# Mass-energy Equivalence

#### Introduction

First proposed by Einstein in 1905, the mass-energy equivalence is a counter-intuitive idea which says that mass and energy are the same thing. This principle is represented by the most famous equation in the world, E = mc^{2} where E is the energy, m is mass and c^{2 }is the speed of light squared. The mass-energy equivalence also shows that mass can be converted into energy and energy can be converted into mass. The c^{2} in the equation is a very large number (9 x 10^{16}) and shows that a small amount of mass can be converted to produce an enormous amount of energy. How do we know this equation works? This is the principle used in nuclear bombs and nuclear power plants and both of them work.

#### Variations in the Equation Due to certain Limitations

Interestingly, the equation E = mc^{2 }cannot be used in every case. It has 2 limitations. The equation does not work where the object whose energy is to be calculated is in motion relative to the observer. If the relative motion is high enough, the mass of the object is greater than what is was when the object was at rest. This mass is known as relativistic mass (mass of object in relative motion). The equation also does not work for massless particles such as photons. In these cases, the variations of the equation are used.

When considering an object in relative motion, the equation for mass-energy equivalence is as follows:

E = γmc^{2}, where γ is greek letter gamma which in this case is given by-

Here, γm is relativistic mass. it can be seen mathematically when the relative velocity v is 0 then γ=1 meaning, therefore we get the orignal equation.

In case of massless particles such as photons, the equation of mass energy equivalence is as follows:

E^{2} = (pc)^{2 }+ (mc^{2})^{2}

here p is the momentum of the massless particle and c is again the speed of light. when m=0, the equation becomes E = pc.

#### Applications

The mass-energy equivalence principle has had many applications. Some were destructive whereas some were good. E = mc^{2} is used in nuclear power plants which electrify our cities, it is used in satellite technology and it is used in various space exploration missions. it is also used to explain how the stars shine and other mysterious stuff in the universe.

The Mass-energy equivalence principle really altered the way we looked at reality.