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The most convenient unit of energy to use is the electron volt E (14924 10 10 J)(1 eV/160217 10 93149 108 eV 93149 MeV

Hence, 1 u of mass is equivalent to 93149 MeV of energy Figure 30-2 shows how the binding energy per nucleon depends on the mass of the nucleus Heavier nuclei are bound more strongly than lighter nuclei Except for a few nuclei, the binding energy per nucleon becomes more negative as the mass number, A, increases to a value of 56, which is that of iron, Fe The most tightly bound nucleus is 56Fe; thus, nuclei become more 26 stable as their mass numbers approach that of iron Nuclei whose mass numbers are larger than that of iron are less strongly bound, and are therefore less stable A nuclear reaction will occur naturally if energy is released by the reaction; that is, if the nucleus is transformed into one closer to the lowpoint of the graph at A 56 At lower mass numbers, below 56Fe, a nuclear 26 reaction will occur naturally if it increases the atomic mass In the Sun and other stars, hydrogen is converted into helium, carbon, and other heavier elements in a reaction that releases energy, causing the electromagnetic radiation that you experience as visible light

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Average Binding Energy per Nucleon v Number of Nucleons 0 Average binding energy per nucleon (MeV)

you can set it like this:

Number of nucleons (A)

At mass numbers above 56, a nuclear reaction will occur naturally if it decreases the atomic mass When uranium-238 decays to thorium-234, the resulting thorium nucleus is more stable than the uranium nucleus Energy is released in the form of a radioactive particle with mass and kinetic energy Thorium will not spontaneously transform into uranium because energy would have to be added to the nucleus The heaviest nuclei in the periodic table are created in this way, by slamming together smaller nuclei in particle accelerators In general, such heavy elements can exist only for fractions of a second before the nuclei decay into smaller, more stable nuclei In contrast, when small nuclei gain nucleons, the binding energy of the larger nucleus is more negative, and thus, more stable than the sum of the binding energies of the smaller nuclei In the next section, calculations of binding energy will be used to understand nuclear reactions The binding energy explains the energy released when small nuclei fuse, as in stars, and large nuclei split, as in the decay of radioactive elements

Mass Defect and Nuclear Binding Energy Find the mass defect and binding energy of tritium, 3H The mass of the tritium isotope is 3016049 u, the mass of a hydrogen atom 1 is 1007825 u, and the mass of a neutron is 1008665 u

Known:

mass of 1 hydrogen atom 1007825 u mass of 1 neutron 1008665 u mass of tritium 3016049 u binding energy of 1 u 93149 MeV

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Unknown:

Add the masses of the hydrogen atom (one proton and one electron) and two neutrons 1007825 u mass of 1 hydrogen atom: 2017330 u plus mass of 2 neutrons: total mass of nucleons: 3025155 u The mass defect is equal to the actual mass of tritium less the mass of the sum of its parts 3016049 u mass of tritium: 3025155 u less mass of nucleons: mass defect: 0009106 u The binding energy is the energy equivalent of the mass defect E (mass defect in u)(binding energy of 1 u) E ( 0009106 u)(93149 MeV/u) Substitute mass defect 0009106 u, binding energy per u 93149 MeV 84821 MeV

Are the units correct Mass is measured in u, and energy is measured in MeV Does the sign make sense Binding energy should be negative Is the magnitude realistic According to Figure 30-2, binding energies per nucleon in this range are between 2 MeV and 3 MeV, so the answer for three nucleons is reasonable

Use these values to solve the following problems: mass of hydrogen 1007825 u, mass of neutron 1 u 93149 MeV

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1008665 u,

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