Physics • Year 12 • Module 8 • Lesson 15
Radioactive Decay
Lock in the three decay modes, decay equations, the exponential decay law, half-life, activity, and carbon dating before tackling harder questions.
1. Term–definition match
The definitions below are shuffled. In the right-hand column write the matching term from this list: alpha decay, beta-minus decay, beta-plus decay, gamma decay, half-life, decay constant, activity, becquerel, antineutrino, carbon-14 dating. 10 marks (1 each)
| # | Definition | Matching term |
|---|---|---|
| 1.1 | A decay mode in which an unstable nucleus emits a helium-4 nucleus ($^4_2$He), reducing A by 4 and Z by 2. | |
| 1.2 | A decay mode in which a neutron in the nucleus converts to a proton, emitting an electron and an antineutrino. | |
| 1.3 | A decay mode in which a proton converts to a neutron, emitting a positron and a neutrino. | |
| 1.4 | A decay mode in which an excited nucleus releases excess energy as a high-energy photon without changing A or Z. | |
| 1.5 | The time taken for half the radioactive nuclei in a sample to decay; related to the decay constant by $t_{1/2} = \ln(2)/\lambda$. | |
| 1.6 | The probability of a single nucleus decaying per unit time; symbol $\lambda$; units s$^{-1}$. | |
| 1.7 | The rate of radioactive decay; the number of disintegrations per second; equal to $\lambda N$. | |
| 1.8 | The SI unit of activity; equal to one disintegration per second. | |
| 1.9 | An antiparticle of the electron neutrino; emitted alongside the electron in beta-minus decay. | |
| 1.10 | A radiometric dating technique using the known half-life of $^{14}$C (5,730 years) to estimate the age of once-living organic materials. |
2. True or false — with correction
Circle T or F for each statement. If the statement is false, write the corrected version on the line below it. 12 marks (1 T/F + 1 correction each)
2.1 In alpha decay, the daughter nucleus has a mass number 4 less and an atomic number 2 less than the parent. T / F
2.2 In beta-minus decay, the atomic number of the daughter nucleus decreases by 1 compared to the parent. T / F
2.3 Gamma decay changes both the mass number and the atomic number of the nucleus. T / F
2.4 After three half-lives, one-eighth of the original radioactive sample remains. T / F
2.5 Activity is measured in becquerels, where 1 Bq = 1 decay per second. T / F
2.6 Alpha radiation has the highest penetrating power of the three decay types and cannot be stopped by paper. T / F
3. Fill-in-the-blank paragraph
Use the word bank to complete the passage. Each word is used once. 8 marks (1 per blank)
Word bank:
activity · antineutrino · decay constant · exponential · half-life · ionisation · neutron · proton
Radioactive decay is a random, quantum mechanical process. The rate at which a large sample decays follows an ___________ law: N = N0e−λt, where λ is the ___________. The time for half the nuclei to decay is the ___________, given by t1/2 = ln(2)/λ. The ___________ of a sample is the number of disintegrations per second and equals λN. In beta-minus decay, a ___________ inside the nucleus is converted to a ___________, emitting an electron and an ___________. Alpha particles cause intense ___________ of surrounding matter but are stopped by a sheet of paper or the outer layer of skin.
4. Function recall
Answer each question in 1–2 sentences using precise terms from the lesson. 8 marks (2 each)
4.1 Why is radioactive decay described as a random process at the individual nucleus level, yet follows a precise exponential law for large samples?
4.2 In complete beta-minus decay equations, an antineutrino must be included. Explain why, referring to conservation laws.
4.3 Why is alpha radiation the most dangerous type of radiation internally (inside the body), even though it is stopped by skin externally?
4.4 State the key assumption made in carbon-14 dating, and explain the age range over which it is valid.
5. Build a concept map
Draw labelled arrows between the six terms below to show how they connect. Each arrow must carry a linking phrase. Aim for at least 6 labelled arrows. 6 marks (1 per valid labelled arrow)
Supplied terms: unstable nucleus · radioactive decay · half-life · activity · decay constant · exponential decay.
6. Complete the decay equations
Fill in the missing symbol, mass number, or atomic number for each decay equation. 6 marks (1 each)
| # | Decay equation (fill in the blank) | Decay type |
|---|---|---|
| 6.1 | $^{238}_{92}$U → $^{234}_{90}$Th + $^{?}_{?}$He | |
| 6.2 | $^{14}_{6}$C → $^{14}_{?}$N + e$^-$ + $\bar{\nu}_e$ | |
| 6.3 | $^{60}_{27}$Co$^*$ → $^{60}_{27}$Co + $^{?}$ | |
| 6.4 | $^{22}_{11}$Na → $^{22}_{?}$Ne + e$^+$ + $\nu_e$ | |
| 6.5 | $^{222}_{86}$Rn → $^{?}_{84}$Po + $^{4}_{2}$He | |
| 6.6 | $n \rightarrow p + e^- + ?$ | Fundamental beta-minus process |
Q1 — Term–definition match
1.1 alpha decay • 1.2 beta-minus decay • 1.3 beta-plus decay • 1.4 gamma decay • 1.5 half-life • 1.6 decay constant • 1.7 activity • 1.8 becquerel • 1.9 antineutrino • 1.10 carbon-14 dating.
Q2 — True / false with correction
2.1 True. Alpha decay: A decreases by 4, Z decreases by 2 (the alpha particle carries away 2 protons and 2 neutrons).
2.2 False. In beta-minus decay, a neutron becomes a proton, so the atomic number of the daughter increases by 1.
2.3 False. Gamma decay does not change A or Z. The nucleus simply loses excess energy as a gamma photon; only the nuclear energy state changes.
2.4 True. After n half-lives, the fraction remaining is (1/2)n. After 3 half-lives: (1/2)3 = 1/8.
2.5 True. 1 Bq = 1 disintegration (decay) per second. The curie (Ci) is an older unit: 1 Ci = 3.7 × 1010 Bq.
2.6 False. Alpha radiation has the lowest penetrating power of the three types — it is stopped by a sheet of paper or the outer layer of skin. Gamma radiation has the highest penetrating power.
Q3 — Cloze paragraph
In order: exponential / decay constant / half-life / activity / neutron / proton / antineutrino / ionisation.
Q4.1 — Random vs exponential
Each individual nucleus has a fixed probability per unit time of decaying (the decay constant λ), but exactly which nucleus decays next and when cannot be predicted — it is a quantum mechanical random event. However, when a very large number of nuclei are present, the average statistical behaviour is precisely predictable: the fraction decaying per unit time is constant (λ), leading to the exponential decay law N = N0e−λt.
Q4.2 — Why include the antineutrino
Conservation of energy, momentum, and lepton number must all be satisfied. Without the antineutrino, the electron would carry all the energy released, but experiments show beta electrons have a continuous spectrum of energies (not a single value). The antineutrino carries the missing energy and momentum. Its inclusion also conserves lepton number: the electron has lepton number +1 and the antineutrino has lepton number −1, giving a net lepton number of zero on both sides.
Q4.3 — Alpha most dangerous internally
Alpha particles are massive (4 u) and carry charge +2, so they interact very strongly with surrounding matter, causing intense ionisation and depositing all their energy in a very short range (a few centimetres in air or a fraction of a millimetre in tissue). When an alpha source is inside the body (e.g. inhaled or ingested), all this energy is absorbed by delicate biological tissue, causing far more cellular damage per unit path length than beta or gamma radiation, which deposit energy less densely.
Q4.4 — Carbon-14 dating assumption
The key assumption is that the ratio of $^{14}$C to $^{12}$C in the atmosphere has remained approximately constant over time, so that the initial activity of $^{14}$C in living organisms was the same in the past as it is today. This assumption is approximately valid for roughly the past 50,000 years (approximately 9 half-lives of $^{14}$C), which defines the practical dating range; beyond this, too little $^{14}$C remains to measure accurately.
Q5 — Sample concept map
Accept any six valid labelled arrows, for example:
- unstable nucleus — undergoes → radioactive decay
- radioactive decay — follows → exponential decay
- exponential decay — characterised by → half-life
- decay constant — related to half-life by → half-life (t1/2 = ln2/λ)
- activity — equals λ × N; decreases via → exponential decay
- decay constant — determines rate of → activity
Q6 — Decay equations
6.1: $^4_2$He (alpha particle); decay type = alpha decay. 6.2: atomic number = 7 (Z increases by 1 in β− decay); decay type = beta-minus decay. 6.3: missing particle = γ (gamma photon); decay type = gamma decay. 6.4: atomic number = 10 (Z decreases by 1 in β+ decay); decay type = beta-plus decay. 6.5: mass number = 218 (222 − 4); decay type = alpha decay. 6.6: missing particle = $\bar{\nu}_e$ (antineutrino).