Nuclear binding energy 1 Nuclear binding energy Nuclear binding energy is the energy required to split a nucleus of an atom into its component parts. The component parts are neutrons and protons, which are collectively called nucleons. The binding energy of nuclei is always a positive number, since all nuclei require net energy to separate them into individual protons and neutrons. Thus, the mass of an atom's nucleus is always less than the sum of the individual masses of the constituent protons and neutrons when separated. This notable difference is a measure of the nuclear binding energy, which is a result of forces that hold the nucleus together. Because these forces result in the removal of energy when the nucleus is formed, and this energy has mass, mass is removed from the total mass of the original particles, and the mass is missing in the resulting nucleus. This missing mass is known as the mass defect, and represents the energy released when the nucleus is formed. Nuclear binding energy can also apply to situations when the nucleus splits into fragments composed of more than one nucleon, and in this case the binding energies for the fragments (as compared to the whole) may be either positive or negative, depending on where the parent nucleus and the daughter fragments fall on the nuclear binding energy curve (see below). If new binding energy is available when light nuclei fuse, or when heavy nuclei split, either of these processes result releases the binding energy. This energy—available as nuclear energy—can be used to produce nuclear power or build nuclear weapons. When a large nucleus splits into pieces, excess energy is emitted as photons (gamma rays) and as kinetic energy of a number of different ejected particles (fission products, see nuclear fission). Total mass is conserved throughout all such processes, so long as the system is isolated. During each nuclear transmutation, the "mass defect" mass is relocated to, or carried away by, other particles that are no longer a part of the original nucleus. The nuclear binding energies and forces are on the order of a million times greater than the electron binding energies of light atoms like hydrogen.[1] The mass defect of a nucleus represents the mass of the energy of binding of the nucleus, and is the difference between the mass of a nucleus and the sum of the masses of the nucleons of which it is composed. Determining the relevant nuclear binding energy encompasses three steps of calculation, which involves the creation of mass defect by removing the mass as released energy.[2] Introduction Nuclear binding energy is explained by the basic principles involved in nuclear physics. Nuclear energy An absorption or release of nuclear energy occurs in nuclear reactions or radioactive decay; those that absorb energy are called endothermic reactions and those that release energy are exothermic reactions. Energy is consumed or liberated because of differences in the nuclear binding energy between the incoming and outgoing products of the nuclear transmutation.[3] Binding energy per nucleon of common isotopes. Nuclear binding energy 2 The best-known classes of exothermic nuclear transmutations are fission and fusion. Nuclear energy may be liberated by atomic fission, when heavy atomic nuclei like uranium and plutonium are broken apart into lighter nuclei. The energy from fission is used to generate electric power in hundreds of locations worldwide. Nuclear energy is also released during atomic fusion, when light nuclei like hydrogen are combined to form heavier nuclei such as helium. The Sun and other stars use nuclear fusion to generate thermal energy which is later radiated from the surface, a type of stellar nucleosynthesis. In any exothermic nuclear process, nuclear mass may ultimately be converted to thermal energy, which is given off as heat and in doing so, carries away the mass with it. In order to quantify the energy released or absorbed in any nuclear transmutation, one must know the nuclear binding energies of the nuclear components involved in the transmutation. Nuclear and chemical energies Nuclear energy is typically hundreds of thousands or millions of times greater than chemical energy or approximately 1% of the mass energy from the Einstein mass formula. The mass of a proton is : The chemical energy of the hydrogen atom is the separation energy of an electron from a proton. It is given by the Rydberg constant from the Bohr theory of the hydrogen atom : . The relative change of mass is the hydrogen chemical energy divided by its mass, here the proton mass : It is so small as to be unmeasurable directly by weighing, but can be calculated, using the Einstein formula, from the measured chemical energy. Nuclear energy is usually "explained" by a hypothetical strong force. However, it has been shown [4] that it may be obtained by a similar formula with values intermediate between the Einstein mass and the Rydberg constant : This value is not far from the deuteron binding energy, , which is also the neutron-proton separation energy. The relative change in mass is : Knowing the formulas characterizing the nuclear and chemical energies, one obtains their ratio : hundreds of thousands The two preceding calculated values are comparable with the one million and one per cent ratios evaluated from experimental binding energies. The symbols used are Mass energy of the proton Nuclear energy Chemical energy Proton mass Electron mass : Fine structure constant : Nuclear binding energy 3 The nuclear force Electrons and nuclei are kept together by electric attraction (negative attracts positive). Furthermore, electrons are sometimes shared by neighboring atoms or transferred to them (by processes of quantum physics), and this link between atoms is referred to as a chemical bond, and is responsible for the formation of all chemical compounds.[5] The force of electric attraction does not hold nuclei together, because all protons carry a positive charge and repel each other. Thus, electric forces do not hold nuclei together, because they act in the opposite direction. It has been established that binding neutrons to nuclei clearly requires a non-electrical attraction.[5] Therefore, another force, called the nuclear force (or residual strong force) holds the nucleons of nuclei together. This force is a residuum of the strong interaction, which binds quarks into nucleons at an even smaller level of distance. The nuclear force must be stronger than the electric repulsion at short distances, but weaker far away, or else different nuclei might tend to clump together. Therefore it has short-range characteristics. An analogy to the nuclear force is the force between two small magnets: magnets are very difficult to separate when stuck together, but once pulled a short distance apart, the force between them drops almost to zero.[5] Unlike gravity or electrical forces, the nuclear force is effective only at very short distances. At greater distances, the electrostatic force dominates: the protons repel each other because they are positively charged, and like charges repel. For that reason, the protons forming the nuclei of ordinary hydrogen—for instance, in a balloon filled with hydrogen—do not combine to form helium (a process that also would require some to combine with electrons and become neutrons). They cannot get close enough for the nuclear force, which attracts them to each other, to become important. Only under conditions of extreme pressure and temperature (for example, within the core of a star), can such a process take place.[6] Physics of nuclei The nuclei of atoms are found in many different sizes. In hydrogen they contain just one proton, in deuterium or heavy hydrogen a proton and a neutron; in helium, two protons and two neutrons, and in carbon, nitrogen and oxygen - six, seven and eight of each particle, respectively. A helium nucleus weighs less than the sum of the weights of its components. The same phenomenon is found for carbon, nitrogen and oxygen. For example, the carbon nucleus is slightly lighter than three helium nuclei, which can combine to make a carbon nucleus. This illustrates the mass defect. Mass defect The fundamental reason for the "mass defect" is Albert Einstein's famous formula E = mc2, expressing the equivalence of energy and mass. By this formula, adding energy also increases mass (both weight and inertia), whereas removing energy decreases mass. If a combination of particles contains extra energy—for instance, in a molecule of the explosive TNT—weighing it reveals some extra mass, compared to its end products after an explosion. (The weighing must be done after the products have been stopped and cooled, however, as the extra mass must escape from the system as heat before its loss can be noticed, in theory.) On the other hand, if one must inject energy to separate a system of particles into its components, then the initial weight is less than that of the components after they are separated. In the latter case, the energy injected is "stored" as potential energy, which shows as the increased mass of the components that store it. This is an example of the fact that energy of all types is seen in systems as mass, since mass and energy are equivalent, and each is a "property" of the other. The latter scenario is the case with nuclei such as helium: to break them up into protons and neutrons, one must inject energy. On the other hand, if a process existed going in the opposite direction, by which hydrogen atoms could be combined to form helium, then energy would be released. The energy can be computed using E = Δmc2 for each Nuclear binding energy 4 nucleus, where Δm is the difference between the mass of the helium nucleus and the mass of four protons (plus two electrons, absorbed to create the neutrons of helium).