Liquid Drop Model

Liquid Drop Model

This nuclear model is statistical in nature and was developed by N. Bohr and J. Wheeler. It treats the nucleus as a homogeneous entity containing a certain number of nucleons, each nucleon being assumed to interact strongly with all its neighbours.
Bohr tried to compare properties of a nucleus with a drop of liquid and found many similarities. Some of these are given below-
1. A liquid drop has a large number of molecules just as a nucleus has a large number of nucleons.
2. Both the liquid drop and the nucleus are homogeneous and incompressible. The density, charge and other properties are the same throughout the liquid drop and the nucleus except at the surface boundaries. It can be easily visualised that the nuclear volume ∝ nuclear mass ∝ A, where A is the mass number.
Thus, the nuclear radius is given by-
r = R_o√A.
Where R_o 1.5 × 10^-15 m)
3. Comparison of a nucleus with a liquid drop implies that the force between all the nucleons is the same, that is-
fn-n ≈ fn-p ≈ fp-p
The nuclear force is thus independent of charge and spin.
4. Heat of vaporisation of a liquid corresponds to binding energy of nucleons in a nucleus.
5. Evaporation of a liquid drop corresponds to radioactive emission from a radioactive isotope.
6. Surface tension in a liquid arises from the fact that surface molecules in a drop are not so tightly bound as are the molecules in the interior. There is evidence to show that this is so in the case of nucleons present in a nucleus as well.
7. In a liquid drop, molecules are influenced only by those which lie in immediate neighbourhood. This means that intermolecular foces are short-range forces only. The same is the case in a nucleus. The nucleon-nucleon forces operate within short ranges only as has been discussed before.
8. A nucleus may form a compound nucleus by capturing a high energy particle from outside as does a liquid drop to get excited. The excess energy of the captured particle is shared by all the particles of the nucleus or the liquid drop.
9. The compound nucleus or the excited liquid drop may get de-excited by undergoing any of the following changes-

Compound Nucleus	Liquid Drop
By emission of radiation	By cooling
By emission of radiation	By evaporation
By nuclear fission	By breaking up into droplets

10. Just as two liquid drops may undergo fusion to give a bigger drop, similarly, two light nuclei may undergo fusion to give a bigger nucleus.
Based on these and some other similar ideas, it has been possible to develop an equation for calculating binding energies of different nuclei. The values obtained are in good agreement with experimental data. provides a good evidence in favour of the liquid drop model.
Another evidence in favour of the liquid drop model follows from the ability of the model to explain nuclear fission. With the help of this model, it is possible to explain why U²³⁵ isotope of uranium can undergo fission when bombarded by slow neutrons of low energies of about 0.025 eV while U²³⁸ isotope requires fast neutrons having high energies of about 1.2 MeV. The absorption of low energy neutron by U²³³ results in the formation of an excited nucleus which instead of undergoing fission, undergoes ß-ray decay to ultimately give plutonium.

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