Learning outcomes
- Describe radioactive decay as a nuclear change.
- Balance nucleon and proton numbers in alpha decay.
- Balance beta-minus equations.
- Represent gamma emission without changing A or Z.
- Identify an unknown daughter nuclide.
8.1 Conservation in nuclear equations
A nuclear equation uses nuclide notation to show a parent nucleus changing into a daughter nucleus and emitted radiation. The total nucleon number A must balance on both sides, and the total proton number or charge number Z must also balance.
This balancing is a powerful way to identify unknown products. It does not mean individual protons and neutrons are always separately unchanged in beta decay; rather, the equation conserves total nucleon number and electric charge.
8.2 Alpha decay
An alpha particle is ⁴₂He. When a nucleus emits alpha, the daughter has A smaller by 4 and Z smaller by 2. The element changes because its proton number changes.
Example: ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He. Check A: 238 = 234 + 4. Check Z: 92 = 90 + 2.
8.3 Beta-minus decay
A beta-minus particle is represented as ⁰₋₁e. During beta-minus decay, a neutron in the nucleus changes into a proton and an electron is emitted. Therefore A remains the same while Z increases by 1.
Example: ¹⁴₆C → ¹⁴₇N + ⁰₋₁e. Check A: 14 = 14 + 0. Check Z: 6 = 7 + (−1). The emitted electron came from the nuclear change, not from the atom’s electron shells.
8.4 Gamma emission
Gamma emission removes excess energy from a nucleus. Gamma has A = 0 and Z = 0, so the identity and nucleon number of the nucleus do not change. A star or asterisk may be used to indicate the initial excited state.
Gamma is often emitted after alpha or beta decay when the daughter nucleus remains excited. An equation may show the same nuclide on both sides plus γ.
8.5 Solving unknowns systematically
Write A and Z for every known term. Subtract the emitted radiation values from the parent values to find the daughter. Then use the new proton number to identify the element from a periodic table if provided.
Never change A and Z by memorising vague rules alone. Balance both rows explicitly to prevent sign errors in beta decay.
Worked examples
Alpha daughter
²²⁶₈₈Ra emits alpha. Daughter A = 226 − 4 = 222 and Z = 88 − 2 = 86, so the daughter is ²²²₈₆Rn.
Beta daughter
²⁴₁₁Na emits beta-minus. A stays 24 and Z becomes 12, giving ²⁴₁₂Mg.
Missing emission
A parent changes from A = 131, Z = 53 to A = 131, Z = 54. The emission must have A = 0 and Z = −1, so it is beta-minus.
Practical focus
Investigation
Use a set of equation cards with missing parent, daughter or emission. Balance A and Z in columns. Verify every completed equation by summing both sides. This activity develops symbolic accuracy without using a radioactive source.
Examination guidance
- Balance A and Z separately.
- Alpha changes A by −4 and Z by −2.
- Beta-minus leaves A unchanged and raises daughter Z by 1.
- Gamma leaves A and Z unchanged.
- Use the daughter proton number to identify the element.
Check your understanding
- Complete: ²¹⁰₈₄Po → ? + ⁴₂He.
- Complete: ³²₁₅P → ? + ⁰₋₁e.
- What changes in the nucleus during gamma emission?
Answers
- ²⁰⁶₈₂Pb.
- ³²₁₆S.
- The nucleus loses excess energy; its proton and nucleon numbers do not change.
