Nuclear Bookkeeping
Decay equations — A and Z must always balance
What this lesson covers
Why it matters
When a nucleus fires an alpha, it signs a receipt: 4 units of mass gone, 2 of charge. Nature audits every decay — and the books have balanced for 13.8 billion years.
The idea in plain words
The two rules of the audit. Tap them.
α: A−4, Z−2 · β: A same, Z+1
²²⁶Ra (Z=88) emits an α. Identify the daughter.
²²²Rn — the radioactive gas in basements
- rule 1: α decay — ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He — element moves 2 back
- rule 2: β decay — ¹⁴₆C → ¹⁴₇N + e⁻ — a neutron became a proton, element moves 1 FORWARD
- rule 3: γ emission — no change in A or Z — just the nucleus shedding excess energy after a decay
- A: 226 − 4 = 222
- Z: 88 − 2 = 86 → element 86 is radon
Predict first
After α emission, the daughter nucleus has…
The α carries off 2 protons + 2 neutrons. Lose 2 protons = move 2 places back in the periodic table: transmutation, for real.
- A − 4 and Z − 2 (a new element, 2 steps back) — correct
- A − 2 and Z − 4
- the same A and Z
What you do
Balance both decays: keep A and Z honest on each side.
Check yourself
In β emission the mass number stays the same because…
n → p + e⁻: one nucleon swaps identity, none leave. Z climbs, A holds.
γ emission changes…
γ is the flash after the bang — pure energy leaving an excited nucleus.
²³⁴Th (Z=90) β-decays. The daughter is…
β: A stays 234, Z rises to 91 — protactinium. The U-238 chain's second step.
- a neutron just converts into a proton — the nucleon count is unchanged — correct
- the electron weighs nothing at all
- it doesn't — A drops by 1
- neither A nor Z — only the energy state — correct
- Z by 1
- A by 4
- ²³⁴Pa (Z=91) — correct
- ²³⁰Ra (Z=88)
- ²³⁴Ac (Z=89)