Einstein's Theory of Relativity & E = mc2 Explained for JEE Physics

In physics, mass–energy equivalence is the relationship between mass and energy in a system's rest frame, where the two values differ only by a constant and the units of measurement. The principle is famously described by Albert Einstein's equation:

E = mc^2

Where:

$E$ is the relativistic energy of the system
$m$ is the relativistic mass
$c$ is the speed of light in a vacuum ( $3 \times 10^8 \text{ m/s}$ )

The Derivation and Relativistic Mass

When an object is in motion, its relativistic mass increases according to the Lorentz factor:

m = \frac{m_0}{\sqrt{1 - \frac{v^2}{c^2}}}

Where $m_0$ represents the rest mass of the object and $v$ represents its velocity. As $v$ approaches $c$ , the mass $m$ approaches infinity, which explains why no object with rest mass can accelerate to the speed of light.

Importance for JEE/NEET aspirants

In modern physics chapters, you will often find numerical problems asking to compute the energy released during nuclear fission or fusion reactions. In these cases, the mass defect $\Delta m$ is converted directly into energy using the modified form:

\Delta E = \Delta m \cdot c^2

Remember that if $\Delta m$ is given in atomic mass units (amu), the equivalent energy is approximately calculated as:

\Delta E = \Delta m \times 931.5 \text{ MeV}