Physics the great Zone: Energetics or Einstein’s equation

Einstein’s equation for the equivalence between mass and energy

governs the energetics of nuclear reactions:

Mass is a form of energy? In 1905, Albert Einstein (1873-1955) suggested that mass and energy are equivalent while developing his special theory of relativity. The famous mass-energy equivalence relation states that

E=mc²

where E is the energy equivalent or mass energy,

m is the mass of a body and

c~ 3.8*10⁸ is the speed of light.

It is difficult to show a simple logical path through which Einstein came to his equation. It was merely an hypothesis made by him from special relativity and Maxwell's equations.

Energy gain/loss in everyday examples can, however, hardly show any noticeable change in mass. This is because the total mass of an object changes only by a tiny fraction. To check Einstein's equation, we need something with tiny mass, so that an appreciable change in total mass can be measured. Radioactive decay, a nuclear reaction, is a choice. In fact, Einstein tested his own equation with a lump of radium salt to see if it lost weight as it gave off radiation.

Today, the mass-energy equivalence relation has an important implication in nuclear industry.

Etotal=mc² .........(1.9)

where Etotal,m, and c represent the total energy of a nucleus, its mass,
and the speed of light, respectively. The mass in this equation, however,
depends on the particles speed relative to the speed of light
m = m0 / \/1-(v/c)² , ............(1.10)
where m0 is the rest mass, or the mass of the particle when its speed v = 0. For situations in which v<²,

these same arguments apply to chemical as to nuclear reactions.
However, when one is dealing with the energy changes of the order of
a few eV in chemical reactions, as opposed to changes ofMeVmagnitudes
in nuclear reactions, the changes inmass are much too small to measure.