Structure of Atom and Nucleus

Atom and Nucleus are the basic topics of Modern Physics. These are the fundamentals of all other topics. It is important to understand the concepts of structure of atom and nucleus as they lay the groundwork for others. One cannot afford to skip these vital topics as they easily fetch around 2-3 questions in the JEE.

The various heads included under the structure of atom and nucleus are listed below:

• Bohr Model

• Energy Levels of Hydrogen Atom

• Short Review of Formulas

• Solved Examples of Structure of Atom

• Nucleus

• Mass Defect and Binding Energy

• Nuclear Forces

All these heads are extremely important and have been discussed in detail in the coming sections. We shall give a brief outline of these topics one by one.

Atom:

An atom is the basic unit of matter that consists of dense nucleus at the center. The nucleus contains both protons and neutrons. While neutrons carry a neutral charge, protons have positive charge. Around the nucleus, the electrons keep on moving in orbits. The electrons carry a negative charge. The electrons of an atom are attached to the nucleus by the electromagnetic force.

Bohr Model: Rutherford was the first to describe the model of an atom. It was after him that Neils Bohr proposed the Bohr Model of the atom in 1915. Since the Bohr Model is basically a modification of the Rutherford Model, so some even call it the Rutherford-Bohr Model.
The modern version of the model of the atom is based on quantum mechanics. Though, even the Bohr Model is not perfect and contains some errors, yet it is important because it explains the Rydberg formula for the spectral emission lines of atomic hydrogen. In the Bohr-Model, the negatively charged electrons orbit a small positively charged nucleus like the planets orbit the sun. Moreover, there is one more similarity between the two. The gravitational force of the solar system is the same as the electrical force between the positively charged nucleus and the negatively charged electrons. 

As we know that the nucleus is at the center of the atom. The electrons move around the nucleus in orbits that have a fixed size and energy. The energy of the orbit is directly proportional to its size. This means that the largest orbit has the maximum energy. When an electron moves from one orbit to another, there is an absorption or emission of energy.

A stable atom has a fixed size and hence the equation describing it must contain some combination of constants with a dimension of length. Bohr was the one who noticed that the quantum constant formulated by the German physicist Max Planck has dimensions which, when combined with the mass and charge of the electron, produce a measure of length. This measure is almost the same as the size of atoms and this encouraged Bohr to use Planck’s constant in framing a theory of atom. With its help, Bohr worked out an accurate formula for energy levels of hydrogen atom. He concluded that the angular momentum of the electron has discrete values else electrons follow the laws of classical mechanics by moving around the nucleus in circular paths. It is due to quantization that the orbits have fixed sizes and energies.  

Loop holes in the Bohr Model

The Bohr Model explains the structure quite well but misses out on some aspects. Some of the problems with the model include:

• The Bohr Model fails to provide an accurate value of the ground state angular momentum.

• It fails to predict the relative intensities of spectral lines and it’s prediction of spectra of larger atoms are also quite poor.

• The model does not explain the fine and hyperfine structure in spectral lines. It does not explain the Zeeman Effect.

Nucleus: 

The dense region located at the center of an atom is called the nucleus. The nucleus contains protons and electrons and almost the entire mass of the atom is located in the nucleus.

The diameter of the nucleus is in the range of 1.75 fm for hydrogen to 15 fm for heavier atoms like the uranium. These dimensions are much smaller than the diameter of the atom itself. The electrons move around the nucleus in orbits and the cloud of electrons that define the size of an atom is roughly 100000 times as large as atom’s nucleus. 

Electrons are the smallest parts of the atom. An electron is an elementary particle which has no known substructures. Its mass is 1/1836 of a proton. Positron is the antiparticle of electron. They are both the same except for the fact that they carry opposite charges. When a collision of an electron and a positron happens, both the particles either get destroyed or get scattered thus producing gamma ray photons.

The proton is the main part of an atom and carries a positive charge. The number of protons and neutrons is usually the same except in the case of hydrogen atom which contains a single proton which exists on its own. The atomic number is decided by the number of protons in the nucleus of an atom.

A neutron does not have any charge. Protons and neutrons together are often termed as nucleons. If the number of neutrons exceeds the number of protons, then the atom is considered an isotope. Whenever a neutron becomes free of its proton, it becomes unstable and hence undergoes beta decay and finally disintegrates in around 15 minutes. Neutrons hold great importance in nuclear chain reactions. 

Nuclear Force
The nuclei are bound together with the help of strong residual force called nuclear forces. This force is quite weak between neutrons and protons as it is usually neutralized between them. The nuclear forces are quite active at the distance of particular nucleon separation. This overpowers the repulsion between protons which occurs as a result of electromagnetic force, thus resulting in the existence of a stable nucleus. The force between two or more nucleons is termed as the nuclear force. It binds the protons and neutrons into the atomic nuclei. This binding releases certain energy which causes the masses of the nuclei to be less than the total mass of the protons and neutrons comprising them.
The electromagnetic force controls the motion of the atomic electrons. But a stronger force is required to bind the nucleus together which has the ability to overpower the repulsive force of the positively charged nuclear protons and can bind both the protons and the neutrons. The nuclear force should be of short range as its influence does not very far from the nuclear surface. 

Nuclear Binding energy:
Binding energy or the nuclear binding energy is the energy required for splitting the nucleus into separate nucleons. It may also be defined as the energy released during the formation of nucleus from separate nucleons. This energy is equal to the decrease in potential nuclear energy of the nucleons when they come together.
The mass of the individual nucleons that make up the nucleus exceeds the mass of the nucleus. The mass difference, denoted by ?m, between the two is equal to the binding energy of the nucleus.
The Einstein’s equation describes the relation between binding energy and mass difference

Eb = ?mc²

The stability of a nucleus depends on the binding energy per nucleon. The higher the binding energy per nucleon, the more stable is the nucleus.

The topics of atom and nucleus are quite simple and must be mastered to remain competitive in the JEE. askIITians offers comprehensive study material containing numerous solved examples on these topics.

Related Resources:

• Click here for the Complete IIT JEE Physics Syllabus.

• Look into the Previous Papers with Solutions to get a hint of the kinds of questions asked in the exam.

• You can get the knowledge of Most Useful Books of Physics here.

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