Question

Write Einstein’s mass energy relation and explain the terms?

Answer 1

Hint To answer this question, we need to appreciate the significance of the mass energy relation which is given by the formula $ m = \dfrac{{{m_0}}}{{\sqrt {1 - \dfrac{{{v^2}}}{{{c^2}}}} }} $ . Also, we have to mention the condition when it is applicable.

Formula Used: The formula used in this solution is given by
 $ m = \dfrac{{{m_0}}}{{\sqrt {1 - \dfrac{{{v^2}}}{{{c^2}}}} }} $ , here $ m $ is the relativistic mass of an object moving with a relativistic speed of $ v $ , $ {m_0} $ is the rest mass of the object, and $ c $ is the speed of light in vacuum.

Complete step by step answer
Before the development of the mass energy relation, it was believed that the mass and the energy are the separate entities. So, in a reaction they were believed to be conserved separately. But the development of the special theory of relativity in 1905 by Albert Einstein changed this notion completely. He proved from his theory that the mass and the energy are actually equivalent. So he showed that it is possible to convert the mass into energy and vice-versa. He represented this equivalence between the mass and the energy by the following equation.
 $ E = m{c^2} $
Here $ E $ is the energy corresponding to a mass $ m $ of a substance, and $ c $ is the speed of light in vacuum or free space.
From this equation, it is easy to conclude that the mass is actually a form of energy just like its other forms such as the kinetic energy, the potential energy etc.
This equivalence, known as the mass-energy equivalence, is based on the concept of relativistic mass. In classical mechanics we generally take the mass of a substance as a constant. But in modern physics, where objects move with relativistic speeds (close to the speed of light in vacuum), the mass is a function of the object’s velocity. It is given by the relation
 $ m = \dfrac{{{m_0}}}{{\sqrt {1 - \dfrac{{{v^2}}}{{{c^2}}}} }} $
Using the above relation for the relativistic mass, we can derive the mass energy relation.
Since it is based on the relativistic mass, the above equivalence is appreciable only when the particles move with relativistic speeds.

Note
The mass energy equivalence relation is widely used in many fields of physics. For example, it is used in creating nuclear weapons. It is also used in determining the mass defect of an atom, and thereby the binding energy corresponding to the atom. The binding energy principle is applied to create nuclear fission chain reactions.