Table of Contents
What Is E=mc²?
E=mc² is the most famous equation in physics, published by Albert Einstein in 1905 as part of his special theory of relativity. It establishes that mass and energy are equivalent and interconvertible. A small amount of mass contains an enormous amount of energy because the speed of light squared (c²) is approximately 9 × 10¹&sup6; m²/s².
This equation revolutionized our understanding of the universe. It explains why the Sun shines (nuclear fusion converts mass to energy), how nuclear power plants generate electricity, and why particle-antiparticle annihilation releases tremendous energy. Every object with mass possesses intrinsic rest energy, even when stationary.
The Formula
Where E is energy in joules, m is mass in kilograms, and c is the speed of light (299,792,458 m/s). Converting 1 gram of matter yields about 9 × 10¹³ joules, enough to power a 100W light bulb for about 28,500 years.
Mass-Energy Examples
| Mass | Energy (J) | Practical Equivalent |
|---|---|---|
| 1 electron (9.1 × 10&sup-;³¹ kg) | 8.19 × 10&sup-;¹&sup4; | 0.511 MeV |
| 1 proton | 1.50 × 10&sup-;¹&sup0; | 938.3 MeV |
| 1 gram | 9.0 × 10¹³ | 21.5 kilotons TNT |
| 1 kilogram | 9.0 × 10¹&sup6; | 21.5 megatons TNT |
Nuclear Applications
- Nuclear fission: Splitting uranium-235 converts about 0.09% of mass to energy, yielding about 200 MeV per fission event.
- Nuclear fusion: Hydrogen fusion in stars converts about 0.7% of mass to energy, making it far more efficient than fission.
- Matter-antimatter: Complete annihilation converts 100% of mass to energy, the theoretical maximum.
- Mass defect: The binding energy of nuclei corresponds to a measurable mass difference between assembled and separated nucleons.
Frequently Asked Questions
Does E=mc² mean we can convert any mass to energy?
In principle, yes, but in practice only nuclear reactions and matter-antimatter annihilation convert significant fractions. Chemical reactions convert negligibly small amounts (about one billionth of the mass involved). Creating antimatter currently requires more energy input than the annihilation produces.
How much mass does the Sun lose per second?
The Sun radiates about 3.846 × 10²&sup6; watts. Using E=mc², this means the Sun converts about 4.27 million metric tons of mass into energy every second through nuclear fusion of hydrogen into helium.
Is mass really converted to energy, or is it just transformed?
Modern physics views mass and energy as two aspects of the same thing. The total mass-energy is always conserved. When we say mass is "converted" to energy, the rest mass decreases while kinetic energy and radiation increase, but the total energy-equivalent mass of the closed system remains constant.