Liquid Drop Model of Nucleus ( Binding Energy Formula)
Liquid Drop Model of Nucleus is one of the popular models to describe the behavior of the nucleus of an atom.
Next Video on Corrections to Liquid Drop Model/ Semi Empirical BE Formula : • Corrections to Liquid Drop Model / Se...
In this Model, a comparison is made between a drop of liquid and the nucleus of an atom. Some of the similarities they have are as follows :
1) Both Nucleus and Liquid Drop contain a large number of particles.
2) Both Nucleus and Liquid Drop are homogeneous and incompressible.
3) In the case of both a Nucleus and a Liquid Drop, the mass density remains constant throughout its volume and drops to zero only near the boundary surface.
4) Each nucleon particle inside a Nucleus interacts only with its nearest neighbors, just as the molecules in a Liquid Drop interact only with its nearest neighbors (and not some general potential field).
5) Both Nucleus and Liquid Drop show surface tension effect. This is the reason, both tends to be spherical in the absence of external forces.
6) Heat of vaporization (Evaporation) of a Liquid Drop can be compared to providing Binding Energy to a Nucleus.
7) The fission of a larger droplet into two smaller ones, and the fusion of two small droplets into a larger can be compared to the fission and fusion of Nuclei.
Because of these above similarities, the Nucleus is compared to a Liquid Drop. Hence, the Liquid Drop Model of the Nucleus.
Using this model, we can calculate the Binding Energy of any given nucleus, and recreate the Binding Energy Curve.
To do that, we can first calculate the different energy terms contributing towards the overall Binding Energy (by finding the necessary relationship with Mass Number, A and Atomic Number, Z)
These terms include :
a) The Volume Energy
b) The Surface Energy
c) The Coulombic Energy
This leads to an expression which gives us a theoretical way to calculate the Binding Energy of a Nucleus. Using that we can also plot the Binding Energy Curve, and see that it closes resembles the Binding Energy Curve of experimental data. Thus, we can see that The Liquid Drop Model of the Nucleus has some validity.
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