Mass-Energy Relation, Mass Defect

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.

Because energy is withdrawn when the nucleus is created, the mass is always smaller than the sum of the separate masses of the component protons and neutrons. The mass of this energy is subtracted from the overall mass of the original particles.

The energy released when the nucleus is produced is represented by the mass defect, lacking in the subsequent nucleus.

Body

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 (roughly = 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.

Einstein’s mass-energy relation is derived in the following way:

Consider an object traveling at around the speed of light. A unified force is acting upon it. Energy and momentum are induced in it due to the applied force. The increase in momentum of the object = mass x velocity of the body because the force is constant.

We know,

Energy acquired= Force x Distance through which force acts

E = F x c

………………………………………… (1) Also,

the momentum gained = the force x the time it takes for the force to act.

As, momentum = mass x velocity,

The momentum gained = m x C

Hence, Force= m x C ……………………………. (2) 

When we combine equations (1) and (2), we get E=mC2.

The equation is used to calculate binding energy in an atomic nucleus. 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.

Binding Energy

The smallest amount of energy needed to remove a particle from a system of particles is known as Binding Energy. To put it another way, it’s the energy used to break down a system of particles into single units. The binding energy term is used to describe the separation of energy in nuclear physics.

Because all nuclei require net energy to divide them into individual protons and neutrons, the binding energy of nuclei is always positive.

Nuclear Binding Energy

The energy required to disassemble a nucleus into free unbound neutrons and protons is known as nuclear binding energy. It is the energy equivalent of the mass defect, which is the difference between a nucleus’s calculated mass and its mass number. The leftover strong force or nuclear force, controlled by three types of particles, is used to generate nuclear binding energy.

Once the mass defect has been calculated, the nuclear binding energy can be estimated by transforming mass to energy using E=mC2. When you calculate the energy in joules for a nucleus, you can scale it down to per-mole and per-nucleon amounts. To translate from joules per nucleon to joules per mole, multiply by Avogadro’s number and divide by the number of nucleons.

Mass Defect

The difference between the actual mass of an atom’s nucleus and its expected mass based on the sum of its non-bound components is explained by nuclear binding energy.

Because the following equation describes the relationship between energy and mass:

E=mC2

The speed of light is denoted by C. 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 constituent neutrons and protons. This energy is made up of mass, called mass defect since it is ejected from the overall mass of the original components. This mass is absent from the final nucleus and describes the energy released during nuclear reactions.

𝚫M = (Zmp + Nmn) – MA

M – mass defect

MA – the mass of the nucleus

mp – mass of a proton (1.00728 amu)

mn – the mass of a neutron (1.00867 amu)

Z – number of protons

N – number of neutrons

Binding Energy Calculation

Binding energy calculation can be done in the following way:

Binding Energy = mass defect x C2

where C = speed of light in vacuum

C = 2.9979 x 108 m/s. 

Binding Energy is expressed in terms MeV’s/nucleon or kJ/mole of nuclei.

Conclusion 

The difference between the overall mass and the sum of the masses of all its component nucleons is called the mass defect of a nucleus. 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.

The ionization energy of an electron in an atom is equivalent to the binding energy of a nucleon in a nucleus.