understand that nucleon number and charge are conserved in nuclear processes

Atoms, Nuclei and Radiation (Cambridge IGCSE/A‑Level 9702 – Syllabus 11.1)

Learning objective

Students will be able to show that the total mass number (A) and the total atomic number (Z) are conserved in every nuclear process. This includes:

• Writing complete nuclear equations (including all emitted particles – α, β⁻, β⁺, γ, neutrinos/antineutrinos, and electron‑capture particles).
• Balancing the equations by checking the sums of A and Z on both sides.
• Identifying the type of decay or reaction from the change in A and Z.

1. Nuclear notation

The standard symbol for a nuclide is

• A (mass number) – total number of nucleons (protons + neutrons).
• Z (atomic number) – number of protons; determines the element.
• N = A − Z – number of neutrons.

Example: ²³⁸₉₂U has 92 protons, 146 neutrons and a mass number of 238.

2. Isotopes and nuclide tables

Isotopes are nuclides with the same Z but different A (hence different N). The Cambridge syllabus expects students to recognise at least the following common isotopes.

Element	Isotope (common name)	Notation	Neutrons (N)	Typical use / comment
Carbon	Carbon‑12	⁽¹²⁾₆C	6	Stable; defines the atomic‑mass unit
Carbon	Carbon‑14	⁽¹⁴⁾₆C	8	β⁻ emitter; radiocarbon dating
Uranium	Uranium‑235	⁽²³⁵⁾₉₂U	143	Fissile; nuclear reactors & weapons
Uranium	Uranium‑238	⁽²³⁸⁾₉₂U	146	α emitter; most abundant uranium isotope
Technetium	Technetium‑99m	⁽⁹⁹ᵐ⁾₄₃Tc	56	γ emitter; medical imaging

3. Conservation laws in nuclear reactions

• Mass‑number conservation: ∑ A (reactants) = ∑ A (products)
• Atomic‑number (charge) conservation: ∑ Z (reactants) = ∑ Z (products)
• Neutrinos (ν) and antineutrinos ( \(\bar{u}\) ) are electrically neutral and have negligible mass; they do not affect the A‑ or Z‑balance but must be written in a complete equation.

4. Common nuclear processes

4.1 Alpha (α) decay

α particle = helium‑2 nucleus: ⁴₂He (2 p + 2 n).

• A decreases by 4, Z decreases by 2.
• No leptons are emitted.

4.2 Beta‑minus (β⁻) decay

Particle level: n → p + e⁻ + \(\bar{u}_e\)

• A unchanged.
• Z increases by 1; the emitted electron (charge −1) balances the charge.

4.3 Beta‑plus (β⁺) decay – positron emission

Particle level: p → n + e⁺ + ν_e

• A unchanged.
• Z decreases by 1; the positron (charge +1) restores overall charge balance.

4.4 Electron capture (EC)

Particle level: p + e⁻ → n + ν_e

• A unchanged, Z decreases by 1.
• Often written without the explicit orbital electron when the capture is understood.

4.5 Gamma (γ) emission

An excited nucleus releases excess energy as a high‑energy photon.

• No change in A or Z.
• Only energy (and a tiny amount of momentum) is carried away.

4.6 Summary of emitted particles

Particle	Symbol	A	Z	Charge
Alpha	α	4	2	+2 e
Beta‑minus	e⁻	0	0	−1 e
Beta‑plus (positron)	e⁺	0	0	+1 e
Neutrino	νe	0	0	0
Antineutrino	\(\bar{u}_e\)	0	0	0
Gamma photon	γ	0	0	0

5. Worked examples – checking A and Z balance

Example 1: α decay of ²³⁸₉₂U

	Mass number (A)	Atomic number (Z)
LHS	238	92
RHS	234 + 4 = 238	90 + 2 = 92

Example 2: β⁻ decay of ¹⁴₆C

	Mass number (A)	Atomic number (Z)
LHS	14	6
RHS	14 + 0 = 14	7 + (−1) = 6

Example 3: Electron capture of ⁵⁵₂₆Fe

	Mass number (A)	Atomic number (Z)
LHS	55 + 0 = 55	26 + (−1) = 25
RHS	55 + 0 = 55	25 + 0 = 25

6. Step‑by‑step procedure for balancing a nuclear equation

1. Write the reaction skeleton – include the parent nuclide and any known emitted particles.
2. Assign A and Z values to every species (use the particle table for leptons, neutrinos, α, γ).
3. Sum A on each side. If they differ, look for a missing α particle or for a possible β⁺/β⁻/EC adjustment.
4. Sum Z on each side (remember: e⁻ = −1, e⁺ = +1, neutrinos = 0, γ = 0). Adjust by adding the appropriate lepton or by changing the decay mode.
5. Check charge balance – the total electrical charge must be the same on both sides.
6. Write the final, complete equation including any neutrinos or antineutrinos.

7. Common pitfalls & how to avoid them

• Omitting leptons – β⁻ always includes an electron; β⁺ always includes a positron; EC always includes an orbital electron.
• Forgetting neutrinos/antineutrinos – they do not affect A or Z but a complete equation must show them.
• Assuming γ changes A or Z – it never does; only energy is emitted.
• Mixing up charge signs – e⁻ = −1 e, e⁺ = +1 e. Remember to include the lepton’s charge when balancing Z.
• Incorrect mass‑number change in α decay – always subtract 4 from A and 2 from Z.
• Confusing β⁺ decay with positron emission from a different process – β⁺ emission and electron capture are alternative ways for a nucleus to reduce Z by 1.

8. Quick reference table

Process	Change in A	Change in Z	Typical emitted particle(s)
α decay	−4	−2	α (⁴He)
β⁻ decay	0	+1	e⁻ + \(\bar{u}_e\)
β⁺ decay	0	−1	e⁺ + νe
Electron capture	0	−1	νe (captures an orbital e⁻)
γ emission	0	0	γ photon

9. Suggested classroom diagram (placeholder)

10. Summary

Every nuclear transformation obeys two inviolable conservation laws:

• The total mass number (A) – the count of all nucleons – remains unchanged.
• The total atomic number (Z) – the net positive charge – remains unchanged when the charges of all emitted particles (including antiparticles) are taken into account.

By writing complete nuclear equations, assigning A and Z to every species, and systematically checking the balances, students can confidently analyse all nuclear processes required by the Cambridge IGCSE/A‑Level syllabus.