2. Nuclear Models
Here we will discuss various models of proposed for nuclear structure
Following models we have to discuss here -
Liquid drop model
2. Nuclear shell model
3. Collective model
Liquid drop model
The liquid drop model of the nucleus was first proposed by Neils
Bohr and F. Kalcar in the year 1937.
They observed that there exists many similarities between the drop
of a liquid and a nucleus.
This model doesn`t focus on the individual quantum mechanical
properties of the nucleons.
Similarities between liquid drop and nucleus
Nucleus Liquid drop
1. Surface Tension
2. Density of the nucleus is
constant and is independent of A
Density of liquid drop is independent of
3. BE/A = constant Latent heat of vaporization
4. Disintegration of nuclei by the
emission of particles
Evaporation of molecules from the
surface of liquid
5. Absorption of bombarding particles Condensation of drops
6. Internal energy of the nucleus
Thermal vibrations of molecules
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Assumptions of liquid model -
The nucleus consists of incompressible matter so that r = r A
2. The nuclear force is identical for every nucleon.
3. The nuclear force saturates.
4. In equilibrium state, the nuclei of atom remains spherically symmetric
under the action of strong attractive nuclear force.
Semi-Empirical Mass formula-
Binding energy (B) = Zm +Nm -M
M = Zm +Nm -B
Binding energy = B + B + B + B + B
2 3 4 5
Volume energy (B ) -
A molecule interacts only with its neighbours and number of
neighbours is independent of size of the drop
B = a A
Surface energy (B ) -
Nucleons at the surface of nucleus do not have the same level of
interactions as nucleons in the interior of the nucleus.
Binding energy is reduced by an amount proportional to surface area.
B = -a A
Coulomb energy (B ) -
Energy due to the presence of protons in the nucleus.
B = -a Z(Z-1)
Asymmetry energy (B ) -
It arises due to the asymmetry in the number of protons and number of neutrons.
B = -a (A-2Z)
Pairing energy (B ) -
B = a A
Achievements of liquid drop model-
It predicts the atomic masses and BE of various nuclei accurately.
2. It predicts emission of alpha and beta particles in radioactivity.
3. It explain the theory of compound nucleus and the basic features of
the fission process.
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Drawbacks of liquid drop model -
It fails to explain the stability of certain nuclei with number of protons or
neutrons are 2, 8,20,28,50,82and 126 i.e. magic numbers
2. It fails to explain the measured magnetic moments of many nuclei.
3. It fails in explaining the excited states in most of the nuclei.
4. LDM is not very successful in describing the excited states of the