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Nuclear Physics and Radioactivity
The Nucleus
Physics Textbooks Boundless Physics Nuclear Physics and Radioactivity The Nucleus
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Physics
Concept Version 8
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Binding Energy and Nuclear Forces

Nuclear force is the force that is responsible for binding of protons and neutrons into atomic nuclei.

Learning Objective

  • Explain how nuclear force varies with distance.


Key Points

    • The nuclear force is powerfully attractive at distances of about 1 femtometer (fm), rapidly decreases to insignificance at distances beyond about 2.5 fm, and becomes repulsive at very short distances less than 0.7 fm.
    • The nuclear force is a residual effect of the a strong interaction that binds together particles called quarks into nucleons.
    • The binding energy of nuclei is always a positive number while 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.

Terms

  • nucleus

    the massive, positively charged central part of an atom, made up of protons and neutrons

  • quark

    In the Standard Model, an elementary subatomic particle that forms matter. Quarks are never found alone in nature, but combine to form hadrons, such as protons and neutrons.

  • gluon

    A massless gauge boson that binds quarks together to form baryons, mesons and other hadrons; it is associated with the strong nuclear force.


Full Text

The nuclear force is the force between two or more component parts of an atomic nuclei. The component parts are neutrons and protons, which collectively are called nucleons. Nuclear force is responsible for the binding of protons and neutrons into atomic nuclei.

Drawing of Atomic Nucleus

A model of the atomic nucleus showing it as a compact bundle of the two types of nucleons: protons (red) and neutrons (blue).

To disassemble a nucleus into unbound protons and neutrons would require working against the nuclear force. Conversely, energy is released when a nucleus is created from free nucleons or other nuclei—known as the nuclear binding energy. The binding energy of nuclei is always a positive number, since all nuclei require net energy to separate into individual protons and neutrons. Because of mass-energy equivalence (i.e., Einstein's famous formula $E=mc^2$), releasing this energy causes the mass of the nucleus to be lower than the total mass of the individual nucleons (leading to "mass deficit"). Binding energy is the energy used in nuclear power plants and nuclear weapons.

The nuclear force is powerfully attractive between nucleons at distances of about 1 femtometer (fm) between their centers, but rapidly decreases to relative insignificance at distances beyond about 2.5 fm. At very short distances (less than 0.7 fm) it becomes repulsive; it is responsible for the physical size of nuclei since the nucleons can come no closer than the force allows.

The nuclear force is now understood as a residual effect of an even more powerful "strong force" or strong interaction. It is the attractive force that binds together particles known as quarks (to form the nucleons themselves). This more powerful force is mediated by particles called gluons. Gluons hold quarks together with a force like that of an electric charge (but of far greater power).

The nuclear forces arising between nucleons are now seen as analogous to the forces in chemistry between neutral atoms or molecules (called London forces). Such forces between atoms are much weaker than the attractive electrical forces that hold together the atoms themselves (i.e., that bind electrons to the nucleus), and their range between atoms is shorter because they arise from a small separation of charges inside the neutral atom.

Similarly, even though nucleons are made of quarks in combinations which cancel most gluon forces (they are "color neutral"), some combinations of quarks and gluons leak away from nucleons in the form of short-range nuclear force fields that extend from one nucleon to another nucleon in close proximity. These nuclear forces are very weak compared to direct gluon forces ("color forces" or "strong forces") inside nucleons, and the nuclear forces extend over only a few nuclear diameters, falling exponentially with distance. Nevertheless, they are strong enough to bind neutrons and protons over short distances, as well as overcome the electrical repulsion between protons in the nucleus. Like London forces, nuclear forces also stop being attractive, and become repulsive when nucleons are brought too close together.

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