From the theory of relativity, Einstein showed that mass and energy are interchangeable according to:
E = mc2
Where E is energy in Joules (J), m is mass in kilograms (kg) and c is the speed of light ≈ 3.0 × 108 ms-1
e.g. if 1 g of matter were converted entirely into energy, it would release 9 × 1013 J or 2.5 × 107 KWh
Example calculation
How much energy is released by an electron-positron annihilation?
me = 9.1 × 10-31 kg
c = 3.0 × 108 ms-1
E = mc2
E = 2 × 9.1 × 10-31 x (3.0 × 108)2 = 1.6 × 10-13 J
This works both ways
Mass-energy conversion is a two-way process, so in the atmosphere electron-positron pairs can be formed from pure energy.
For the electron-positron pair, the energy will be in the form of an electro-magnetic wave with frequency E/h
λ = 1.2 × 10-12 m ∴ it will be a gamma ray.
Energy units
Often the energy in nuclear reactions is expressed in MeV, mega electron-volts.
1 eV = energy given to an electron when accelerated through 1 V
Wd = energy transferred = V x e
V = 1 V
e = 1.6 × 10-19 C
∴ 1 eV = 1.6 × 10-19 J
∴ 1 MeV = 1.6 × 10-13 J
Another unit for energy/mass is the unified atomic mass unit, u. This is 1/12th of a carbon-12 atom:
1 u = 1.66 × 10-27 kg
1 u = 934 MeV