radioactive decay

Meaning: Radioactive decay is the spontaneous change of an unstable nucleus into a more stable one by emitting particles or radiation. Mass number A and atomic number Z must balance. Alpha: a helium-4 nucleus is lost (A − 4, Z − 2). Beta-minus: a neutron becomes a proton, an electron and an antineutrino (Z + 1, A unchanged). Beta-plus: a proton becomes a neutron, a positron and a neutrino (Z − 1); electron capture also lowers Z by 1. Gamma: a photon is emitted, and A and Z are unchanged. Each nucleus decays at random, but a large sample follows first-order kinetics, and its rate is essentially unaffected by temperature or chemical state.

Equation: N = N₀e^(−λt), with t½ = ln 2 / λ ≈ 0.693 / λ. N is the number of nuclei remaining (a count), N₀ the initial count, λ the decay constant (s⁻¹), t the time (s) and t½ the half-life (s). Activity = λN, in becquerels (1 Bq = 1 decay per s).

On the MCAT: You may complete a nuclear equation by balancing A and Z, name the emitted particle, or find the fraction left after n half-lives (1/2ⁿ). Decay curves are exponential, and they are straight lines on a semilog plot.

Common confusion: After two half-lives 25% remains, not zero, because each half-life halves whatever is left. A larger λ means a shorter half-life, not a longer one.