Frontier physics

Radioactivity and decay modes

Unstable nuclei decay probabilistically; an exponential law describes survival, while each decay mode obeys conservation rules.

Unstable nuclei decay probabilistically; an exponential law describes survival, while each decay mode obeys conservation rules.

Model and interpretation

Each nucleus has decay probability λ per unit time, giving N(t)=N₀e^(−λt); activity A is decays per second, measured in becquerels. Alpha emits a helium-4 nucleus; beta-minus converts a neutron to a proton plus electron and antineutrino; beta-plus converts a proton to neutron plus positron and neutrino; gamma de-excites without changing A or Z.

Quick check

The decay law $N(t)=N_0e^{-\lambda t}$ gives half-life $T_{1/2}=\ln2/\lambda$; activity $A=-dN/dt=\lambda N$ falls with the same exponential. In beta decay, charge and nucleon number are conserved by emission of an electron or positron together with a neutrino or antineutrino; alpha decay emits a helium nucleus. These laws predict ensemble averages, not the decay time of an individual nucleus.

The decay constant $\lambda$ is the probability per unit time for decay; identical nuclei in the same state share that instantaneous probability. Randomness makes counts over short intervals fluctuate statistically around the mean. Half-life does not depend on sample mass, but initial activity grows with the number of nuclei. With multiple isotopes or decay chains, coupled rate equations replace a single exponential.

Activity is measured in becquerels, one decay per second, but absorbed dose also depends on radiation energy and type. Alpha particles ionize strongly but are stopped by thin material; gamma rays penetrate more deeply. Radiation safety distinguishes activity, absorbed dose, and equivalent dose rather than treating them as interchangeable.