Homework 1 Solutions Due Wednesday 1 27 1 Read the article Isaac Asimov The Future of Energy Climate Education and Humanity in the course s portal In no more than one page answer the following a What predictions by Asimov were realized 2 b What predictions by Asimov have not been realized 2 c Discuss what you agree with and disagree with Asimov about the future of humanity 3 Realized predictions i Moon landings and resistance to space travel ii Energy prices will continue to increase iii Lower birth rates iv Women s lib end of sexism getting there v Continuing education Unrealized predictions i We will run out of fossil fuels ii Climate will continue to get colder iii Seven billion people by 2000 with stagnant food supplies leading to global famines iv Multiple mothers rare v End of ageism racism war vi Education for all vii Manned based on the Moon 2 Calculate the speed in meters per second of neutrons possessing the following energies a Fast neutron from fission at 2 MeV 1 b Intermediate energy neutron at 10 keV 1 c Thermal energy neutrons at 0 025 eV 1 Fast neutron energies E 12 mv 2 2 2 10 6 eV 1 61 10 12 erg 2E eV v 1 96 10 7 m s 24 m 1 675 10 g Intermediate neutron energies 2 10 10 3 eV 1 61 10 12 erg 2E eV v 1 39 10 6 m s 24 m 1 675 10 g Thermal neutron energies 2 0 025eV 1 61 10 12 erg 2E eV v 2 192 10 3 m s 2200 m s 24 m 1 675 10 g Homework 2 Solutions Due Friday 1 29 Access the Table of the Nuclides and data mine for the following information about the naturally occurring isotopes of the given elements of interest in nuclear power generation a Natural abundances in atomic percent a o b Atomic mass in atomic mass units amu Uranium Thorium Lithium Carbon Hydrogen Lead Beryllium Boron Cadmium Sodium Isotope U 234 U 235 U 238 Natural abundance a o 0 0055 0 72 99 2745 Th 232 100 Li 6 Li 7 7 5 92 5 C 12 C 13 98 89 1 11 0 0000000 12 000000 0 0000000 12 0033548 H 1 H 2 99 985 0 015 0 0000000 1 0078750 0 0000000 2 0141018 Pb 204 Pb 206 Pb 207 Pb 208 1 4 24 1 22 1 52 4 Be 9 100 B 10 B 11 19 9 80 1 Cd 106 Cd 108 Cd 110 Cd 111 Cd 112 Cd 113 Cd 114 Cd 116 1 25 0 89 12 49 12 80 24 13 12 22 28 73 7 49 Na 23 100 Atomic mass amu 234 0409456 0 0000021 235 0439231 0 0000021 238 0507826 0 0000021 0 0000022 232 0380504 6 0151223 0 0000005 0 0000005 7 0160040 203 9730288 205 9744490 206 9758806 207 9766359 0 0000031 0 0000031 0 0000031 0 0000031 0 0000004 9 0121821 10 0129370 0 0000004 0 0000005 11 0093055 105 9064580 107 9041834 109 9030056 110 9041816 111 9027572 112 9044009 113 9033581 115 9047554 0 0000065 0 0000061 0 0000032 0 0000032 0 0000030 0 0000030 0 0000030 0 0000035 0 0000002 22 9897697 Homework 3 Solutions Due Monday 2 1 If a single fission reaction produces about 180 MeV of energy excluding the unrecoverable energy of antineutrinos use Avogadro s law to calculate the number of grams of the fissile elements that would release 1 kT of TNT equivalent energy that is equal to 1012 calories 1 U235 2 Pu239 3 U233 4 Np237 NM m We know that the energy release needed Av and so m Av M is 1kT of TNT so the equivalent number of nuclei required can be calculated using a simple unit conversion From Avogadro s law N 1012 cal 2 6 10 25 MeV 1 fission N 1kT 1 44 10 23 nuclei 1kT 1012 cal 180MeV Now we just need to calculate the mass in grams of the following fuels for a given value of N 1 U235 1 44 10 m 23 g nuc 235 mol 6 02 10 23 nuc mol 56 21g 2 Pu239 1 44 10 m 23 g nuc 239 mol 6 02 10 23 nuc mol 57 17g 3 U233 1 44 10 m 23 g nuc 233 mol 6 02 10 23 nuc mol 55 73g 4 Np237 1 44 10 m 23 6 02 10 g nuc 237 mol 23 nuc mol 56 69g Homework 4 Solutions Due Monday 2 8 The yield from the Hiroshima gun barrel device was 12 5 kT of TNT equivalent and the yield from the Nagasaki implosion device was 22 kT of TNT equivalent Assuming that one critical mass of lead reflected U235 Oralloy at about 30 kg and one critical mass of Pu239 at about 10 kg were used to generate these yields compare the energy release efficiencies of the two devices as the fraction or percentage of the fissile material converted into energy in the case of the gun barrel versus the implosion process We are using the same equations that we used in HW 3 to convert energy released into mass consumed For the Hiroshima gun barrel device 1012 cal 2 6 10 25 MeV 1 fission N 12 5kT 1 8 10 24 nuclei 1kT 1012 cal 180MeV g 1 8 10 24 nuc 235 mol m 702 66g nuc 6 02 10 23 mol So the efficiency can be calculated as mconverted 702 66g 0 0234 2 34 mtotal 3 10 4 g Similarly for the Nagasaki implosion device 1012 cal 2 6 10 25 MeV 1 fission N 22kT 3 18 10 24 nuclei 12 1kT 10 cal 180MeV g 24 3 18 10 nuc 239 mol 1261 61g m nuc 6 02 10 23 mol So the efficiency can be calculated as mconverted 1 262 10 3 g 0 1261 12 61 mtotal 1 10 4 g So in the case of these two devices the implosion device dropped on Nagasaki was more efficient than the gun barrel device dropped on Hiroshima Homework 5 Solutions Due Monday 2 8 Calculate the Q values or energy releases in MeV from the following nuclear reactions In order to calculate Q values first we need to balance the equation using conservation of charge and mass Then we use the mass energy relationship given by the following equation Note that all masses are recorded to at least the fourth decimal place Masses are taken from KAERI Q m a b m c d amu 931 481 MeV amu 1 1 D2 1 T 3 0 n1 2 He 4 DT fusion reaction Q m 1 D2 1 T 3 m 0 n1 2 He 4 amu 931 481 MeV amu Q 2 0141018 3 0160493 1 0086649 4 0026032 amu 931 481 MeV amu Q 17 59MeV 2 1 D2 1 D2 1 H1 1 T 3 Proton branch of the DD fusion reaction Q m 1 D2 1 D2 m 1 H1 …