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Lecture 19

# Lecture 19 - Energy in Nuclear Reac/ons •  High...

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Unformatted text preview: Energy in Nuclear Reac/ons •  High amount of energy is stored in nuclei. •  E = mc2 relates directly to the calcula/on of this energy. •  In chemical reac/ons the amount of mass converted to energy is minimal. •  Nuclear reac/ons are linked to nuclear mass changes. The Interconversion of Mass and Energy The mass of the nucleus is less than the combined masses of its nucleons. The mass decrease that occurs when nucleons are united into a nucleus is called the mass defect. The mass defect (Δm) can be used to calculate the nuclear binding energy in MeV (mega ­electron volts). 1 amu = 931.5 x 106 eV = 931.5 MeV Energy in Nuclear Reac/ons The mass change for the decay of 1 mol of uranium ­238 is −0.0046 g. The change in energy, ΔE = (Δm) c2 ΔE = (−4.6 × 10−6 kg)(3.00 × 108 m/s)2 ΔE = −4.1 × 1011 J Nuclear binding energy (BE) is the energy required to break up a nucleus into its component protons and neutrons. BE + 19F 91p + 101n 1 0 E = mc2 BE = 9 x (p mass) + 10 x (n mass) – 19F mass BE (amu) = 9 x 1.007825 + 10 x 1.008665 – 18.9984 BE = 0.1587 amu 1 amu = 1.49 x 10 ­10 J Converts amu to kg and mul/plies by c2 BE = 2.37 x 10 ­11J binding energy binding energy per nucleon = number of nucleons = 2.37 x 10 ­11 J 19 nucleons = 1.25 x 10 ­12 J 23.2 Sample Problem 23.6 PROBLEM: PLAN: CalculaAng the Binding Energy per Nucleon Iron ­56 is an extremely stable nuclide. Compute the binding energy per nucleon for 56Fe and compare it with that for 12C (mass of 56Fe atom = 55.934939 amu; mass of 1H atom = 1.007825 amu; mass of neutron = 1.008665 amu). Find the mass defect, Δm; mul/ply that by the MeV equivalent and divide by the number of nucleons. SOLUTION: Mass Defect = [(26 x 1.007825 amu) + (30 x 1.008665 amu)]  ­ 55.934939 Δm = 0.52846 amu Binding energy = (0.52846 amu)(931.5 MeV/amu) 56 nucleons = 8.790 MeV/nucleon 12C has a binding energy of 7.680 MeV/nucleon, so 56Fe is more stable. Energy in Nuclear Reac/ons For example, the mass change for the decay of 1 mol of uranium ­238 is −0.0046 g. The change in energy, ΔE, is then ΔE = (Δm) c2 ΔE = (−4.6 × 10−6 kg)(3.00 × 108 m/s)2 ΔE = −4.1 × 1011 J Fission •  Nuclear ﬁssion occurs when a large unstable nucleus is bombard with a neutron. •  This collision causes the larger element to break apart into two or more elements. •  These reacAons release a lot of energy. •  One can calculate the amount of energy produced during a nuclear reacAon using an equaAon: E=mc2 Nuclear Fission •  How does one tap all that energy? •  Nuclear ﬁssion is the type of reac/on carried out in nuclear reactors. Nuclear Fission •  Bombardment of the radioac/ve nuclide with a neutron starts the process. •  Neutrons released in the transmuta/on strike other nuclei, causing their decay and the produc/on of more neutrons. •  This process con/nues in what is called a nuclear chain reac/on. Nuclear Fission •  If there are not enough radioac/ve nuclides in the path of the ejected neutrons, the chain reac/on will die out. •  Therefore, there must be a certain minimum amount of ﬁssionable material present for the chain reac/on to be sustained: Cri/cal Mass. Nuclear Reactors In nuclear reactors the heat generated by the reac/on is used to produce steam that turns a turbine connected to a generator. Nuclear Reactors •  The reac/on is kept in check by the use of control rods. •  These block the paths of some neutrons, keeping the system from reaching a dangerous supercri/cal mass. Nuclear Fusion •  Fusion is when lighter nuclei are fused into a heavier nucleus. •  Fusion powers the sun. Four isotopes of hydrogen ­1 are fused into a helium ­4 with the release of a tremendous amount of energy. •  On Earth, H ­2 (deuterium) & H ­3 (triAum) are used. Nuclear Fusion Fusion small nuclei combine 2H + 3H 4He + 1n + 1 1 2 0 Occurs in the sun and other stars Nuclear Fusion •  The ﬁrst demonstraAon of nuclear fusion – the hydrogen bomb – was conducted by the military. –  A hydrogen bomb is approximately 1,000 Ames as powerful as an ordinary atomic bomb. •  The goal has been the controlled release of energy from a fusion reacAon. –  If the energy can be released slowly, it can be used to produce electricity. –  It will provide an unlimited supply of energy that has no wastes to deal with or contaminants to harm the atmosphere. –  The 3 problems are: temperature, Ame, containment Nuclear Fusion •  Temperature –  Hydrogen isotopes must be heated to 40,000,000 K (ho]er than the sun). –  Electrons are gone…all that’s le` is posiAvely charged plasma. •  Time –  The plasma needs to be held together for about one second at 40,000,000 K. •  Containment –  Everything is a gas…ceramics vaporize. A magneAc ﬁeld could be used but the plasma leaks from those as well. Nuclear Fusion •  Fusion would be a superior method of genera/ng power. –  The good news is that the products of the reac/on are not radioac/ve. –  The bad news is that in order to achieve fusion, the material must be in the plasma state at several million kelvins. –  Tokamak appara/ like the one shown at the right show promise for carrying out these reac/ons. –  They use magne/c ﬁelds to heat the material. Nuclear binding energy per nucleon vs Mass number •  •  •  •  Greater the binding energy per nucleon, more stable is that nuclide. The binding energy per nucleon peaks at A ~60. In ﬁssion, heavier nucleus splits into stable lighter ones of A ~60. In fusion, lighter nuclei combine to form heavier ones of A ~60. ...
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