Nuclear Physics

Every atom contains at its center an extremely dense, positively charged nucleus, which is much smaller than the overall size of the atom but contains most of its total mass. The stability or instability of a particular nucleus is determined by the competition between the attractive nuclear force among the protons and neutrons and the repulsive electrical interactions among the protons. Unstable nuclei decay, transforming themselves spontaneously into other nuclei by a variety of processes. Nuclear reactions can also be induced by impact on a nucleus of a particle or another nucleus. Two classes of reactions of special interest are fission and fusion. Fission is the process that takes place within a nuclear reactor used for generating power. We could not survive without the energy released by one nearby fusion reactor, our sun. The branch of physics dealing with the study of atomic molecules is called nuclear physics. 

Discovery of Atomic Nucleus 

The discovery of the atomic nucleus is usually attributed to Ernest Rutherford and his team of researchers, who conducted a famous experiment in 1911. In this experiment, they fired alpha particles at a thin sheet of gold foil and observed the scattering patterns. They found that most particles passed straight through the foil, but a small fraction were deflected at large angles, suggesting the presence of a compact central structure in the atoms, which they called the nucleus. This experiment led to the modern understanding of the atomic structure, with a central nucleus consisting of protons and neutrons surrounded by electrons in orbit.

Rutherford's Experiment on Scattering of α-Particles

Ernest Rutherford's experiment on the scattering of alpha particles is a landmark experiment in the history of atomic physics. In this experiment, Rutherford and his team aimed a beam of alpha particles (helium nuclei) at a thin sheet of gold foil. They then measured the deflection of the alpha particles using a screen coated with a fluorescent material. They found that most of the alpha particles passed straight through the foil, but a small fraction were deflected at large angles, suggesting the presence of a highly concentrated, positive charge in the center of the atom. This led to the discovery of the atomic nucleus, a small, dense region at the center of the atom containing protons and neutrons. The results of this experiment challenged the previously accepted "plum pudding" model of the atom, in which electrons were thought to be randomly distributed throughout the entire atom, and demonstrated that the atom has a definite, structured form with a central nucleus and orbiting electrons. The experiment remains an important milestone in the development of our understanding of atomic structure.

The whole apparatus was inside a vacuum chamber to prevent  the scattering of α-particle from air molecule. From his experiment, they found that:

The nucleus is composed of protons and neutrons, and the number of protons in the nucleus determines the atomic number and therefore the identity of the element. The electrons occupy quantized energy levels, known as electron shells, at specific distances from the nucleus. The Rutherford atomic model provided a clear and structured picture of atomic structure for the first time and remains an important concept in the history of atomic physics.

Let an a-particle with kinetic energy E is directed towards the center of the nucleus of an atom. Due to Coulomb's repulsive force between nucleus and a-particle, kinetic energy of a-particle goes on decreasing and at the same time; potential energy of the a-particle goes on increasing. At a certain distance r, from the nucleus, KE of a-particle reduces to zero. The a-particle stops and it cannot go closer to the nucleus. It is repelled by the nucleus and goes back over its path, i.e. returns through 180. Hence, the distance r. is called distance of closest approach, at which the total kinetic energy of a-particle is converted into potential energy.

Let, charge on a-particle = q₁ = + 2e and charge on nucleus = q₂= + Ze, where Z is the atomic number of material of the foil and +e is charge on a proton.

It is clear that, the radius of the nucleus must be smaller than the calculated value of ro, as an α-particle cannot touch the boundary of the nucleus because of strong repulsion.

Suppose in an experiment, an a-particle of kinetic energy 7.7 MeV comes to momentarily rest and reverse its direction due to repulsion of gold nucleus (Z = 79) as shown in figure below. The distance of closest approach, (i.e. ≈ radius of gold nucleus) can be estimated as below.

Fig: Distance of Closest Approach for size of nucleus

Constituents of a Nucleus

A nucleus is composed of two main types of particles: protons and neutrons. Protons are positively charged particles, while neutrons are neutral. The number of protons in the nucleus, also known as the atomic number, determines the element it represents. The total number of protons and neutrons in the nucleus is known as the atomic mass number.

A schematic representation of a nucleus can be represented as a central dot or circle representing the protons and neutrons tightly packed together, with the protons shown as small positive charges (represented by "+" signs) and neutrons shown as neutral particles (represented by dots or a "o" sign). The number of protons is indicated by the atomic number (Z), and the total number of protons and neutrons is represented by the atomic mass number (A).

General Properties of Nucleus

The general properties of a nucleus include:

1. Size: The size of a nucleus is on the order of 10^-15 meters, which is much smaller than the size of an atom.
2. Charge: The nucleus has a positive charge due to the presence of protons. The charge of a nucleus is equal to the number of protons it contains, which is also known as the atomic number.
3. Mass: The mass of a nucleus is the sum of the masses of the protons and neutrons it contains. The mass of a nucleus is much greater than the mass of the individual protons and neutrons.
4. Nuclear spin: Nuclear spin is a intrinsic property of a nucleus, much like the spin of an electron. It arises from the movement of the protons and neutrons within the nucleus and is represented by a quantum number.
5. Magnetic moment: The magnetic moment of a nucleus arises from the combined magnetic properties of the protons and neutrons in the nucleus. It is proportional to the nuclear spin and is used in nuclear magnetic resonance (NMR) spectroscopy. Magnetic moments are expressed in nuclear magneton (μN). In SI units, it's value is approximately 5.051 × 10-27 J/T.
6. Nuclear Density: The mass per unit volume of a nucleus is called nuclear density.

   This shows that the density of nucleus is very high and is independent with mass number A. Hence, the nuclei of all the atoms have       nearly the same density. This value is about 1013  times as that of density of iron. It advocates nucleus is highly compact.