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# Nuclear Physics

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 Sub Topics Nuclear physics is an intriguing subject because of the great variety of phenomena that occur. Nuclei exhibit many different types of behavior from the classical, where the nucleus behaves like a liquid drop, to the quantum mechanical, where nuclei show a shell structure similar to that found in atoms. It is a considerable intellectual challenge to try and understand this behavior and many models have been devised.

## Definition

Nuclear physics is a branch of physics which deals with the atomic structure, properties and interactions and different laws regarding the interaction between their constituents. It also deals with strong interactions of many body. This branch of physics includes the verification of different fundamental theories. Nuclear physics plays a key role in cosmology and astrophysics.

## Equations

Mass number is given by
A = Z + N
where Z is the proton number,
N is the neutron number

The average radius R of the nucleus is given by

R = Ro A1/3

where Ro = 1.1 fm and A is the mass number

The volume of the nucleus is given by

V = $\frac{4}{3}$ $\pi R^{3}$

## Atomic and Nuclear Physics

Physics is the discipline of science that concerns itself with the study of the most general laws of matter and energy and the fundamental structure of matter. The branch of atomic physics aims primarily at the study of that structure at what is called the atomic scale-a term for sizes between those of molecules and the nuclei of atoms. While the concept of atoms has a history of more than 2000 years, atomic physics as we know it today is a discipline that began to form in the present century and parallels the development of modern physics.

Nuclear physics concerns itself with the structure and behavior of the next layer of matter, which forms the tiny inner core of the atom. The atomic nucleus is about 100000 times smaller than the atom but contains all the positive charge and essentially all the mass of the atom. One of the long sought goals of nuclear physics is to understand the strong nuclear force which holds protons and neutrons together in the nucleus.

## Applications

Nuclear physics is on the threshold of new and exciting developments stemming both from new understandings of the nuclear many body systems and new higher energy probes-electrons, kaons and heavy ions. The study of nuclear physics remained a curiosity and intellectual challenge to scientists but had little practical use outside its own field. The situation changed totally in the 1930s with discoveries that culminated in the cataclysmic demonstrations near the end of the second world war of the immense energy locked up by the force that holds the atomic nucleus together. Today, nuclear physics has entered into our modern world in a significant way. It influences other branches of science: chemistry, biology, archaeology, geology, astrophysics and cosmology. It is used widely in society at large- in industry, the environment, medicine, defense, criminology, power production and many other areas. Applications are found even in religion and the arts, where equipment and methods developed originally for nuclear research have found novel application.

The radioactive decays of naturally occurring minerals containing uranium and thorium are in large part responsible for the birth of the study of nuclear physics. These decays have half lives that are of the order of the age of the earth, suggesting that the materials are survivors of an early period in the creation of matter by aggregation of nucleons; the shorter lived nuclei have long since decayed away and we observe today the remaining long lived decays. In addition to this naturally occurring radioactivity, we also have the capability to produce radioactive nuclei in the laboratory through nuclear reactions.

## Problems

Some of the solved problems related to the given nuclear equation are given below:

### Solved Examples

Question 1: Calculate the average radius of Si nucleus whose mass number is given as 28?

Solution:

Given parameter is,
Mass number of Si atom, A = 28
The average radius R of the nucleus is given by
R = Ro A1/3
R0 = 1.1fm = 1.1$\times10^{-15}$m
So, R = 1.1$\times10^{-15}\times (28)^{\frac{1}{3}}$
R = 3.340$\times10^{-15}$m

Question 2: Calculate the average radius of Pb nucleus whose mass number is given as 207?

Solution:

Given parameter is,
Mass number of Pb atom, A = 207
The average radius R of the nucleus is given by
R = Ro A1/3
R0 = 1.1fm = 1.1$\times10^{-15}$m
So, R = 1.1$\times10^{-15}\times (207)^{\frac{1}{3}}$
R = 6.507$\times10^{-15}$m