Isotopes are atoms of the same element with different numbers of neutrons. Some isotopes have unstable nuclei, which break down (decay) at random, giving out radiation. This is radioactivity.

Alpha particles are helium nuclei (2 protons + 2 neutrons). Beta particles are fast electrons made when a neutron turns into a proton. Gamma rays are high-energy electromagnetic waves.

In a nuclear equation, the mass numbers (top) and atomic numbers (bottom) must add up to the same total on both sides. In alpha decay the mass number falls by 4 and the atomic number by 2. In beta decay the mass number stays the same and the atomic number rises by 1, so a new element forms.

The half-life of an isotope is the time taken for half of the radioactive nuclei in a sample to decay, so the activity (count rate) halves. After 1 half-life, ½ remains; after 2, ¼; after 3, ⅛.

Number of half-lives = time passed ÷ half-life. Then halve the starting amount that many times.