Conserve nucleon number and charge in nuclear equations
Balance radioactive decay equations and use the unified atomic mass unit as a particle-mass unit.
AS Level; Cambridge International Physics 9702, 2025–2027 syllabus, Topic 11. These original particle models and equations are study aids; full timed assessment and human subject-teacher review remain outstanding.
Before you begin
- Use atomic number, nucleon number, electric charge and conservation with signed values.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What totals are conserved in nuclear equations?
What you will learn
- Apply conservation of nucleon number and charge to nuclear processes
- Represent alpha and beta decay with balanced equations
- Use u as a unit of mass
Balance both nuclear totals
In nuclear processes, total nucleon number A and total charge (proton number Z) are conserved. Write the nuclide symbol for each nucleus and balance the upper and lower numbers separately.
An alpha particle is ⁴₂He or ⁴₂α. In alpha decay, the daughter has A reduced by 4 and Z reduced by 2. In beta-minus decay, a neutron changes to a proton and an electron plus an antineutrino are emitted; the daughter Z rises by 1 while A stays fixed.
Use the unified atomic mass unit
The unified atomic mass unit u is a convenient unit for atomic and nuclear masses. One u is defined as one twelfth of the mass of a neutral carbon-12 atom in its ground state.
Use supplied masses and keep units consistent when applying mass data. The symbol u is a mass unit, not a charge or an energy unit.
Pause and explain
In beta-minus decay, how does daughter Z change?
Worked example
Complete ²³⁸₉₂U → ? + ⁴₂α by conserving nucleon number and charge.
Show the worked solution
- A daughter nucleon number is 238 − 4 = 234.
- Daughter proton number is 92 − 2 = 90.
- Element 90 is thorium.
Answer ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂α.
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Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Complete ²¹⁰₈₄Po → ? + ⁴₂α.
Give me a hint
Subtract the alpha nucleon and proton numbers from the parent.
Compare my reasoning
- A = 210 − 4 = 206.
- Z = 84 − 2 = 82.
- Element 82 is lead.
²¹⁰₈₄Po → ²⁰⁶₈₂Pb + ⁴₂α.
Look for these in your work
- A conserved
- Z conserved
- Daughter symbol correct
Complete the nuclide change ¹⁴₆C → ? + ⁰₋₁e + ⁰₀ν̄ₑ.
Give me a hint
In beta-minus decay A stays fixed and daughter Z rises by one.
Compare my reasoning
- Daughter A = 14.
- Daughter Z = 6 + 1 = 7.
- Element 7 is nitrogen.
¹⁴₆C → ¹⁴₇N + ⁰₋₁e + ⁰₀ν̄ₑ.
Look for these in your work
- Nucleon number retained
- Charge balance applied
- Electron antineutrino included
A particle mass is reported as 3.0 u. State what u measures and one conservation check for a nuclear decay equation.
Give me a hint
Separate the mass unit from the equation's conserved quantum numbers.
Compare my reasoning
- u is the unified atomic mass unit, a unit of mass.
- It is defined from one twelfth of a carbon-12 atom's mass.
- Check total nucleon number and charge on both sides of a decay equation.
u is a mass unit based on carbon-12; independently balance nucleon number and charge in the nuclear equation.
Look for these in your work
- Mass unit identified
- Definition recalled
- Two conserved totals checked
Common mistakes
- Balancing only nucleon number and not charge
- Changing A during beta decay
- Writing an alpha particle with mass number 2
What can you explain now?
What totals are conserved in nuclear equations?
Compare with the explanation
Nucleon number and charge
Balance the upper and lower numbers separately.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Why must both upper and lower nuclide numbers balance in a nuclear equation?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.