One of the most profound results of Einstein's theory of special relativity is that mass and energy are equivalent — they are different forms of the same thing. Mass can be converted to energy, and energy can be converted to mass.
Where c = 3.00 × 10⁸ m s⁻¹ is the speed of light in a vacuum. This equation tells us that:
- A small amount of mass corresponds to an enormous amount of energy (because c² is huge)
- In nuclear reactions, measurable mass changes occur, releasing significant energy
- Energy has mass — even a hot object is slightly more massive than a cold one!
Units for Nuclear Physics
In nuclear physics, we typically work with much smaller masses and energies than in macroscopic physics. Two convenient units are:
| Unit | Definition | Value |
|---|---|---|
| Atomic mass unit (u) | 1/12 of the mass of a carbon-12 atom | 1 u = 1.661 × 10⁻²⁷ kg |
| Electronvolt (eV) | Energy gained by an electron crossing 1 V | 1 eV = 1.60 × 10⁻¹⁹ J |
Using E = mc² with the atomic mass unit:
1 u → E = (1.661 × 10⁻²⁷) × (3.00 × 10⁸)² = 1.49 × 10⁻¹⁰ J = 931.5 MeV
This is given in your data booklet. Memorise: 1 u = 931.5 MeV
Particle–Antiparticle Pairs
Energy can be converted into mass in the form of particle–antiparticle pairs. For example, a gamma photon with sufficient energy can spontaneously create an electron–positron pair:
The reverse process, annihilation, occurs when a particle meets its antiparticle — all the mass is converted to energy as gamma photons:
The minimum photon energy for pair production equals the rest energy of the particles created. For an electron–positron pair: