Mass Energy Relation | Physics Optional Notes for UPSC PDF Download

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 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Because energy is withdrawn when the nucleus is created, the mass is always smaller than the sum of the separate masses of the component protons and neutrons.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.

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 the 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 travelling 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 d  ……………… (1) 
Also,
the momentum gained = the force x the time it takes for the force to act.
P = F x t
As, momentum = mass x velocity,
The momentum gained P = m x c
Hence, Force= (m x c)/t …………… (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.

Derivation II

At whatever point an article is in speed, it appears to get heavier. The accompanying condition gives the increment in mass because of speed.
m= m₀/ [(1 − v²)/c²]
Where,
m-mass of the article at the voyaging speed
m₀-mass of the article at a fixed position
v-speed of the article
c-speed of the light
We know, a moving object has active energy, and it is given by
E= ½ (mv²)
All-out energy moved by the item is roughly equivalent to dynamic energy and expansion in mass because of speed.
E≅ (mc²) + ½ (mv²)
E-(mc²) = ½ (mv²), for little v/c 
E = Relativistic dynamic energy + mc²
The relativistic dynamic energy includes kinetic energy and rest mass energy 
E = 0+mc²
E= mc²

Conclusion

Mass-energy relation expresses that each article has specific energy even in a fixed position. A fixed body doesn’t have active energy. It just has expected energy and likely compound and nuclear power. As indicated by the field of applied mechanics, the amount of this multitude of points is more modest than the result of the particle’s mass and the square of the speed of light.

Mass-energy relation implies mass and energy are very similar and can be changed over into one another. Einstein put this thought forward, yet he was not quick to uncover this. He portrayed the connection between mass and energy precisely utilising his relativity hypothesis. The condition is known as Einstein’s mass-energy condition and is communicated as, 
E=mc² 
​where E= comparable dynamic energy of the article, 
​m = mass of the item (Kg) and 
c = speed of light (roughly = 3 x 10⁸ m/s)