define half-life

Radioactive Decay ⚛️

What is Radioactive Decay?

Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation. Think of it like a leaking balloon: the balloon (nucleus) slowly lets out air (particles) until it stabilises. In the same way, an unstable atom releases particles or energy until it becomes stable.

Types of Decay

• α‑decay: emission of a helium nucleus (2 protons + 2 neutrons)
• β‑decay: conversion of a neutron into a proton (or vice versa) with emission of an electron or positron
• γ‑decay: emission of high‑energy photons (gamma rays) from an excited nucleus

Defining Half‑Life ⏳

The half‑life of a radioactive isotope is the time taken for half of the atoms in a sample to decay. It is a constant for each isotope and gives a convenient way to describe how quickly a substance decays.

Mathematically, if N₀ is the initial number of atoms, then after time t the remaining number N(t) is: $$N(t) = N_0 \, e^{-\lambda t}$$ where λ is the decay constant. The half‑life t_{1/2} is related to λ by: $$t_{1/2} = \frac{\ln 2}{\lambda} \approx \frac{0.693}{\lambda}.$$

Common Half‑Lives