# Chapter 13 – Nuclei

The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:

Introduction

The fundamentals of nuclear physics are based on the study of nuclei and its properties. These properties generally include the structure, composition, mass, and energy of the nucleus.

#### What is Nuclei?

The nucleus (plural: nuclei) is the central core of every atom. It is composed of positively charged particles (protons) and electrically neutral particles (neutrons). In an atom, the protons and neutrons are held together by nuclear force and form the nucleus. Though the size of the nucleus is much smaller than the size of an atom, yet it constitutes 99% of the total mass of an atom.

#### Atomic Masses and Composition of Nucleus

The atomic mass of a nucleus is expressed in terms of the atomic mass unit (AMU or u).

Atomic Mass Unit

One atomic mass unit refers to 1/12th of the mass of one carbon atom. The mass of one carbon atom is 1.992647 x 10-26 kg. Therefore,

1 u = 1.992647 x 10-26/ 12 kg = 1.660539 x 10-27 kg

It is observed that the atomic masses (in AMU) of several elements is approximately equal to the integral multiples of the atomic mass of a hydrogen atom. Generally, the exact atomic mass is measured with the help of a mass spectrometer.

Composition of the Nucleus

As the nucleus contains protons, it is positively charged, and each proton has one unit of fundamental charge. This is balanced by an equal number of electrons on the outside of the nucleus, which is also equal to the element’s atomic number. So, the number of protons in an atom is equivalent to its atomic number.

The presence of neutrons was confirmed by the total weight and different masses of the atoms in the same element. This further gives rise to the concept of isotopes, the atomic species of the same element that vary in mass and neutron number. So, the composition of a nucleus is expressed as follows:

A = Z + N; where A is the Mass number, N is the neutron number, and Z is the atomic (proton) number.

Size of the Nucleus

The size of the nucleus was mainly computed through Rutherford’s α-particle scattering experiment. The experiments revealed that an atom is a mostly empty space while the size of the nucleus is much smaller. In similar scattering experiments, the size of nuclei of different elements has been estimated using fast electrons in place of α-particles.

The radius of a nucleus with mass number A can be calculated as:

R =R0A1/3;

here, R0 = 1.2 × 10-15 m.

This implies that the volume of a nucleus is proportional to A (as the volume itself is proportional to R3). So, the density of a nucleus remains constant, irrespective of the value of A.

Nuclear density is relatively high compared to any ordinary matter. The density of a nucleus is almost 2.3 × 1017 kg m–3.

#### Mass Energy and Nuclear Binding Energy

Einstein’s theory of special relativity proves that mass is just another form of energy. Mass-energy equivalence can be shown as:

E = mc2, where ‘E’ is the energy equivalent of mass ‘m,’ and ‘c’ is the velocity of light in a vacuum, that is equal to 3 × 108 ms-1.

Several experiments involving nuclear reactions amongst electrons, nuclei, nucleons (protons/neutrons), and other particles verify Einstein’s mass-energy relation theory, further forming the basis of nuclear binding energy.

Mass Defect

As every nucleus consists of neutrons and protons, its mass is assumed to be the sum of the neutrons and protons’ total masses. However, most spectroscopy experiments show that the nuclear mass is less than this expected sum. This difference is termed as a mass defect.

Nuclear Binding Energy

The mass defect can be converted into energy with the use of Einstein’s mass-energy relation. If a nucleus has to be broken into its constituent protons and neutrons, and energy equivalent to mass defect has to be supplied. This energy is called nuclear binding energy. So, the relation between binding energy (Eb) and mass defect (ΔM) is given by:

Eb = ΔMc2

Alternatively, an energy equal to Eb is released when protons and neutrons of an element bind together to form a nucleus.

#### Nuclear Force

The nuclear force also called the strong force, or nuclear interaction, is the force that exists between nucleons. It is one of the four basic forces of nature, the others being a gravitational force, electromagnetic force, and weak force. Nuclear forces are stronger than the gravity between masses and Coulomb force (electric repulsion) that acts between charges. This is why the nuclear forces can hold the nucleus together.

However, the nuclear force has the shortest range, and it rapidly reduces to zero if the distance between nucleons becomes more than a few femtometers. But unlike the gravitational and Coulomb forces, the nuclear force cannot be expressed in mathematical form.

The applications of nuclear science and technology go a long way in agriculture, medicine, archaeology, energy production, and other sectors. The field is predicted to present more advancements in scientific research in the near future.

We hope this article helped you understand the fundamentals of nuclei. You can revise for your exams from these notes, or you could use MSVgo’s app; it has excellent animated videos for your understanding. Understanding these concepts through videos is a great solution to ace exams. They have detailed explanations and examples related to these concepts and cover every topic and chapter of the syllabus. Check out the video lectures on MSVgo.

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