The Liquid Drop Model of the Nucleus

In the liquid drop model, the nucleons are pictured as particles in a liquid. A given nucleon collides frequently with other nucleons in the nuclear interior, its mean free path as it moves about being substantially less than the nuclear radius, in a manner similar to the way liquid particles move in a liquid. The liquid drop model is consistent with many observations of nuclear binding energies and is useful in explaining many nuclear reactions.

A nucleus will have three types of energy according to the liquid drop model.

  • Volume Energy - Because each bond energy is shared by two nucleons, each has a binding energy of one-half that. When an assembly of spheres of the same size is packed together into the smallest volume, each interior sphere is in contact with 12 other spheres, so this 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 takes that into account and is therefore negative.

  • Coulomb Energy - The electric repulsion between each pair of protons in a nucleus also contributes toward decreasing its binding energy. The coulomb energy of a nucleus is equal to the work that must be done to bring together the protons from infinity into a spherical aggregate the size of the nucleus. This energy is negative because work must be done against this repulsive force.

When all three types of energy are taken into account the overall binding energy per nucleon is very similar to observed values.

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