Final Exam • Wed Dec. 9 from11:30am-2:29pm York 2722 • Will cover all the course material including the last week • 25 questions –multiple choice. • You are allowed to bring 1sheet of paper with equations on both sides, scratch paper for calculation, calculator • You must bring a scantron form and a picture id. 10.1 Nuclear energy Nuclear Fission Nuclear Fusion Curve of the Binding Energy/nucleon Natural radioactivity fission Many elements found in nature are unstable and decay emitting radioactivity. fusion These include Uranium, 238U , Radon 224Ra and Potassium 40K. Carbon 14C, The half lives of natural radio-isotopes are long. Not useful as sources for power. Low Power output. Energy can be released by nuclear reactions of Fusion and Fission Nuclear Power Induced Nuclear reactions Can result in short half lives- fast reactions-high energy density • Nuclear power requires induced nuclear Combining nuclei (Fusion) fission. 22DD+ ⎯⎯→+ 31 TH+ Energy • Nuclear fission can be induced by 11 11 neutrons in a chain reaction. • Nuclear fusion can be induced by Neutron reactions (Fission) collisions at high temperature. 1 235 141 92 1 09256360nU+⎯⎯→++ BaKr3n+ Energy 1 Fission of Uranium Fission of Uranium Strassman and Hahn (1939) Fermi (1936) Irradiated Uranium with neutrons Bombard uranium with Fast Slow Detected Barium neutrons neutrons neutrons Conclude Uranium nuclei splits into smaller fragments Found induced radioactivity 1n+⎯⎯ 235 U→+ 141 Ba other _products Neutron parafilm uranium “Transuranium elements” 09256 Source (radon+Be) Liquid Drop model- Nuclear Chain reaction Explained fission due to the instability of the higher larger nucleus. -12 Lise Meitner T1/2 ~10 s 1235 236 09292nU+⎯⎯→⎯⎯ U→ Ba + products ∆E (average) =208 MeV Chain Reaction binding of 1 neutron releases ~3 neutrons Each neutron can initiate another reaction Two major isotopes of Uranium Critical Condition for Chain reaction 235U (0.7%) Fissionable upon neutron capture 235U (Fission) n n 238 U (99.3%) Non-Fissionable upon neutron capture n 235 U (Escape) n 238U(Capture) Nuclear reactor Reproduction constant K = no. of neutrons that produce a new fission event K=1 ( self –sustained reaction) 2 Centrifuge separation of Enriched 235U isotopes Natural Uranium is a mixture of 235U (0.7%) and 238U(99.3%) Most Uranium nuclear reactors use uranium enriched in 235U. (2-3%) Nuclear weapons used highly enriched 235U. (~90%) Enrichment done by mass separation. Gaseous diffusion Centrifuge process. centrifugal Laser separation separation gaseous UF6 Nuclear reactor Nuclear reactor fast neutrons must be slowed down to react efficiently. Moderator- slows neutrons to thermal velocities. Control rods- neutron absorbers to control the level of neutrons Critical condition. – When each neutron released initiates a new reaction. Plutonium Question How many gallons of gasoline (1.3x108 J of energy/gallon) Plutonium is a fissionable material created in would be equivalent to a kg of Uranium? ∆E=208MeV a nuclear reactor. No. of fissionable nuclei =N m ⎡ 1kg ⎤ 238 1 239 − N = (fraction235U)( ) = (0.0072) = 1.8x1022 mass / atom ⎢238u(1.66x10−27 kg/u)⎥ 92Un+⎯⎯ 0→+ 94 Pu2e ⎣ ⎦ Energy released = E = N(∆E) 239 Pu can be made into nuclear bombs. 22 6 −19 11 E = N(∆E) = 1.8x10 (208x10 eV)[1.6x10 J/ eV]= 6x10 J E Pu can be chemically separated from U in spent fuel gallons of gasoline =V= rods from nuclear reactors. E / gallon E 6x1011J = = 4.6x103 gallons E / gallon 1.3x108 J/ gallon 3 Nuclear Fusion Nuclear Fusion High energy required to bring charged nuclei close together Fusion of small nuclei releases energy v +Z +Z +Z +Z 22 3 1 -15 11DD+⎯⎯→+ 2 Hen 0 ∆E= 3.27 MeV ~10 M Requirements for fusion 22DD 31 TH ∆E= 4.03 MeV 11+⎯⎯→+ 11 High Temperatures (T~ 108 K) 23 4 1 High density (n) for long time (τ) 11DT+⎯⎯→+ 2 Hen 0 ∆E=17.6 MeV Lawson Criterion nτ> 1014 s/cm3 Plasma Fusion Laser fusion- Magnetic Confinement Inertial Confinement Plasma is a gas of ionized atoms Heated to high temperature Confined by magnetic forces Deuterium pellet Lawrence Livermore Lab T~108 K Princeton Tokomak Nova Laser Short times long times High density low density Prospects • Nuclear energy by fission is currently a source of much of the electrical power (~15% USA). • The problems with nuclear energy – Radioactive waste disposal – Atomic bomb threats • Nuclear fusion reactions promise an unlimited source of energy. – Controlled fusion reactions are not yet possible. 4.