The liquid drop model is a model in nuclear physics which treats the nucleus as a drop of incompressible nuclear fluid, first proposed by George Gamow. The fluid is made of nucleons, and is held together by the strong nuclear force. Nuclear physics is the branch of physics concerned with the nucleus of the atom. ... A stylized representation of a lithium atom. ... George Gamow (pronounced GAM-off) (March 4, 1904 – August 19, 1968) , born Georgiy Antonovich Gamow (Георгий Антонович Гамов) was a Ukrainian born physicist and cosmologist. ... Nucleon is the common name used in nuclear chemistry to refer to a neutron or a proton, the components of an atoms nucleus. ... The strong nuclear force or strong interaction (also called color force or colour force) is a fundamental force of nature which affects only quarks and antiquarks, and is mediated by gluons in a similar fashion to how the electromagnetic force is mediated by photons. ...

This is a crude model that does not explain all the properties of nuclei, but does explain the spherical shape of most nuclei.

It also helps to predict results in the field of nuclear fission by calculating the variation of binding energy necessary to change the shape of the drop, and then comparing it to the energy given by a neutron joining this nucleon. If it is sufficient, the drop "breaks" and this is called fission. Sketch of induced nuclear fission, a neutron (n) strikes a uranium nucleus which splits into similar products (F. P.), and releases more neutrons to continue the process, and energy in the form of gamma and other radiation. ...

Mathematical analysis of the theory delivers an equation which attempts to predict the binding energy of a nucleus in terms of the numbers of protons and neutrons it contains. This equation has five terms on its right hand side. These correspond to the cohesive binding of all the nucleons by the strong nuclear force, the electrostatic mutual repulsion of the protons, a surface energy term, an asymmetry term (derivable from the protons and neutrons occupying independent quantum momentum states) and an exchange term. Properties In physics, the proton (Greek proton = first) is a subatomic particle with an electric charge of one positive fundamental unit (1. ... Properties In physics, the neutron is a subatomic particle with no net electric charge and a mass of 939. ... In physics a nucleon is a collective name for the two baryons the neutron and the proton. ... The strong nuclear force or strong interaction (also called color force or colour force) is a fundamental force of nature which affects only quarks and antiquarks, and is mediated by gluons in a similar fashion to how the electromagnetic force is mediated by photons. ... The word quantum, pl. ...

If we consider the sum of the following five types of energies, then the picture of a nucleus as a drop of incompressible liquid roughly accounts for the observed variation of binding energy of the nucleus :

Volume Energy. When an assembly of nucleons of the same size is packed together into the smallest volume, each interior nucleon has 12 other nucleons in contact with it. So, this nuclear energy is proportional to the volume.

Surface Energy. A nucleon at the surface of a nucleus interacts with fewer other nucleons that one in the interior of the nucleus and hence its binding energy is less. This surface energy term takes that into account and is therefore negative and is proportional to the surface area.

Coulomb Energy. The electric repulsion between each pair of protons in a nucleus contributes toward decreasing its binding energy. It has been suggested that this article or section be merged into Electrostatic force. ...

Asymmetry Energy. An energy associated needed as a correction when the number of neutrons is greater than the number of protons.

Pairing Energy. An energy which is a correction term that arises from the tendency of proton pairs and neutron pairs to occur.

These terms are added, and coefficients are derived experimentally to obtain the following rule:

where N is the number of neutrons, Z is the number of protons, and A = N + Z is the atomic mass. E_B is the binding energy in MeV. The final term is added if the number of protons and neutrons are both odd, subtracted if the number of protons and neutrons are both even, and omitted of only one is odd. An electronvolt (symbol: eV) is the amount of energy gained by a single unbound electron when it falls through an electrostatic potential difference of one volt. ...

Reference

• RADIOCHEMISTRY and NUCLEAR CHEMISTRY, Gregory Choppin, Jan-Olov Liljenzin, and Jan Rydberg, 3rd Edition, 2002, the chapter on nuclear stability (PDF)

PDF is an abbreviation with several meanings: Portable Document Format Post-doctoral fellowship Probability density function There also is an electronic design automation company named PDF Solutions. ...

See also

• Interacting boson model
• Shell model
• Nuclear liquid drop model