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CONTENTS Page no.
1. INTRODUTION [1- 26]
1.1 Historical Background. [4-15] 1.1.1 Daltons Atomic Hypothesis 4. 1.1.2 Thomson Model of Atom. 6.
1.1.3 Rutherford Model of Atom. 8. 1.1.4 Hypothesis for Structure of Nucleus. [12- 15]
(a)Proton-Neutron Hypothesis. 12. (b)Proton-Electron Hypothesis. 14.
1.2 What is a Nucleus? 15.1.3 Terms Associated with Nucleus. 16.1.4 Quantitative Facts about the Nucleus. [17-26]
1.4.1 Size 17.
1.4.2 Mass 22.214.171.124 Density 126.96.36.199 Charge 188.8.131.52 Binding Energy 184.108.40.206 Nuclear Spin
220.127.116.11 Magnetic Dipole Moment 26.
2. LITERATURE VIEW [27-40]
NUCLEAR MODELS 28.2.1 Introduction 28.2.2 Liquid Drop Model 29.
2.2.1 Semi Empirical Mass Formula. 18.104.22.168 Achievements of Liquid Drop Model. 22.214.171.124 Limitations of Liquid Drop Model. 35.
2.3 Shell Model 126.96.36.199 The Square wave potential. 188.8.131.52 The Harmonic Oscillator. 184.108.40.206 The Spin-Orbit Interaction. 220.127.116.11 Wood-Saxon Potential. 18.104.22.168 Achievements of Shell Model. 44.
3. Computer Program and Result. [45-55] 4. Conclusion. 56. 5. References. [57-60]
1.1 Historic Development
The beginning of the nuclear physics may be traced back to the studies on atomic
structure started with the discovery of radioactivity in 1896 by Henry Becquerel. Further,
three different modes of radioactivity were observed emitting -particles, -particles and
-rays. It is well known that -particles are Helium nuclei, -particles are either electrons
or positrons and -rays are high-energy electromagnetic radiations. Scattering of -
particles with matter revealed the existence of nucleus inside the atom. In the following
content, we give major models in establishing the structure of atom and nucleus.
1.1.1 Daltons Atomic Theory
Although the concept of the atom dates back to the ideas of Democritus, the
English meteorologist and chemist John Dalton formulated the first modern description
of it as the fundamental building block of chemical structures. Dalton developed the law
of multiple proportions (first presented in 1803) by studying and expanding upon
the works of Antoine Lavoisier and Joseph Proust.
Proust had studied tin oxides and found that their masses were either 88.1% tin and
11.9% oxygen or 78.7% tin and 21.3% oxygen (these were tin (II) oxide and tin dioxide
respectively). Dalton noted from these percentages that 100g of tin will combine either
with 13.5g or 27g of oxygen; 13.5 and 27 forms a ratio of 1:2. Dalton found an atomic
theory of matter could elegantly explain this common pattern in chemistry - in the case of
Proust's tin oxides, one tin atom will combine with either one or two oxygen atoms.
Dalton also believed atomic theory could explain why water absorbed different
gases in different proportions: for example, he found that water absorbed carbon dioxide
far better than it absorbed nitrogen. Dalton hypothesized this was due to the
differences in the mass and complexity of the gases' respective particles. Indeed, carbon
dioxide molecules (CO2) are heavier and larger than nitrogen molecules (N2).
Dalton proposed that each chemical element is composed of atoms of a single,
unique type, and though they cannot be altered or destroyed by chemical means, they can
combine to form more complex structures (chemical compounds). Since Dalton reached
his conclusions by experimentation and examination of the results in an empirical
fashion, this marked the first truly scientific theory of the atom.
Figure 1: - Daltons atomic model.
Dalton's Atomic Theory 
The main points of Dalton's atomic theory are:
1. All atoms of an element are identical.
2. The atoms of different elements vary in size and mass.
3. Compounds are produced through different whole-number combinations of atoms.
4. A chemical reaction results in the rearrangement of atoms in
the reactant and product compounds.
Atomic theory has been revised over the years to incorporate the existence of
atomic isotopes and the inter conversion of mass and energy. In addition, the discovery
of sub atomic particles has shown that atoms can be divided into smaller parts. However,
Dalton's importance in the development of modern atomic theory has been recognized by
the designation of the atomic mass unit  as a Dalton.
1.1.2 Thomson Model Of Atom
In 1897, J.J. Thomson discovered a negatively charged particle known as an
electron. Thomson discovered electron by cathode ray tube experiment. Cathode ray tube
is a vacuum tube. Thomson assumed that an electron is two thousand times lighter than a
proton and believed that an atom is made up of thousands of electrons having the
negative charge. In this model, he considered atoms to have a cloud of negative charge
and the positive charges. He along with Rutherford was also the first to demonstrate the
ionization of air by X-rays. Thomsons model of an atom is similar to plum pudding
model or a watermelon.
Postulates of Thomsons atomic model
1. An atom consists of a positively charged sphere with electrons filled into it. The negative and positive charge present inside an atom is equal and as a whole, an
atom is electrically neutral.
2. Thomsons model of the atom was compared to plum pudding and watermelon.
He compared the red edible part of the watermelon to positively charged sphere
whereas the seeds of watermelon to negatively charged particles.
Figure 2:- Thomson model.
Limitations of Thomsons atomic model
1. This model of atom failed to explain how a positive charge holds the negatively
charged electrons in an atom. Therefore, it failed to explain the stability of an
2. This theory also failed to account for the position of the nucleus in an atom.
3. Thomsons model failed to explain the scattering of alpha particles.
Although Thomsons model was not an accurate model to account for the atomic
structure, it proved to be the base for the development of other atomic models. The study
of the atom and its structure has paved the way for numerous inventions that have played
a significant role in the development of humankind.
1.1.3 Rutherford Model Of AtomRutherford atomic model, also called nuclear atom or planetary model of the atom,
description of the structure of atoms proposed (1911) by the New Zealand-born
physicist Ernest Rutherford. The model described the atom as a tiny, dense, positively
charged core called a nucleus, in which nearly all the mass is concentrated, around which
the light, negative constituents, called electrons, circulate at some distance, much
like planets revolving around the Sun. The nucleus was postulated as small and dense to