A nuclear equation balances when the top numbers (nucleon numbers) and the bottom numbers (proton numbers) add to the same totals on both sides. Two checks are all you need.
This lesson is part of SPM Physics nuclear physics. It uses the radiation types from distinguishing types of radiation.
What are the decay patterns?
- Alpha decay: the nucleus loses ⁴₂He, so the nucleon number falls by 4 and the proton number by 2.
- Beta decay: the nucleus emits ⁰₋₁e, so the nucleon number is unchanged and the proton number rises by 1.
Worked examples
Alpha decay of uranium-238.
²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He
Check nucleon number: 238 = 234 + 4. Check proton number: 92 = 90 + 2.
Beta decay of carbon-14.
¹⁴₆C → ¹⁴₇N + ⁰₋₁e
Check nucleon number: 14 = 14 + 0. Check proton number: 6 = 7 + (−1).
Finding an unknown. ²²⁶₈₈Ra → X + ⁴₂He. The nucleon number of X is 226 − 4 = 222, and the proton number is 88 − 2 = 86. The element with proton number 86 is radon, so X is ²²²₈₆Rn.
The mistake that costs marks
The common slip is to change the nucleon number in beta decay. Writing ¹⁴₆C → ¹³₇N + ⁰₋₁e is wrong, because the electron is not a nucleon and the nucleon number must stay at 14.
| Decay | Wrong | Right |
|---|---|---|
| Beta of ¹⁴₆C | ¹⁴₆C → ¹³₇N + ⁰₋₁e | ¹⁴₆C → ¹⁴₇N + ⁰₋₁e |
| Alpha of ²³⁸₉₂U | ²³⁸₉₂U → ²³⁴₉₂Th + ⁴₂He | ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He |
Write the two sums as a check line under every equation.
How do you find the new element?
The proton number identifies the element. Count back or forward in the periodic table from the parent: two places back after alpha decay, one place forward after beta decay.
Check yourself
Complete ²⁴¹₉₅Am → ? + ⁴₂He, and complete ²¹⁴₈₂Pb → ? + ⁰₋₁e.
Answer
Alpha: nucleon number 241 − 4 = 237, proton number 95 − 2 = 93, so ²³⁷₉₃Np. Check: 237 + 4 = 241 and 93 + 2 = 95.
Beta: nucleon number stays at 214, proton number rises to 82 + 1 = 83, so ²¹⁴₈₃Bi. Check: 83 + (−1) = 82.
What to study next
Continue with comparing fission and fusion conceptually, which uses the same conservation rules. Test yourself with the nuclear physics practice set.
The units and significant-figure checker helps with answer presentation. If you want a teacher to go through your equations, see online one-to-one Physics tuition.