lecture 23sf - Nuclear Binding Energy Consider process of...

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Nuclear Binding Energy Consider process of forming a C-12 atom from protons, neutrons, electrons: 6p + 6n + 6e → 12 6 C Mass of 12 6 C : 12.00000 u (exactly 12) or 12.0000 Masses of individual particles: proton 1.00727 u or neutron 1.00866 u or electron 0.00055 u or 6p + 6n + 6e = 12.0989 u or “Loss” of mass = 0.0989 u or What is the explanation for this apparent violation of the Law of Conservation of Matter? How can mass be lost? Energy-mass equivalence expressed by Einstein formula: E = mc 2 . E corresponds to energy released in forming the nucleus from its particles. This is the binding energy of the nucleus m is the “loss” of mass in the process. What is the binding energy of 12 6 C according to this data? E = 1000 0989 . 0 (2.998 x 10 8 ) 2 = 8.89 x 10 12 = 8.89 x 10 9 Binding Energy could be expressed as MeV where 1 Mev = 1.602 x 10 -13 Joule Mev is on a per nucleus basis (not per mol) 8.89 x 10 12 x nuclei 10 x 022 . 6 mol 1 23 x J 10 x 602 . 1 Mev 1 13 - = 92.1 MeV
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Another useful way to calculate binding energy in MeV is to find the equivalent MeV for each u (atomic mass unit) 1.00 u x u kg 10 x 6607 . 1 27 - x (2.998 x 10 8 ) 2 = 1.4924 x 10 -10 J 1.4924 x 10 -10 J x J 10 x 602 . 1 MeV 1 13 - = 931.5 MeV So each atomic mass unit is equivalent to 931.5 Mev of energy. Knowing this conversion factor: 931.5 u Mev , we could directly solve for the binding energy of 12 6 C. The “loss” of mass was 0.0989 u. Therefore: 0.0989 u x 931.5 u Mev = 92.1 Mev To compare the binding energy of different nuclei, we calculate where “nucleon” means any nuclear particle, proton or neutron. For carbon-12, there are 6 protons and 6 neutrons: 12 nucleons For carbon-12: Nucleon energy Binding = nucleon 12 Mev 1 . 92 = 7.68 Figure 19.7 of the text shows a curve of binding energy, plotting binding energy per nucleon vs. mass number. The curve rises steeply at first, maximizing on mass number 56 (iron) which is the nucleus with the highest binding energy. The curve then gradually decreases, meaning that heavier nuclei than iron are less strongly held together. Consider an ordinary chemical reaction, such as the combustion of methane, CH 4 CH 4 (g) + 2O 2 (g) → CO 2 (g) + 2H 2 O(g) H = -802 kJ Would there be any “loss” of mass due to E = mc 2 in this reaction? The binding energy of 12 6 C was 8.9 x 10 9
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The heat released in burning CH 4 is 802 There is much less energy released per mole in chemical reactions than in nuclear reactions.
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