Liquid Drop Model
Weizsacker in 1935 proposed on the basis of experimental facts that a nucleus resembles a drop of liquid. According to the liquid Drop Model, the nucleus is assumed to be a sphere whose mass is given by the semi-empirical mass formula.
|Liquid Drop Model|
Assumptions of the Liquid Drop Model
- The nucleus consists of incompressible matter.
- The nuclear force is identical for every nucleon.
- The nuclear force saturates.
- In an equilibrium state, the nuclei of an atom remain spherically symmetric under the action of strong attractive nuclear forces.
Although insufficient to explain all atomic events, the theory underlying the model provides an excellent estimate of the average properties of nuclei. The individual nucleons must be able to move about within the nucleus much as does an atom of a liquid and one might, therefore, think of a nucleus as being like a small drop of liquid. Such a model is thus known as the liquid drop model.
In 1939, Bohr and Wheeler further developed this model to explain the phenomenon of nuclear fission. The idea that the molecules in the drop of liquid corresponding to the nucleons in the nucleus is confirmed due to the following similarities-
- The nuclear force is analogous to the surface tension force of a liquid.
- The nucleons behave in a manner similar to that of molecules in a liquid.
- The density of the nuclear matter is almost independent of A, showing resemblance to liquid drop.
- The constant binding energy per nucleon is analogous to the latent heat of vaporization.
- The disintegration of nuclei by the emission of particles is analogous to the evaporation of molecules from the surface of the liquid.
- The energy of nuclei corresponds to internal thermal vibrations of drop molecules.
- The absorption of bombarding particles by a nucleus corresponds to the condensation or drops.
Failures of Liquid Drop Model
- It fails to explain the extra stability of certain nuclei, where the numbers of protons or neutrons in the nucleus are 2, 8, 20, 28, 50, 82, or 126 (these numbers are called magic numbers).
- It fails to explain the measured magnetic moments of many nuclei.
- It also fails to explain the spin of nuclei.
- It is also not successful in explaining the excited states in most of the nuclei.
The liquid drop model is not very successful in describing the low-lying excited states of the nucleus. Because of the collective motion of the large number of nucleons involved, the model gives rise to closely spaced energy levels. Actually, however, these are found to be quite widely spaced at low excitation energy.
Achievements of Liquid Drop Model
- It predicts the atomic mass and binding energies of various nuclei accurately.
- It predicts the emission of alpha- and beta-particles in Radioactivity.
- It explains the basic features of the fission process.