Mean binding energy per nucleon

Figure 11.4 Mean binding energy per nucleon as a function of A. From G. Friedlander, J. W. Kennedy, E. S. Macias, and J. M. Miller, Nuclear and Radio chemistry, copyright 1981 by John Wiley and Sons. Reprinted by permission of John Wiley Sons.

If Ab is divided by the mass number, the mean binding energy per nucleon is obtained, which is a measure of the stability of the nucleus ... 

Figure 2.7. Mean binding energy per nucleon for light nuclides.

Mean binding energy per nucleon Eb/A for nuclei lying in the stability valley as a function of the mass number A. The approximate contribution of different terms in Eq. (2.3) is also shown (Based on Kravtsov 1965)... 

Notice that the loss of mass per nucleon, and hence the binding energy per nucleon, is greater for iron (0.0096 amu) than for helium (0.0076 amu). This means that the iron nucleus is more stable relative to protons and neutrons than the helium nucleus is. If some combination of helium nuclei could be induced to produce an iron nucleus, energy would be given off, which would correspond to the increased stability of the product nucleus per nuclear particle. 

This means that 8.00 MeV of energy per nucleon would be released if gO were formed from free neutrons and protons. The energy required to decompose this nucleus into its components has the same numeric value but is positive. This is called the binding energy per nucleon for ]gO. 

Fig. 2.1 Variation in average binding energy per nucleon as a function of mass number. Note that the energy scale is positive, meaning that the nuclei with the highest values of the binding energies release the greatest amount of energy upon formation.

A better indication of the relative stability of nuclei is obtained when the binding energy is divided by the total number of nucleons to give the binding energy per nucleon, Eg/A. For He the value of Eg/A is 28.3/4 or 7.1 MeV, whereas for it is 1.11 for e bond between the two nucleons. Clearly, the He nucleus is considerably more stable than the nucleus. For most nuclei the values of Eg/A vary in the rather narrow range 5 — 8 MeV. To a first approximation, therefore, Eg/A is relatively constant which means that the... 

Fig. 4. Binding energy per nucleon for 0 calculated for various mean values of the density p (see Eq. (1)). The results of the BHF calculation directly for finite nuclei (solid line) and the various local density approximations (LDA, see text) were obtained for the OBE potential A defined in Table A.l of [13].

At this point we notice that iron-56 has the larger binding energy per nucleon, meaning that more energy is required to separate the iron-56 nucleons than those of carbon-12 and uranium-235. In other words, iron-56 is more stable than the other two elements. 

This means that 4.55 X 10 1 J of energy is released per nucleus formed and that 4.55 X 10 12 J would be req uired to decompose the nucleus into the constituent neutrons and protons. Thus the binding energy (BE) per nucleon is... 

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