What holds the nucleus together and how it releases energy
Rutherford’s scattering experiment showed that an atom has a tiny, dense, positively charged nucleus. The nucleus contains protons and neutrons, held together by the strong nuclear force, which acts only over very short distances. The radius of a nucleus is about R = R₀A^(1/3), so nuclear density is nearly the same for all elements. The Bohr model explains hydrogen’s line spectrum through electrons jumping between energy levels, with energy E = −13.6/n² eV.
The mass of a nucleus is slightly less than the total mass of its separate protons and neutrons. This mass defect, Δm, corresponds to the binding energy through E = Δmc². Binding energy per nucleon is highest near iron, so heavy nuclei release energy when they split in fission and light nuclei release energy when they join in fusion. Unstable nuclei decay by emitting alpha particles, beta particles or gamma rays, and the number left follows N = N₀e^(−λt), with half-life T½ = 0.693/λ.
Why it matters
Nuclear power plants generate electricity by controlled fission of uranium, and the Sun shines because of fusion of hydrogen into helium. Radioactive isotopes are used to treat cancer, sterilise medical equipment and date ancient objects through carbon dating. Understanding radiation also helps people use it safely.
Key terms
- Mass defect
- The difference between the total mass of separate nucleons and the actual mass of the nucleus.
- Binding energy
- The energy needed to break a nucleus into its separate protons and neutrons.
- Half-life
- The time taken for half of the nuclei in a radioactive sample to decay.
- Nuclear fission
- The splitting of a heavy nucleus into lighter nuclei with the release of energy.