Nuclear binding energy

Nuclear binding energy in experimental physics is the minimum energy that is required to disassemble the nucleus of an atom into its constituent protons and neutrons, known collectively as nucleons. The binding energy for stable nuclei is always a positive number, as the nucleus must gain energy for the nucleons to move apart from each other. Nucleons are attracted to each other by the strong nuclear force. In theoretical nuclear physics, the nuclear binding energy is considered a negative number. In this context it represents the energy of the nucleus relative to the energy of the constituent nucleons when they are infinitely far apart. Both the experimental and theoretical views are equivalent, with slightly different emphasis on what the binding energy means.
The mass of an atomic nucleus is less than the sum of the individual masses of the free constituent protons and neutrons. The difference in mass can be calculated by the Einstein equation,, where E is the nuclear binding energy, c is the speed of light, and m is the difference in mass. This "missing mass" is known as the mass defect, and represents the energy that was released when the nucleus was formed.
The term "nuclear binding energy" may also refer to the energy balance in processes in which the nucleus splits into fragments composed of more than one nucleon. If new binding energy is available when light nuclei fuse, or when heavy nuclei split, either process can result in release of this binding energy. This energy may be made available as nuclear energy and can be used to produce electricity, as in nuclear power, or in a nuclear weapon. When a large nucleus splits into pieces, excess energy is emitted as gamma rays and the kinetic energy of various ejected particles.
These nuclear binding energies and forces are on the order of one million times greater than the electron binding energies of light atoms like hydrogen.

Introduction

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 released because of differences in the nuclear binding energy between the incoming and outgoing products of the nuclear transmutation.
The best-known classes of exothermic nuclear transmutations are nuclear fission and nuclear fusion. Nuclear energy may be released by fission, when heavy atomic nuclei 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 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 might ultimately be converted to thermal energy, emitted as heat.
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.

The nuclear force

and nuclei are kept together by electrostatic attraction. Furthermore, electrons are sometimes shared by neighboring atoms or transferred to them ; this link between atoms is referred to as a chemical bond and is responsible for the formation of all chemical compounds.
The electric force does not hold nuclei together, because all protons carry a positive charge and repel each other. If two protons were touching, their repulsion force would be almost 40 newtons. Because each of the neutrons carries total charge zero, a proton could electrically attract a neutron if the proton could induce the neutron to become electrically polarized. However, having the neutron between two protons would attract the neutron only for an electric quadrupole arrangement. Higher multipoles, needed to satisfy more protons, cause weaker attraction, and quickly become implausible.
After the proton and neutron magnetic moments were measured and verified, it was apparent that their magnetic forces might be 20 or 30 newtons, attractive if properly oriented. A pair of protons would do 10⁻¹³ joules of work to each other as they approach – that is, they would need to release energy of 0.5 MeV in order to stick together. On the other hand, once a pair of nucleons magnetically stick, their external fields are greatly reduced, so it is difficult for many nucleons to accumulate much magnetic energy.
Therefore, another force, called the nuclear 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 fact that nuclei do not clump together under normal conditions suggests that the nuclear force must be weaker than the electric repulsion at larger distances, but stronger at close range. 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.
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. 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, can such a process take place.

Physics of nuclei

There are around 94 naturally occurring elements on Earth. The atoms of each element have a nucleus containing a specific number of protons, and some number of neutrons, which is often roughly a similar number. Two atoms of the same element having different numbers of neutrons are known as isotopes of the element. Different isotopes may have different properties – for example one might be stable and another might be unstable, and gradually undergo radioactive decay to become another element.
The hydrogen nucleus contains just one proton. Its isotope deuterium, or heavy hydrogen, contains a proton and a neutron. The most common isotope of helium contains two protons and two neutrons, and those of carbon, nitrogen and oxygen – six, seven and eight of each particle, respectively. However, a helium nucleus weighs less than the sum of the weights of the two heavy hydrogen nuclei which combine to make it. The same is true 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 difference is known as the mass defect.

Mass defect

Mass defect is the difference between the mass of an object and the sum of the masses of its constituent particles. Mass defect can be explained using Albert Einstein's formula E = mc², published in 1905, which describes the equivalence of energy and mass. The decrease in mass is equal to the energy emitted in the reaction of an atom's creation divided by c². By this formula, adding energy increases mass, whereas removing energy decreases mass. For example, a helium atom containing four nucleons has a mass about 0.8% less than the total mass of four hydrogen atoms. The helium nucleus has four nucleons bound together, and the binding energy which holds them together is, in effect, the missing 0.8% of mass.
For lighter elements, the energy that can be released by assembling them from lighter elements decreases, and energy can be released when they fuse. This is true for nuclei lighter than iron/nickel. For heavier nuclei, more energy is needed to bind them, and that energy may be released by breaking them up into fragments. Nuclear power is generated at present by breaking up uranium nuclei in nuclear power reactors, and capturing the released energy as heat, which is converted to electricity.
As a rule, very light elements can fuse comparatively easily, and very heavy elements can break up via fission very easily; elements in the middle are more stable and it is difficult to make them undergo either fusion or fission in an environment such as a laboratory.
The reason the trend reverses after iron is the growing positive charge of the nuclei, which tends to force nuclei to break up. It is resisted by the strong nuclear interaction, which holds nucleons together. The electric force may be weaker than the strong nuclear force, but the strong force has a much more limited range: in an iron nucleus, each proton repels the other 25 protons, while the nuclear force only binds close neighbors. So for larger nuclei, the electrostatic forces tend to dominate and the nucleus will tend over time to break up.
As nuclei grow bigger still, this disruptive effect becomes steadily more significant. By the time polonium is reached, nuclei can no longer accommodate their large positive charge, but emit their excess protons quite rapidly in the process of alpha radioactivity—the emission of helium nuclei, each containing two protons and two neutrons. Because of this process, nuclei with more than 94 protons are not found naturally on Earth. The isotopes beyond uranium with the longest half-lives are plutonium-244 and curium-247.

Nuclear reactions in the Sun

The nuclear fusion process works as follows: five billion years ago, the new Sun formed when gravity pulled together a vast cloud of hydrogen and dust, from which the Earth and other planets also arose. The gravitational pull released energy and heated the early Sun, much in the way Helmholtz proposed.
Thermal energy appears as the motion of atoms and molecules: the higher the temperature of a collection of particles, the greater is their velocity and the more violent are their collisions. When the temperature at the center of the newly formed Sun became great enough for collisions between hydrogen nuclei to overcome their electric repulsion, and bring them into the short range of the attractive nuclear force, nuclei began to stick together. When this began to happen, protons combined into deuterium and then helium, with some protons changing in the process to neutrons. This released nuclear energy now keeps up the high temperature of the Sun's core, and the heat also keeps the gas pressure high, keeping the Sun at its present size, and stopping gravity from compressing it any more. There is now a stable balance between gravity and pressure.
Different nuclear reactions may predominate at different stages of the Sun's existence, including the proton–proton reaction and the carbon–nitrogen cycle—which involves heavier nuclei, but whose final product is still the combination of protons to form helium.
A branch of physics, the study of controlled nuclear fusion, has tried since the 1950s to derive useful power from nuclear fusion reactions that combine small nuclei into bigger ones, typically to heat boilers, whose steam could turn turbines and produce electricity. No earthly laboratory can match one feature of the solar powerhouse: the great mass of the Sun, whose weight keeps the hot plasma compressed and confines the nuclear furnace to the Sun's core. Instead, physicists use strong magnetic fields to confine the plasma, and for fuel they use heavy forms of hydrogen, which burn more easily. Magnetic traps can be rather unstable, and any plasma hot enough and dense enough to undergo nuclear fusion tends to slip out of them after a short time. Even with ingenious tricks, the confinement in most cases lasts only a small fraction of a second.