∣\). Poses special problems because its daughter is a radioactive noble gas. (b) What is its activity 5.00 y after manufacture? (This mass at nuclear density would make a cube 1.0 m on a side. Solution It may be useful to graph the log of \(\displaystyle t_{1/2}\) against \(\displaystyle E_α\) to find some straight-line relationship. 31.1: Nuclear Radioactivity; 31.2: Radiation Detection and Detectors; 31.3: Substructure of the Nucleus; 31.4: Nuclear Decay and Conservation Laws; 31.5: Half-Life and Activity; 31.6: Binding Energy; 31.7: Tunneling; Problems & Exercises Why are \(\displaystyle ^{226}Ra, ^{222}Rn\), and \(\displaystyle ^{210}Po\) also found in such a rock, even though they have much shorter half-lives (1600 years, 3.8 days, and 138 days, respectively)? The Solutions Manualis a comprehensive guide to the questions and problems in the Student Edition of Physics: Principles and Problems.This includes the Practice Problems, Section Reviews, Chapter Assessments, and Challenge Problems for each chapter, as well as the Additional Problems that appear in Appendix B of the Student Edition. 83. Nuclear Physics Problem Solution Manual book pdf free download link book now. Its power source is 11.0 kg of \(\displaystyle ^{238}Pu\), a by-product of nuclear weapons plutonium production. 57. Explain. Paul Peter Urone (Professor Emeritus at California State University, Sacramento) and Roger Hinrichs (State University of New York, College at Oswego) with Contributing Authors: Kim Dirks (University of Auckland) and Manjula Sharma (University of Sydney). (a) Write the complete \(\displaystyle β^−\) decay equation for \(\displaystyle ^{90}Sr\), a major waste product of nuclear reactors. (b) How long ago did it actually have a 4.00-mCi activity? The Galileo space probe was launched on its long journey past several planets in 1989, with an ultimate goal of Jupiter. 45. (c) The two \(\displaystyle γ\) rays must travel in exactly opposite directions in order to conserve momentum, since initially there is zero momentum if the center of mass is initially at rest. Solution Spontaneous radioactive decay occurs only when the decay products have less mass than the parent, and it tends to produce a daughter that is more stable than the parent. 90. The mass of \(\displaystyle ^{222}Ra\) is 222.015353 u. 25. When a nucleus \(\displaystyle α\) decays, does the \(\displaystyle α\) particle move continuously from inside the nucleus to outside? Explain. (a) Write the decay equation for the \(\displaystyle α\) decay of \(\displaystyle ^{235}U\). (d) A solid with high density composed of high-mass atoms. Explain your ordering in terms of how radiation loses its energy in matter. Solution This should confirm that βs travel much faster than αs even when relativity is taken into consideration. Copyright © 2020 NWC Books. \(\displaystyle α\) decay of \(\displaystyle ^{210}Po\), the isotope of polonium in the decay series of \(\displaystyle ^{238}U\) that was discovered by the Curies. Calculate \(\displaystyle BE/A\), the binding energy per nucleon, for \(\displaystyle ^2H\) and compare it with the approximate value obtained from the graph in Figure. (a) Write the complete \(\displaystyle β^+\) decay equation for \(\displaystyle ^{11}C\). (d) Where does the \(\displaystyle ^{234}U\) come from if it is not primordial? 20. 86. For more information contact us at info@libretexts.org or check out our status page at https://status.libretexts.org. This result found in (a) is extremely large. In a \(\displaystyle 3×10^9\)-year-old rock that originally contained some \(\displaystyle ^{238}U\), which has a half-life of \(\displaystyle 4.5×10^9\) years, we expect to find some \(\displaystyle ^{238}U\) remaining in it. Construct a problem in which you calculate the mass of a radioactive isotope you need in order to supply power for a long space flight. 2. The parent nuclide is a major waste product of reactors and has chemistry similar to calcium, so that it is concentrated in bones if ingested (\(\displaystyle ^{90}Y\) is also radioactive.). 68. (a) What is the kinetic energy in MeV of a \(\displaystyle β\) ray that is traveling at \(\displaystyle 0.998c\)? Note that a photon having this energy is difficult to produce and interacts poorly with the nucleus, limiting the practicability of this probe. In the following eight problems, write the complete decay equation for the given nuclide in the complete \(\displaystyle ^A_ZX_N\) notation. 48. 63. Some is absorbed within the source, some is absorbed by the detector, and some does not penetrate the detector. 12. 87. Construct a problem in which you estimate the activity in a cubic meter of earth rock? What is the current? Natural thorium is almost 100% \(\displaystyle ^{232}Th\), with a half-life of \(\displaystyle 1.405×10^{10}y\). What is the mass of the 48Ca in the sample? 81. (b) 2.754 MeV. \(\displaystyle β^−\) decay of \(\displaystyle ^{40}K\), a naturally occurring rare isotope of potassium responsible for some of our exposure to background radiation. \(\displaystyle ^{137}_{55}Cs_{82}→^{137}_{56}Ba_{81}+β^−+\bar{ν_e}\), 52. Explain in terms of the statistical nature of radioactive decay. Verify that this amount of mass converted to energy yields 931.5 MeV. The mass of \(\displaystyle ^{234}Th\) is 234.043593 u. (c) The assumption of \(\displaystyle 1.00μA\) is unreasonably large. Electrical energy is generated thermoelectrically from the heat produced when the 5.59-MeV \(\displaystyle α\) particles emitted in each decay crash to a halt inside the plutonium and its shielding. To do this, identify the values of each before and after the capture. 73. \(\displaystyle β^−\) decay producing \(\displaystyle ^{90}Y\). (b) An extremely large activity, many orders of magnitude greater than permitted for home use. Among the things to consider are the activity per cubic meter, the energy per decay, and the size of the Earth. Solution What types of radiation (if any) do you think these suits protect the worker from, and how? 23. In the following four problems, identify the parent nuclide and write the complete decay equation in the \(\displaystyle ^A_ZX_N\) notation. From inside to out rate of 4140 Bq original activity of the largest nucleus is still much smaller the. Unit is defined to be too low in frequency to be \ ( \displaystyle 2^ { 10 } )! 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nuclear physics problems and solutions pdf

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