Energy from the Nucleus

1. Energy from the Nucleus A deeper understanding of the nucleus

2. Nuclear Stability You might expect that the very large repulsive Coulomb forces between the close packed protons in a nucleus should cause the nucleus to fly apart. Because that does not happen, there must be a counteracting attractive force. The nuclear force is a very short range (about 2 fm) attractive force that acts between all nuclear particles. The protons attract each other by means of the nuclear force, and, at the same time, they repel each other through the Coulomb force. The nuclear force also acts between pairs of neutrons and between neutrons and protons. The nuclear force dominates the Coulomb repulsive force within the nucleus (at short ranges), so stable nuclei can exist.

3. Nuclear Force The nuclear force is independent of charge. In other words, the forces associated with the proton–proton, proton–neutron, and neutron–neutron interactions are the same, apart from the additional repulsive Coulomb force for the proton–proton interaction.

4. Potential Energy (a) Potential energy versus separation distance for a neutron–proton system. (b) Potential energy versus separation distance for a proton–proton system. To display the difference in the curves on this scale, the height of the peak for the proton–proton curve has been exaggerated by a factor of 10. The depth of the n–p potential energy well is 40 to 50 MeV, and there is a strong repulsive component that prevents the nucleons from approaching much closer than 0.4 fm.

5. Stable Nuclei The existence of the nuclear force results in approximately 270 stable nuclei; hundreds of other nuclei have been observed, but they are unstable. A plot of neutron number N versus atomic number Z for a number of stable nuclei is shown here

6. The stable nuclei are represented by the black dots, which lie in a narrow range called the line of stability. Notice that the light stable nuclei contain an equal number of protons and neutrons; that is, N = Z.

7. Also notice that in heavy stable nuclei, the number of neutrons exceeds the number of protons: above Z = 20, the line of stability deviates upward from the line representing N = Z. This deviation can be understood by recognizing that as the number of protons increases, the strength of the Coulomb force increases, which tends to break the nucleus apart.

8. As a result, more neutrons are needed to keep the nucleus stable because neutrons experience only the attractive nuclear force. Eventually, the repulsive Coulomb forces between protons cannot be compensated by the addition of more neutrons. This point occurs at Z = 83, meaning that elements that contain more than 83 protons do not have stable nuclei.

9. Binding Energy • The total mass of a nucleus is less than the sum of the masses of its individual nucleons. Therefore, the rest energy of the bound system (the nucleus) is less than the combined rest energy of the separated nucleons. rest energy (ER ) of a particle: ER = mc2

10. This difference in energy is called the binding energy of the nucleus and can be interpreted as the energy that must be added to a nucleus to break it apart into its components. Therefore, to separate a nucleus into protons and neutrons, energy must be delivered to the system. When separate nucleons are combined to form a nucleus, the energy of the system is reduced. Therefore, the change in energy is negative. The absolute value of this change is called the binding energy. This difference in sign may be confusing. For example, an increase in binding energy corresponds to a decrease in the energy of the system.

11. Binding energy per nucleon Using the conservation of energy and the Einstein mass–energy equivalence relationship binding energies can be calculated for any nucleus. The binding energy per nucleon is plotted for selected stable nuclei here:

12. Fission and Fusion Notice that the binding energy peaks in the vicinity of A = 60. That is, nuclei having mass numbers either greater or less than 60 are not as strongly bound as those near the middle of the periodic table. The decrease in binding energy per nucleon for A >60 implies that energy is released when a heavy nucleus splits, or fissions, into two lighter nuclei. Energy is released in fission because the nucleons in each product nucleus are more tightly bound to one another than are the nucleons in the original nucleus. The important process of fission and a second important process of fusion, in which energy is released as light nuclei combine, shall be considered in more detail later.