# Energy Momentum Formula

The energy-momentum relation is considered to be a relativistic equation through which one can relate to the object’s mass when at rest, its total energy, and momentum. This relativistic equation is applicable for a macroscopic body whose mass at rest is m0, the total energy is E, and the magnitude of the momentum is p, with c as the constant representing the speed of light.

## Formula of Energy Momentum

$$\begin{array}{l}E=\sqrt{(p^{2}c^{2})+ (m_{0}c^{2})^{2}}\end{array}$$

Where,

• E is the energy
• p is the momentum
• c is the speed of light
• m0 is the rest mass

### Solved Examples

Example 1:

400 kJ is the energy of the particle which is in motion. The mass of this particle is 2× 10-9 g. Calculate the momentum of the particle.

Solution:

Given:

The energy, E = 400 kJ

The mass, m0 = 2× 10-9 g

We know that the speed of light, c = 3 × 108 m/s

Substituting the above values in the energy-momentum formula, we get

$$\begin{array}{l}E=\sqrt{(p^{2}c^{2})+ (m_{0}c^{2})^{2}}\end{array}$$

p = 119070.4 × 108 kg.m/s

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