Chapter 28 Nuclear Fission Fission, Fusion, Binding Energy, and Half Life How would we write this Nuclear Reaction? Uranium Isotopes Naturally occurring Uranium contains two major isotopes Uranium-238 (99.3%) Uranium-235 (0.7%) As it turns out the only isotope of Uranium that undergoes fission is Uranium-235 Why do you think U-235 can undergo fission? 235 U Fission 235 92U U + 1 0n 236 92U * and 10-14 seconds later... 236 92U * 92 36Kr + 141 56Ba + 3 1 0n + ENERGY 50 possible sets of fission products (sum of atomic numbers = 92) 3 neutrons released for ONE 235 92U each neutron can split another 235 92U CHAIN REACTION POSSIBLE If amount of 235 92U U is sufficient (CRITICAL MASS) then the number of neutrons generated is high enough to result in a nuclear explosion ) Nuclear Fission Representation of a fission chain process. The Fission Chain Reaction Begins 1
The Critical Mass Needed for the Chain Reaction 2
Are there other Fuels for the Fission Chain Reaction? UraniumUranium -235 235.. (Keep in mind, the abundant form of Uranium found in nature is UraniumUranium-238 (~99%). PlutoniumPlutonium -239 but Plutonium Plutonium-239 is scarce now what? Here s what scientists discovered during World War II: 238 U 92 239 U 92 239 U 92 239 Np 93 239 Np 93 239 Pu 94 + 1 n 0 + γ + + 0 β -1 0 β -1 Development of the Atomic Bomb During WW2 the American set up a secret project called the Manhattan Project recruiting all the best physicists and nuclear chemists available By 1945 they developed two types of nuclear bombs A U-235 fission bomb and a Pu-239 fission bomb Little Boy and Fat Man The Arrangement of Uranium in the First Atomic Bombs 10 feet 3
Arranging U-235 to get a Controlled Nuclear Reaction Arrangement of U-235 in a critical mass, where there s enough U-235 in a small space so that the neutrons cause a chain reaction, would be difficult to control in a nuclear power plant. How can this conversion of small amounts of mass into great amounts of energy be used to produce electricity? In the 1930, Enrico Fermi, an Italian Physicist, discovered that Uranium can be arranged in what he called a Fission Pile, where the Uranium would be arranged in rows, or in a lattice, so that the fission reaction could be controlled. Arranging U-235 to get a Controlled Nuclear Reaction By arranging the Uranium fuel in a lattice structure, CONTROL RODS could be inserted between the Uranium fuel rods to stop the flow of neutrons flowing between the rods, and thus, slowing/stopping the reaction. Water is used to slow the neutrons down, within the reactor, so that they are more likely to strike the Uranium fuel rods water is the MODERATOR, which is another discovery by Fermi. Arranging U-235 to get a Controlled Nuclear Reaction By arranging the Uranium fuel in a lattice structure, there is NO POSSIBILITY of an uncontrolled nuclear explosion, like in a nuclear warhead or bomb. Simply stated, there Uranium is not in a close-enough proximity for an uncontrolled chain reaction, or blast. So, this is an important point: the threat of a nuclear explosion, within a nuclear power plant, is an imagined danger. A Schematic of a Nuclear Power Plant Walls of reactors are made of Graphite, which slows down the neutrons, increasing the chance that neutrons will strike U-235. Control Rods made of Cadmium or Boron, which absorb large quantities of neutrons, and stop the flow of neutrons w/o dissipation of energy. Also use water as a moderator to slow down fast moving neutrons Modern reactors have a containment building make of 6 feet of concrete, used to contain radioactive material in the event of an accident. A Schematic of a Nuclear Power Plant Nuclear Fission & POWER With a Fission Pile, its impossible to have a Nuclear Explosion. What type of Explosion is possible? Currently about 103 nuclear power plants in the U.S. and about 435 worldwide. 17% of the world s energy comes from nuclear. http://www.nrc.gov/reading-rm/basic-ref/students/reactors.html 4
We ll take a closer look at Nuclear Power Plant Mishaps in a bit Nuclear Fusion Fusion small nuclei combine 2 H + 3 H 4 He + 1 n + 1 1 2 0 Energy Occurs in the sun and other stars Nuclear Fusion Fusion Excessive heat can not be contained Attempts at cold fusion have FAILED. Hot fusion is difficult to contain Recall Mass Defect It is experimentally observed that the mass of an atom (containing neutrons) is always slightly less than the sum of the masses of its component particles. The difference between the atomic mass and the sum of the masses of its protons, neutrons, and electrons is called the mass defect. Can we calculate the Energy given off by a nuclear reaction based on the weight difference from reactants to products based on Einstein s Equation, E = mc 2? Calculation of Nuclear Energy Released Calculation of Binding Energy Calculate the energy released (per mole of tritium consumed) for the fusion reaction of tritium and deuterium, The molar nuclear mass of carbon-14 is 14.003241 g/mol. 3 2 4 1 The molar mass of a proton is 1.007825 g/mol. The molar 1H + 1H 2He + 0n mass of a neutron is 1.008665 g/mol. Calculate the given the following molar masses of nucleons and nuclei. (c = binding energy of the C-14 nucleus (c = 3.00 10 8 m/s). 3.00 10 8 m/s) Mass Reactants = 3.01605 + 2.0140g mass (g/mol) Mass Reactants = 5.03005g C-14 has 6 protons and 8 neutrons: particle Mass Products = 4.00260 + 1.008665g Mass C-14 should be (6 x 1.007825)+(8 x 1.008665) proton 1.007825 Mass Products = 5.011265 g Mass C-14 should be = 14.11627 neutron 1.008665 deuterium 2.0140 Mass Diff. = Mass Reactants Mass Mass Defect = 14.11627 14.003241 = 0.113029 grams Products Mass Difference = 0.018785 g Mass Defect = 1.13029 x 10-4 kg tritium 3.01605 Mass Difference = 1.8785x10-5 kg E = mc 2 = 1.13029 x 10-4 kg x (3x10 8 m/s) 2 helium 4.00260 E = mc 2 = 1.8785x10-5 kgx(3x10 8 m/s) 2 E =1.02 x 10 kg-m 2 /s 2 = 1.02 x 10 J E = 1.69 x 10 kg-m 2 /s 2 = 1.69 x 10 J 5
Calculation of Binding Energy Calculate the Mass Defect, and the Binding Energy (in Joules) for 11 5B, the Boron isotope (including the electrons) with a weight of 11.05113 grams/mole. The mass of a proton, neutron, and electron are 1.0073, 1.0087, and 0.00055 grams/mole, respectively. B-11 has 5 protons, 5 electrons, and 6 neutrons: Mass B-11 should be (5 x 1.0073)+(5 x 0.00055)+(6 x 1.0087) Mass B-11 should be = 11.09145 Mass Defect = 11.09145 11.05113 = 0.04032 grams Mass Defect = 4.032 x 10-5 kg E = mc 2 = 4.032 x 10-5 kg x (3x10 8 m/s) 2 E =3.63 x 10 12 kg-m 2 /s 2 = 3.63 x 10 12 J Binding Energy Worksheets (2) Half-Life Half-Life HALF-LIFELIFE is the time that it takes for 1/2 a sample to decompose. The rate of a nuclear transformation depends only on the reactant concentration. Decay of 20.0 mg of 15 O. What remains after 3 half-lives? lives? After 5 half-lives? lives? Kinetics of Radioactive Decay For each duration (half-life), life), one half of the substance decomposes. For example: Ra-234 has a half-life life of 3.6 days If you start with 50 grams of Ra-234 Half-Life of Radioisotopes Half life life is the time required for one-half of any given quantity of isotope to decay After 3.6 days > 25 grams After 7.2 days > 12.5 grams After 10.8 days > 6.25 grams 6
Learning Check! Learning Check! The half life of I-123 is 13 hr. How much of a 64 mg sample of I-123 is left after 39 hours? The half life of I-123 is 13 hr. Only 4 mg are present from a sample that had originally contained 128 mg sample of I-123. How old is the sample? How Old is Oetzi, the Iceman? Oetzi the Iceman was discovered on the border between Italy and Austria in 1991, in the Otztal Alps, partially submerged in a melting glacier. It s estimated that he is from the Neolithic age, some 5300 years ago. How Old is Oetzi, the Iceman? Oetzi was discovered in an extraordinarily warm summer season, which led to abnormal melting of glacier ice. It s estimated that Oetzi, along with animals and plants from his time, were covered by a sudden, deep snow, followed by a prolonged cold period. Examination of the body suggests that Oetzi died from an arrow wound to his back/shoulder. How can we estimate his age using the Half life of C-14. Radiocarbon (C-14) Dating How Old is Oetzi, the Iceman? Radioactive C-14 is formed in the upper atmosphere by nuclear reactions initiated by neutrons in cosmic radiation 14 7 N + 1 on 14 6C + 1 1H The C-14 is oxidized to CO 2, which circulates through the biosphere. When a plant dies, the C-14 is not replenished. But the C-14 continues to decay with t 1/2 = 5730 years. Activity of a sample can be used to date the sample. How much C-14 would be remaining in Oetzi s bones, given his estimated age of 5300 years? The T 1/2 of C-14 is 5730 years. 7
C-14 Dating Solves The Shroud of Turin (Torino) Question The Shroud of Turin (Torino) The Shroud bearing the image of Jesus should be approximately 2000 years old C-14 analysis revealed the presence of 92% of the original amount of C-14 This decrease of 8% corresponds to a time period of about 700 years Learning Check! The C-14 content of a fossilized bone is 12.5% of that of a live bone. Knowing that the t 1/2 of C-14 is 5730 years, how old is the artifact? How Old is the Earth? Perhaps the Half life of naturally occurring U-238 can help us U-238 that is present in certain rocks slowly decays to Pb-206 by the following Radioactive Decay Series: What is happening during each decay in the sequence? http://wps.prenhall.com/wps/media/objects/607/621588/decayseriesactivity.html How Old is the Earth? How Old is the Earth? As time progresses the amount of U-238 decreases and Pb-206 increases Most abundant form of Pb is Pb-207 By measuring the ratio of Pb-206 / Pb-207, scientists can determine the age of a rock The oldest rocks can then be used to determine the minimum age of the Earth By dating rocks from the Moon even better estimates can be obtained! Why? 206 Pb/ 207 207 Pb natural ratio determined from Fe meteorites (don t have U, therefore the 206 Pb/ 207 Pb ratio = original 206 Pb/ 207 Pb ratio when Earth formed) 8
The Coinium Activity Using a fictitious, naturally radioactive isotope called Coinium, you ll estimate the Half life of the isotope, and plot it s radioactive decay in Excel. From the best fit line, you should be able to graphically estimate the half-life life, or time required to go from 100% to 50%, 50% to 25%, etc. Nuclear Medicine: Imaging Thyroid imaging using Tc-99m TcO4-, a monovalent anion which has a size similar to iodide (iodine). As a result it is taken up by the thyroid iodine pump (see radionuclide thyroid imaging) but not bound to the organic structures into which iodine is incorporated to produce thyroid hormone. Food Irradiation Geiger Counter Used to detect radioactive substances Food can be irradiated with γ rays from 60 Co or 137 Cs. Irradiated milk has a shelf life of 3 mo. without refrigeration. USDA has approved irradiation of meats and eggs. Effects of Radiation 9
Nuclear Chemistry & t 1/2 Worksheets (2) 10