Radioactive Decay
Radioactive decay is the spontaneous process by which an unstable atomic nucleus transforms into a different, more stable nuclear configuration, emitting radiation (alpha particles, beta particles, or gamma rays) in the process, at a rate governed by a fixed, characteristic probability per unit time regardless of the nucleus's age or history.
Curious
Not every combination of protons and neutrons makes a stable nucleus. Some nuclei — like carbon-14 or uranium-238 — are unstable, and will eventually undergo a spontaneous transformation into a different nucleus, releasing energy and radiation in the process. Crucially, this decay is genuinely random at the level of any individual nucleus: there is no way to predict exactly when a specific unstable nucleus will decay, only the probability that it will decay within a given time window.
Despite this individual randomness, radioactive decay is remarkably predictable in aggregate: given a large enough sample of identical unstable nuclei, the fraction that decays in any given time period is extremely consistent and well-described by a simple exponential formula — one of the clearest everyday examples of how genuinely random individual events can combine into precise, predictable statistical behaviour.
Exploring
| Symbol | Name | SI Unit |
|---|---|---|
| N(t) | Number of undecayed nuclei remaining at time t | dimensionless (count) |
| N₀ | Initial number of nuclei at t = 0 | dimensionless (count) |
| λ | Decay constant — probability of decay per unit time for a single nucleus | s⁻¹ |
Three main types of radioactive decay are commonly observed: alpha decay (emission of a helium nucleus, reducing both proton and neutron count), beta decay (a neutron converts to a proton or vice versa, emitting an electron/positron and a neutrino), and gamma decay (emission of a high-energy photon as an excited nucleus drops to a lower energy state, with no change in proton or neutron count at all).
Worked example: A sample starts with N₀ = 1,000,000 nuclei of a substance with decay constant λ = 0.0231 per year (corresponding to a roughly 30-year half-life). After 60 years: N(60) = 1,000,000 × e^(−0.0231×60) = 1,000,000 × e^(−1.386) ≈ 1,000,000 × 0.2501 ≈ 250,100 nuclei remaining.
Deep Dive
Rutherford and Soddy's 1902 paper first established that radioactivity involves the spontaneous transformation of one chemical element into another — a genuinely radical idea at the time, since the transmutation of elements had long been considered impossible (a discredited goal of medieval alchemy), and their proposal initially met considerable scepticism from the broader chemistry community before being firmly established experimentally.
Quantum tunnelling origin of alpha decay: Alpha decay in particular was one of the first phenomena successfully explained by quantum mechanics (Gamow, 1928; see also the Codex's quantum tunnelling entry): classically, an alpha particle inside a nucleus does not have enough energy to overcome the strong-force-plus-Coulomb potential barrier confining it, yet quantum tunnelling gives it a small but nonzero probability of escaping regardless — a probability sensitively dependent on the barrier's height and width, which explains why observed alpha-decay half-lives vary by an astonishing 20+ orders of magnitude across different unstable nuclei, despite the emitted alpha particles' energies varying comparatively little.
Radioactive decay chains — sequences in which one radioactive isotope decays into another radioactive isotope, which decays into another, and so on, until a stable end product is reached — are common for heavy elements; for example, uranium-238 undergoes a chain of 14 sequential decays before finally reaching stable lead-206, a process spanning a combined timescale of billions of years.
Concept Relationship Map
Requires: atomic nucleus, quantum tunnelling
Enables: half-life, alpha decay [PENDING FULL ENTRY], beta decay [PENDING FULL ENTRY]
Commonly confused with: the false idea that decay rate depends on a sample's age or history (it depends only on the fixed decay constant)
Sources
- Rutherford, E., Soddy, F. (1902). Philosophical Magazine, 4(21), 370–396.
- Gamow, G. (1928). "Zur Quantentheorie des Atomkernes." Zeitschrift für Physik, 51(3–4), 204–212.
- Krane, K.S. (1987). Introductory Nuclear Physics. Wiley, Ch. 6.