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Because energy has to be added to take a nucleus apart, the mass of the assembled nucleus is less than the sum of the masses of the nucleons that compose it For example, the helium nucleus, 4He, consists of two protons and two 2 neutrons The mass of a proton is 1007276 u The mass of a neutron is 1008665 u If the mass of the helium nucleus were equal to the sum of the masses of the two protons and the two neutrons, you would expect that the mass of the nucleus would be 4031882 u Careful measurement, however, shows that the mass of a helium nucleus is only 4002603 u The actual mass of the helium nucleus is less than the mass of its constituent parts by 0029279 u The difference between the sum of the masses of the individual nucleons and the actual mass is called the mass defect Mass spectrometers usually measure the masses of isotopes; that is, the nuclides with all their electrons When calculating the mass defect of a nucleus, one must make sure that the mass of the electrons is accounted for properly Thus, the mass of hydrogen (one proton and one electron) usually is given in mass-defect problems

Masses normally are measured in atomic mass units It will be useful, then, to determine the energy equivalent of 1 u (16605 10 27 kg) To determine the energy, you must multiply the mass by the square of the speed of light in a vacuum (29979 108 m/s) This is expressed to five significant digits E mc2 (16605 10 27 kg)(29979 108 m/s)2 14924 10 10 kg m2/s2 14924 10 10 J

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

4:

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

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

Number of nucleons (A)

Incidentally, many end users prefer to see dates on columns rather than on rows, so maybe the first query looks a little better

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

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