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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 18.1.4.3 Density 19.1.4.4 Charge 20.1.4.5 Binding Energy 21.1.4.6 Nuclear Spin

    25.1.4.7 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. 30.2.2.2 Achievements of Liquid Drop Model. 34.2.2.3 Limitations of Liquid Drop Model. 35.

    2.3 Shell Model 36.2.3.1 The Square wave potential. 37.2.3.2 The Harmonic Oscillator. 39.2.3.3 The Spin-Orbit Interaction. 42.2.3.4 Wood-Saxon Potential. 43.2.3.5 Achievements of Shell Model. 44.

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    3. Computer Program and Result. [45-55] 4. Conclusion. 56. 5. References. [57-60]

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    INTRODUTION

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    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[1].

    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[3]. Dalton hypothesized this was due to the

    differences in the mass and complexity of the gases' respective particles. Indeed, carbon

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    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.

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    Dalton's Atomic Theory [2]

    The main points of Dalton's atomic theory are:

    1. All atoms of an element are identical[4].

    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 [5] 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.[6]

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    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.

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    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

    atom.

    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