Chapter 21 Worksheet #3 Name __________________________ The mass of a stable nucleus is less than the sum of the masses of the protons and neutrons that make up that nucleus. The difference in mass is called the mass defect (Δm): Δm = [Zmproton + (A-Z)mneutron] - (matom - Zmelectron) = [Zmproton + (A-Z)mneutron] - mnucleus Δm = [Z(mH-atom) + (A-Z)mn] - matom Einstein relation: E = mc2 (mass/energy equivalency); c is the speed of light (3.00x108 m/s) The energy equivalence of the mass defect is called the nuclear binding energy. BE = Δmc2 (usually in MeV; 1 MeV = 1.60x10-13 joules) (931.5 MeV = 1 amu; 1 amu = 1.50x10-10 joules) The binding energy represents the amount of energy that must be supplied to break the nucleus into its individual protons and neutrons. A more useful quantity for comparing the stability of nuclides is the binding energy per nucleon. BE BE nucleon # protons#neutrons The greater the BE/nucleon, the more stable the nucleus. Example: Determine the BE and BE/nucleon for Osmium-190. m(190Os) = 189.95863 amu; m(1n) = 1.00867 amu; m(1H) = 1.00783 amu The binding energy per nucleon generally falls around 8 MeV. A plot of BE/nucleon vs Z shows that the most stable nuclei occur around Z = 26 (see text, Fig. 21.8, page 983). Fe-56 is the most stable nucleus in the universe. The existence of a maximum in this curve indicates that energy is released in either a fission or fusion process in which more stable nuclei are produced. Fission - the splitting of a heavy nucleus into two nuclei with smaller mass numbers (with the concomitant release of one or more neutrons). For example: 239 1 144 94 1 94 Pu0n 58Ce36Kr 20 n (this is only one of many possible fission outcomes) Fusion - the combining of two light nuclei to form a heavier, more stable nucleus. For example: 2 3 4 1 1 H1H2 He0n Because of the large binding energies involved in a nucleus, both fission and fusion involve energy changes of more than a million times larger than those energy changes associated with chemical reactions. Calculate the amount of energy released (in kJ) when 1 mole (235 g) of 235U fissions to form 137Te + 96Zr. m(235U) = 235.043915 amu m(1n) = 1.0086654 amu m(137Te) = 136.925449 amu m(96Zr) = 95.908286 amu Calculate the mass (in g) of methane (CH4) required to yield the same amount of energy as the fissioning 235 of one mole of U when methane is combusted to produce CO2(g) and H2O(l). .