A nuclear equation must balance. The total of the mass numbers is the same on both sides, and the total of the charges (the atomic numbers) is the same on both sides. An alpha particle is two protons and two neutrons, the same as a helium nucleus. It has mass number 4 and charge +2. When a nucleus emits one, its mass number falls by 4 and its atomic number falls by 2. For example, radium-226 (atomic number 88) decays to radon-222 (atomic number 86):
22688Ra → 22286Rn + 42He
Check: 226 = 222 + 4 and 88 = 86 + 2.
A beta particle is a fast electron made in the nucleus when a neutron changes into a proton. It has a mass number of 0 (its mass is negligible) and a charge of −1. The mass number of the nucleus does not change, but its atomic number increases by 1. Carbon-14 (atomic number 6) becomes nitrogen-14 (atomic number 7):
146C → 147N + 0−1e
Check: 14 = 14 + 0 and 6 = 7 + (−1).
A gamma ray is electromagnetic radiation. It has no mass and no charge, so when a nucleus emits one, neither the mass number nor the atomic number changes. The nucleus just loses energy. Because the atomic number sets which element an atom is, alpha and beta decay change the element, but gamma emission does not.