§ 23.1 Mass defect and nuclear binding energy
Key ideas
- Mass-energy equivalence: energy and mass are linked by E = mc²; 1 u of mass is equivalent to about 931 MeV.
- A nucleus is lighter than its separate nucleons; the missing mass defect Δm corresponds to the binding energy holding it together.
- The binding energy per nucleon peaks near iron-56, the most stable region.
- Both fusion of light nuclei and fission of heavy nuclei move products towards the peak, releasing energy.
Equations
E = m c²mass-energy equivalenceJ
E = c² Δmenergy released from a mass defectJ
Fig. 1 · Binding energy per nucleon: light nuclei fuse and heavy nuclei split, both climbing towards the iron peak and releasing energy as binding energy per nucleon rises.
Watch out: energy is released when binding energy per nucleon increases. Iron is the most stable nucleus, so fusing nuclei heavier than iron would cost energy, not release it.
§ 23.2 Radioactive decay
Key ideas
- Decay is random (no telling which nucleus, or when) and spontaneous (unaffected by temperature, pressure or chemistry).
- The activity is proportional to the number of undecayed nuclei: A = λN, with λ the decay constant.
- Numbers and activity fall exponentially; the half-life is fixed for each isotope.
Equations
A = λ Nactivity = decay constant × number of nucleiBq
N = N₀ e^(−λt)exponential decay (A follows the same law)no unit
λ t½ = ln 2 = 0.693linking decay constant and half-lifeno unit
Fig. 2 · Exponential decay: each half-life t½ halves the number remaining, so the count falls to a half, a quarter, an eighth, and so on.
Watch out: the decay constant λ and the half-life are linked by λt½ = 0.693, not λ = 1/t½. A large λ means rapid decay and a short half-life.