An element zSᴬ decays to ₈₅R²²² after emitting 2 α particles and 1 β particle. Find the atomic number and atomic mass of the element S.

Let the element be ₂S^A, decaying to ₈₅R²²² by emitting 2 alpha particles and 1 beta particle.

Effect of each emission: alpha (₂He⁴) : mass number − 4, atomic number − 2 beta (₋₁e⁰) : mass number unchanged, atomic number + 1

Mass number: 2 alpha particles reduce A by 2 × 4 = 8; beta changes nothing. A − 8 = 222 A = 222 + 8 = 230

Atomic number: 2 alpha particles reduce Z by 2 × 2 = 4; 1 beta raises it by 1. Z − 4 + 1 = 85 Z − 3 = 85 Z = 88

Atomic number of S = 88 and mass number of S = 230

Work backwards from the product, and treat mass number and atomic number as two separate sums — never mix them in one line.

The beta particle is what people get wrong. It does not change the mass number at all, and it INCREASES the atomic number by 1 (a neutron turns into a proton and the electron leaves). So going backwards you SUBTRACT that 1, which is why Z is 88 and not 90. Check your answer by going forwards: 88 − 4 + 1 = 85 ✓ and 230 − 8 = 222 ✓.