20.7 Interconversion of Matter and Energy
Matter and energy can be converted into each other, a concept explained by Einstein's equation:
E = mc²
where:
- E = energy
- m = mass
- c = speed of light (3 × 10⁸ m s⁻¹)
A small amount of mass can turn into a huge amount of energy, as seen in nuclear fission and fusion. In nuclear reactions, the total mass of the products is slightly less than the mass of the reactants. This missing mass is called mass defect (Δm).
Example 20.3
Calculate the energy released in the fission reaction:
²³⁵₉₂U + ¹₀n → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + 3¹₀n + Energy
Given masses:
- Mass of ²³⁵₉₂U = 235.0439 u
- Mass of neutron = 1.0087 u
- Mass of ¹⁴¹₅₆Ba = 140.9144 u
- Mass of ⁹²₃₆Kr = 91.9262 u
- Mass of 3 neutrons = 3 × 1.0087 = 3.0261 u
Solution:
Mass defect Δm = (235.0439 + 1.0087) - (140.9144 + 91.9262 + 3.0261)
Δm = 236.0526 - 235.8667 = 0.1859 u
Energy E = Δm × 931.5 MeV/u
E = 0.1859 × 931.5 = 173.2 MeV