← Modern Physics
4 Nuclei & mass–energy
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Radioactive decay is one of the few places where physics and probability genuinely meet:
Statistics: Probability distributions (91586) Radioactive decay is a RANDOM process: any individual nucleus has a fixed probability of decaying per unit time, and we cannot say which one will go next. Counts of decays in a fixed interval follow a Poisson distribution. The same model you use in Statistics for events at a constant average rate. The smooth exponential half-life curve only appears because you are averaging over enormous numbers of nuclei. Mass–energy equivalence E = m c² c = 3.0×10⁸ m s⁻¹. A mass defect Δm releases energy Δm·c². Binding energy E<sub>b</sub> = Δm c² Energy to separate a nucleus into nucleons; from the mass defect. Radioactive decay / half-life N=N_0\left(\tfrac12\right)^{t/t_{1/2}} t½ = half-life; activity falls by half each half-life.Decay types
- Alpha (α): emits a He nucleus (²⁄₄He); mass −4, charge −2.
- Beta (β⁻): a neutron → proton + electron; charge +1, mass ≈ same.
- Gamma (γ): high-energy photon; no change to Z or A, just energy released.
- Fusion (light nuclei join) and fission (heavy nuclei split) both release energy because the products are more tightly bound.