Nuclear equations
A nuclear equation describes a decay or reaction. Two conservation rules apply:
- Conservation of mass number ($A$): top numbers balance.
- Conservation of atomic number ($Z$): bottom numbers balance.
Alpha decay
A nucleus ejects an alpha particle ($^4_2 He$). The new nucleus has $Z' = Z - 2$, $A' = A - 4$.
Example: $^{226}{88} Ra \to, ^{222}{86} Rn + ^4_2 He$.
- $A$: 226 = 222 + 4 ✓
- $Z$: 88 = 86 + 2 ✓
Beta-minus decay
A neutron in the nucleus turns into a proton, emitting an electron (β⁻). $Z' = Z + 1$, $A'$ unchanged.
Example: $^{14}_6 C \to, ^{14}7 N + ^{0}{-1} e$.
- $A$: 14 = 14 + 0 ✓
- $Z$: 6 = 7 + (−1) ✓
The electron is written $^0_{-1} e$ — its mass number is 0, its "atomic number" is −1 (representing −1 charge).
Gamma emission
A gamma photon carries away energy but no mass and no charge, so $A$ and $Z$ are unchanged. The product nucleus is in a lower energy state.
Example: $^{60}{27} Co^* \to, ^{60}{27} Co + \gamma$.
(The asterisk denotes an excited state.)
Neutron emission
$^A_Z X \to, ^{A-1}_Z X + ^1_0 n$.
✦Worked example— Worked example — multistep decay
Uranium-238 decays through a long chain ending at lead-206. Identify the immediate product when U-238 emits an alpha:
- $^{238}{92} U \to, ^{234}{90} Th + ^4_2 He$.
- $A$: 238 = 234 + 4 ✓
- $Z$: 92 = 90 + 2 ✓
- Product: thorium-234.
⚠Common mistakes
- Forgetting to balance Z (or A).
- Writing β with the wrong "atomic number" — it's $-1$, not 0.
- Treating gamma as changing Z or A — it doesn't.
- Reading element from old Z (forgetting the daughter is a different element).
➜Try this— Quick check
Which element forms when $^{14}_6 C$ undergoes beta-minus decay?
- New $Z = 7$ → nitrogen.
- $A$ unchanged → 14.
- Product: $^{14}_7 N$.
AI-generated · claude-opus-4-7 · v3-deep-physics