Relate nuclear charge and relative mass to proton and nucleon numbers
Use positive nuclear charge proportional to Z and approximate relative nuclear mass proportional to A.
Section 5.1.2 · The nucleus
Extended only (Supplement); Physics 0625, 2026–2028. Use labelled nuclides, supplied count intervals and stated background conditions. Model drawings are not to scale. Written practice is self-checked.
Before you begin
- Know proton and neutron charges.
- Read A and Z in nuclide notation.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Which gives the relative charge on a nucleus?
What you will learn
- Use positive nuclear charge proportional to Z and approximate relative nuclear mass proportional to A.
- Apply +Z nuclear charge and approximate A-based relative mass while preserving their limits.
Count the charge-carrying constituents
Each nuclear proton contributes +1 relative charge and each neutron contributes zero, so a nucleus with proton number Z has relative charge +Z. This is nuclear charge: a neutral atom can still have this positive nucleus because surrounding electrons balance it.
A ¹⁴₆C nucleus has relative charge +6. A supplied ¹⁶₈O nucleus has relative charge +8. Their charge ratio is 6:8 = 3:4. The neutron counts affect nuclear mass but do not add electric charge.
Use the mass approximation explicitly
Protons and neutrons each have approximately one unit of relative mass; electron mass is very small by comparison. Therefore the relative mass of a nucleus is approximately its nucleon number A. Carbon-14 and carbon-12 have an approximate nuclear mass ratio 14:12 = 7:6.
The approximation is not an exact rest-mass formula. Nuclear binding and the small constituent mass differences matter for exact masses, so an exact fission or fusion energy cannot be obtained by subtracting integer A labels. Ionisation changes the whole atom’s electron inventory, not the nucleus’s Z or A.
Pause and explain
Can exact fusion energy be obtained by treating integer A values as exact rest masses?
Worked example
State relative nuclear charge and approximate relative nuclear mass for ¹⁴₆C.
Show the worked solution
- Six protons give relative charge +6.
- Fourteen nucleons give approximate relative mass 14.
- Use positive sign for nuclear charge.
Answer Charge +6; approximate relative mass 14.
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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.
Find nuclear charge and approximate relative mass for ¹⁶₈O.
Give me a hint
Assign a different role to each nuclide number.
Compare my reasoning
- Z = 8 counts protons.
- Charge is +8.
- A = 16 gives approximate relative nuclear mass 16.
+8; approximately 16.
Look for these in your work
- Keep the positive sign.
- State the mass approximation.
Compare approximate nuclear masses of carbon-14 and carbon-12 as a simplest ratio.
Give me a hint
Use A for both isotopes.
Compare my reasoning
- The approximate masses are 14 and 12.
- Divide both by two.
- The ratio is seven to six.
7:6 approximately.
Look for these in your work
- Use nuclear rather than electron counts.
- Do not claim exact mass equality to A.
A neutral carbon-14 atom is reported to have a zero-charge nucleus. Correct the account.
Give me a hint
Balance nucleus and electrons separately.
Compare my reasoning
- Its nucleus has six protons.
- That nucleus has relative charge +6.
- Six surrounding electrons balance the whole neutral atom.
The nucleus is +6; the complete neutral atom totals zero.
Look for these in your work
- Distinguish subsystem and whole atom.
- Retain the supplied isotope identity.
Common mistakes
- Use Z for charge and A for mass.
- Nuclear charge is not ion charge.
- Relative mass is approximate.
What can you explain now?
Which nuclear constituent adds charge zero but contributes mass?
Compare with the explanation
A neutron
A neutron is uncharged but is a nucleon with approximately one relative mass unit.
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Make it stick
Apply +Z nuclear charge and approximate A-based relative mass while preserving their limits.
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