decay
Summary
Decay is the spontaneous change of an unstable nucleus into a more stable one by emitting alpha, beta or gamma radiation. Each nucleus decays at random, but a sample's undecayed amount falls exponentially, halving every half-life.
Detail
Meaning: Radioactive decay is the spontaneous transformation of an unstable nucleus by emitting particles or radiation. Alpha decay emits a helium nucleus (mass number A falls by 4, atomic number Z by 2). Beta-minus decay turns a neutron into a proton and emits an electron (Z + 1, A unchanged). Positron emission and electron capture lower Z by 1. Gamma decay emits a photon and changes neither A nor Z. A single nucleus decays randomly, but each nuclide has a fixed decay probability per second, so the rate is proportional to the number of nuclei left.
Equation: N = N₀e^(−λt) and t½ = ln 2 / λ ≈ 0.693/λ. N is the number of undecayed nuclei at time t (dimensionless), N₀ is the initial number, λ is the decay constant (s⁻¹), t is time (s), and t½ is the half-life (s). Equivalently, N = N₀(½)^(t/t½).
On the MCAT: Expect balancing a decay equation (A and Z must match on both sides), finding the fraction remaining after several half-lives, or reading an exponential decay curve. A shorter half-life means a larger λ.
Common confusion: Two half-lives do not remove everything. Half of the remainder decays each period, leaving 25%, then 12.5%. Half-life is a property of the nuclide, so it does not depend on sample size.
Sources
- Physics (Giancoli)
- Physics (Cutnell and Johnson)
- University Physics (Young and Freedman)
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.