Decay probability is the likelihood that a particle will undergo a specific decay process within a given time.Decay probability is the likelihood that an unstable particle or quantum state will undergo a specific decay process within a given time interval. In quantum mechanics, decay is inherently probabilistic: an excited atom, a radioactive nucleus, or an unstable elementary particle has no definite 'lifetime' but rather a probability per unit time of decaying. This probability is governed by the transition rate, often calculated using Fermi's Golden Rule, which depends on the strength of the interaction causing the decay and the density of available final states. The concept is fundamental to nuclear physics, particle physics, and quantum optics, where it explains phenomena from radioactivity to spontaneous emission.
The probabilistic nature of decay was established in the early 20th century with the work of Rutherford and Soddy on radioactive decay (1902), who empirically found the exponential law. The quantum mechanical explanation was developed by Dirac (1927) and later formalized by Fermi (1950) in his Golden Rule, which remains the standard tool for calculating decay rates.
For a system in an initial state |i⟩, the decay probability to a final state |f⟩ per unit time is given by the transition rate Γ = (2π/ℏ) |⟨f|H'|i⟩|² ρ(E_f), where H' is the perturbing interaction and ρ(E_f) is the density of final states. The total decay probability over time t is then P(t) = 1 − exp(−Γt), assuming a constant Γ. This exponential behavior arises when the decay is Markovian—the system has no memory of its past. The decay probability is measured by preparing many identical particles and counting how many decay in successive time intervals, yielding the characteristic exponential decay curve.
Decay probability is used in radiocarbon dating, nuclear reactor design, particle physics experiments (e.g., measuring the Higgs boson's decay channels), and in quantum computing to predict qubit relaxation times and optimize error correction.
The decay probability of a single particle is constant per unit time, but if you watch it continuously, the quantum Zeno effect can suppress the decay—frequent measurements can freeze the particle in its initial state.
