11.4 The Equivalence Between Mass and Energy

11.4 The Equivalence Between Mass and Energy

According to the special theory of relativity, mass and energy are distinct entities but are interconvertible. The total energy $E$ and mass $m$ of an object are related by the expression:

where $m$ depends on the speed of the object. At rest, the energy equivalent of an object's mass $m_{0}$ is called its rest mass energy $E_{0}$. Thus:

As $mc^{2}$ is greater than $m_{0}c^{2}$, the difference of energy $(mc^{2} - m_{0}c^{2})$ is due to the motion, and it represents the kinetic energy of the mass. Hence:

From Eq. 11.4, the change in mass $\Delta m$ due to change in energy $\Delta E$ is given by:

Because $c^{2}$ is a very large quantity, this implies that small changes in mass require very large changes in energy. In our everyday world, energy changes are too small to provide measurable mass changes. However, energy and mass changes in nuclear reactions are found to be exactly in accordance with the aforementioned equations.