Writing nuclear decay equations

A nuclear equation shows the nucleus before decay on the left and the new nucleus and the emitted particle on the right. In a balanced equation the total mass number is the same on both sides and the total atomic number (charge) is the same on both sides. Particles have their own symbols: an alpha particle is ⁴₂He, a beta particle is ⁰_-1e, and a neutron is ¹₀n. A gamma ray is shown as γ and has no mass number or atomic number.

Alpha decay of uranium-238 (atomic number 92) gives thorium: ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He. Check the top numbers: 238 = 234 + 4. Check the bottom numbers: 92 = 90 + 2. Radium-226 (atomic number 88) also decays by alpha emission, to radon-222: ²²⁶₈₈Ra → ²²²₈₆Rn + ⁴₂He.

In beta decay the electron has mass number 0 and atomic number -1, so the new nucleus has the same mass number and an atomic number one higher. Carbon-14 decays to nitrogen-14: ¹⁴₆C → ¹⁴₇N + ⁰_-1e. Check: 14 = 14 + 0 and 6 = 7 + (-1).