Mass Defect

Introduction

Before special relativity, mass and energy were considered separate things in theoretical approaches. The mass-energy relation, E = mc2, is an equation in Albert Einstein’s special relativity theory that states that mass and energy are the same physical objects that may be converted into one another. The kinetic energy (E) of a body is equal to its increased relativistic mass (m) times the speed of light squared (c2) in the equation.

The binding energy of nuclei is so high that it accounts for a large portion of their mass.

What is Mass Defect?

Given equation describes the relationship between energy and mass:

E=mc2

The speed of light is denoted by c. 

Definition of mass defect

The binding energy of nuclei is so great that they can hold a lot of mass.

Because energy is released when the nucleus is produced, the actual mass is always smaller than the sum of the atomic masses of the nucleons. This energy is made up of mass, called mass defect, since it is exerted from the overall mass of the initial atom. This mass is absent from the final proton and neutron, then the energy released during nuclear reactions.

𝚫M = (Zmp + Nmn) – MA

𝚫M – mass defect

MA – the mass of the nucleus

mp – a mass of a proton (1.00728 amu)

mn – the mass of a neutron (1.00867 amu)

Z – number of protons

N – number of neutrons

The difference between an atom’s mass and the sum of the masses of its electrons, protons, and neutrons is a defect in the mass.

Whereas, the sum of mass and energy is constant. This follows a conservation law where matter can be converted into energy.

Hence the mass defect leads to a lower mass than expected.

Binding Energy Calculation

Binding energy calculation can be done in the following way:

Binding Energy = mass defect x c2

where c = 2.9979 x 108 m/s

c = speed of light in vacuum.

Binding Energy is expressed in terms of MeV.

Binding energy is calculated by subtracting the sum of the masses of protons and neutrons from the masses of various nuclei. The energy released during nuclear reactions is calculated using binding energy measurements.

Mass-Energy Relation

According to the special theory of relativity, E = mc2 is the relationship between mass and energy. The function of mass is energy. The more mass a body has, the more energy it gains or releases.

The term “mass-energy relation” refers to the fact that mass and energy are the same and may be changed into one another. Einstein proposed this concept. However, he was not the first to do so. With his theory of relativity, he accurately described the relationship between mass and energy. The equation is written as E=mc2 and is known as Einstein’s mass-energy equation.

Where E is the object’s equivalent kinetic energy, m is the object’s mass (Kg), and c is the speed of light (c = 3 x 108 m/s).

Furthermore, the mass-energy relation indicates that the body’s rest mass will drop if energy is released from the body due to such a conversion. Ordinary chemical reactions involve such a transfer of rest energy to other types of energy, while nuclear reactions involve significantly bigger conversions.

Even though a system’s overall mass changes, its total energy, and momentum stay constant, according to mass-energy relation. Consider an electron colliding with a proton. Both particles’ mass is destroyed, but a tremendous amount of energy in photons is generated. The concept of the mass-energy equation was important in the development of atomic fusion and fission theories.

Conclusion 

Mass-energy relation expresses that each particle has specific energy even in a fixed position. A fixed body doesn’t have active energy. The amount of energy produced while forming the nucleus, or the mass defect multiplied by the speed of light squared, is equal to the nuclear binding energy (BE). The graph of binding energy per nucleon (BEN) versus atomic number A shows that dividing or combining nuclei releases a huge amount of energy.