What Is Radioactive Decay? Types, Formulas, and Examples
Radioactive decay is the spontaneous transformation of an unstable atomic nucleus into a more stable one, releasing energy in the form of radiation. It's a purely quantum mechanical process — no external trigger is needed. An unstable nucleus will eventually decay on its own, and no force in the universe can prevent it or predict exactly when a specific atom will decay. What we can predict, with extraordinary precision, is the statistical behaviour of large numbers of atoms.
The rate of decay is governed by the exponential decay law. If you start with N₀ atoms, the number remaining after time t follows N(t) = N₀ × e^(−λt), where λ is the decay constant unique to each isotope. This leads directly to the concept of half-life — the time for half the atoms to decay.
Alpha decay
What happens
The nucleus ejects an alpha particle — a cluster of 2 protons and 2 neutrons, which is essentially a helium-4 nucleus. The parent atom loses 4 mass units and 2 protons, transforming into a different element two places lower on the periodic table.
Parent (Z, A) → Daughter (Z−2, A−4) + α
Alpha particles are heavy and highly charged, so they're easily stopped — a sheet of paper or a few centimetres of air will block them. But if an alpha emitter gets inside the body (inhaled or ingested), the damage is severe because all that energy is deposited in a tiny volume of tissue.
Alpha decay is the dominant mode for very heavy nuclei (Z > 82). The physics involves quantum tunneling through the Coulomb barrier — the alpha particle doesn't have enough energy to classically escape the nucleus, but quantum mechanics gives it a small probability of tunneling through. This tunneling probability is extraordinarily sensitive to energy, which is why alpha decay half-lives range from microseconds to billions of years.
Beta decay
Beta-minus (β⁻)
A neutron inside the nucleus converts into a proton, emitting an electron and an antineutrino. The mass number stays the same but the atomic number increases by one — the atom moves one place up on the periodic table.
Neutron → Proton + electron + antineutrino
This happens in nuclei that have too many neutrons relative to protons. Carbon-14 decaying to Nitrogen-14 is the basis of radiocarbon dating.
Beta-plus (β⁺) and electron capture
The reverse process: a proton converts to a neutron, emitting a positron and a neutrino (β⁺ decay), or the nucleus captures an inner orbital electron (electron capture). Both reduce the atomic number by one. These occur in proton-rich nuclei.
⁴⁰K + e⁻ → ⁴⁰Ar + ν (electron capture)
Beta particles are much more penetrating than alphas — they can pass through paper but are stopped by a few millimetres of aluminium or plastic.
Gamma decay
What happens
After alpha or beta decay, the daughter nucleus is often left in an excited energy state. It drops to its ground state by emitting a gamma ray — a high-energy photon. No particles are emitted and neither Z nor A changes. The nucleus simply sheds excess energy as electromagnetic radiation.
Gamma rays are the most penetrating form of nuclear radiation. You need thick lead or concrete to attenuate them significantly. They're the primary concern in external radiation exposure scenarios, which is why our dose and shielding calculator focuses on gamma sources.
In some cases, the excited state is metastable — it persists for a measurable time before emitting the gamma ray. Technetium-99m is the most famous example: the "m" stands for metastable, and it has a 6-hour half-life in its excited state before releasing a 140 keV gamma ray that's ideal for medical imaging.
Less common decay modes
Beyond the big three, there are several rarer processes. Spontaneous fission occurs in very heavy nuclei (Z ≥ 90) where the nucleus splits into two roughly equal fragments. Proton emission and neutron emission happen near the drip lines — the boundaries of nuclear existence where nuclei are so unstable they shed individual nucleons. Double beta decay, where two neutrons simultaneously convert to protons, has been observed in a handful of isotopes and is one of the rarest processes ever measured, with half-lives exceeding 10¹⁸ years.
Cluster radioactivity, discovered in 1984, involves the emission of fragments heavier than alphas but lighter than fission fragments — things like Carbon-14, Neon-24, or Silicon-34 nuclei. It's extremely rare compared to alpha decay but has been confirmed in several heavy isotopes.
The exponential decay law
Regardless of the decay mode, the statistical behaviour follows the same law. The probability that any given atom decays in a small time interval dt is λ × dt, where λ is the decay constant. This leads to exponential decay of the population:
A(t) = λN(t) = A₀ × e^(−λt)
t½ = ln(2) / λ ≈ 0.693 / λ
The activity A (decays per second) follows the same exponential, measured in Becquerels (1 Bq = 1 decay/s) or Curies (1 Ci = 3.7 × 10¹⁰ decays/s). Our decay and activity calculator computes these directly from the number of atoms or mass of a sample.
Decay chains
Heavy radioactive nuclei rarely decay straight to a stable isotope. Instead, they go through a series of decays — a chain — losing mass and charge step by step until they reach a stable end product. The three natural decay chains start from Uranium-238, Thorium-232, and Uranium-235, and all terminate at stable isotopes of lead. You can explore these step by step in our decay chain visualizer.
The intermediate isotopes in these chains include some important and sometimes dangerous nuclides: Radium-226 and Radon-222 appear in the uranium chain and are responsible for most natural radiation exposure in buildings. The study of these chains was central to the early history of nuclear physics — it's how the Curies, Rutherford, and others first mapped out the structure of the atom.
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