The shape of the lesson
By the end of the lesson, learners can
- Random nuclei, smooth curve: Each nucleus winks out at random, but watch the count: with a whole sample it halves in a fixed half-life and traces the exponential, whatever half-life you choose.
- Activity, constant, half-life: Four ideas, tightly linked.
- Binding energy: Δm = Σ(nucleon masses) − M; binding energy = Δm c²; stability from BE per nucleon.
- Reaction energy: E = c²Δm with Δm = mass of reactants − mass of products.
- Decay: A = λN; N = N₀e⁻λᵗ; λ t½ = ln2; fraction after n half-lives = (½)ⁿ.
One picture every idea returns to
Decay is random and spontaneous: unpredictable for any one nucleus and unaffected by external conditions. The activity is A = λN, where the decay constant λ is the probability of decay per unit time. Because the rate is proportional to the number left, the count falls exponentially, N = N₀e⁻λᵗ, halving every half-life, with λt½ = ln2.
Forty-five minutes, phase by phase
| Time | Phase | What happens in the room | Grouping |
|---|---|---|---|
| 0 to 5 min | Hook: predict | Open with the question in the title, Random nuclei, a certain law.. You can never say which nucleus will decay next, only the chance per second. Put the figure on the board: it is the one picture every idea in the lesson returns to. | Whole class, then pairs |
| 5 to 17 min | Teach and check: Random nuclei, smooth curve | Each nucleus winks out at random, but watch the count: with a whole sample it halves in a fixed half-life and traces the exponential, whatever half-life you choose. Project tab 3 of the lab (Radioactive decay) and let a student drive it while the class predicts. | Whole class, then pairs |
| 17 to 30 min | Teach and check: Activity, constant, half-life | Four ideas, tightly linked. | Frayer Model |
| 30 to 43 min | Check and plenary | The quick-check questions from the student lesson, answered on mini whiteboards one at a time; re-teach the one most get wrong, then a random call on the last. | Individual, then whole class |
| 43 to 45 min | Exit and homework | Set the worksheet below (5 questions, 43 marks) from the topic practice set. Learners self-assess against the objectives before they leave. | Individual |
Protect the parts that carry the learning
The sequence carries about fifty minutes of material, so the lab is driven by one student while the class predicts rather than explored freely. Times are a guide.
Protected: the check at 30 minutes. It is the only individual read on whether the key idea landed, and it is not cut.
Cut first if the build overruns: the last check in Activity, constant, half-life, never the check or the plenary.
In a 60 minute block: run worksheet questions 1 to 3 in class as a Rally Coach set and model both the hardest worked example and its check live.
Frayer Model
Pairs fill a four-box grid for the key term: definition, characteristics, examples and non-examples. The non-examples box is where the misconceptions surface, so give it the most time.
The full structure, with its variations and the other twelve, is on the cooperative-learning page.
What to head off, and how
| Trap learners fall into | Teaching move that pre-empts it |
|---|---|
| Activity and count rate fall on the same exponential as N, because both are proportional to N. | The half-life is a constant for a given isotope, independent of how much is left. After n half-lives the fraction remaining is (½)ⁿ, so three half-lives leave one eighth. Keep λ and t½ in consistent time units before substituting. |
Radioactive decay: topic worksheet
5 questions, 43 marks. Written in the style of the papers; no past paper question is reproduced. These questions cover the whole topic, so sibling lessons share them.
A radioactive source contains 5.0 × 10²₀ undecayed nuclei of a nuclide whose decay constant is 2.0 × 10⁻⁸ s⁻¹.
(a) State what is meant by the decay constant. [1]
(b) Calculate the activity of the source, in Bq. [2]
(c) Calculate the half-life of the nuclide, in seconds. [2]
(d) State and explain how the activity changes as time passes. [3]
A radioactive nuclide has a half-life of 8.0 days.
(a) Calculate its decay constant, in day⁻¹. [2]
(b) State the fraction of the original nuclei remaining after 24 days. [2]
(c) Calculate the fraction remaining after 20 days. [3]
(d) State whether the half-life depends on how much of the sample is left. [1]
A sample of a nuclide of half-life 15 hours has an initial activity A₀.
(a) Calculate the time for the activity to fall to A₀/16. [2]
(b) Calculate the decay constant, in hour⁻¹. [2]
(c) Calculate the time for the activity to fall to 10% of A₀. [3]
(d) State why a measured count rate is usually less than the activity. [1]
Carbon-14 has a half-life of 5730 years. A living sample has a C-14 activity of 0.25 Bq per gram of carbon. An old wooden artefact reads 0.0625 Bq per gram.
(a) State the assumption that makes carbon dating possible. [1]
(b) Calculate the age of the artefact using the number of half-lives. [3]
(c) Confirm the age using N = N₀e⁻λᵗ. [3]
(d) Suggest one reason very old samples cannot be dated this way. [1]
Radium-226 decays by alpha emission to radon: ²²⁶₈₈Ra → ²²²₈₆Rn + ⁴₂He. Masses (u): Ra-226 = 226.0254, Rn-222 = 222.0176, He-4 = 4.0026. The half-life of radium-226 is 1600 years.
(a) Show that the nucleon and proton numbers balance in the equation. [2]
(b) Calculate the change in mass, in u. [2]
(c) Calculate the energy released, in MeV and in joules. [3]
(d) Calculate the decay constant of radium-226, in s⁻¹ (1 year = 3.15 × 10⁷ s). [2]
(e) State whether the energy released per decay changes as the sample ages, and why. [2]
Answer key and marking notes
- (a)The probability per unit time that a given nucleus decays ✓
- (b)A = λN = 2.0 × 10⁻⁸ × 5.0 × 10²₀ ✓ = 1.0 × 10¹³ Bq ✓
- (c)t½ = ln2 / λ = 0.693 / 2.0 × 10⁻⁸ ✓ = 3.5 × 10⁷ s ✓
- (d)The activity falls ✓; as nuclei decay N decreases, and since A = λN the activity decreases too ✓; it does so exponentially, halving each half-life ✓
- (a)λ = 0.693 / 8.0 ✓ = 0.0866 day⁻¹ ✓
- (b)24 days = 3 half-lives ✓; fraction = (½)³ = 1/8 ✓
- (c)N/N₀ = e⁻λᵗ = e⁻⁽⁰.₀₈⁶₆ × ²₀⁾ ✓ = e⁻¹.⁷³ ✓ = 0.18 (about 18%) ✓
- (d)No, the half-life is constant for the nuclide, independent of the amount remaining ✓
- (a)A₀/16 = (½)⁴ A₀, so 4 half-lives ✓ = 4 × 15 = 60 hours ✓
- (b)λ = 0.693 / 15 ✓ = 0.0462 hour⁻¹ ✓
- (c)t = (1/λ) ln(A₀/A) = (1/0.0462) ln(10) ✓ = 21.6 × 2.303 ✓ = 50 hours ✓
- (d)The detector intercepts only a fraction of the radiation, and some is absorbed or misses it ✓
- (a)The C-14 activity per gram in living matter has stayed constant over time ✓
- (b)0.0625 / 0.25 = 1/4 = (½)² ✓, so 2 half-lives ✓ = 2 × 5730 = 11460 years ✓
- (c)λ = 0.693/5730; t = (1/λ) ln(4) = 5730 × (ln4/ln2) ✓ = 5730 × 2 ✓ = 11460 years ✓
- (d)After many half-lives the remaining activity is too small to measure above background ✓
- (a)Nucleon: 226 = 222 + 4 ✓; proton: 88 = 86 + 2 ✓
- (b)Δm = 226.0254 − (222.0176 + 4.0026) ✓ = 226.0254 − 226.0202 = 0.0052 u ✓
- (c)E = 0.0052 × 931 ✓ = 4.8 MeV ✓ = 4.8 × 10⁶ × 1.60 × 10⁻¹⁹ = 7.7 × 10⁻¹³ J ✓
- (d)t½ = 1600 × 3.15 × 10⁷ = 5.04 × 10¹⁰ s; λ = 0.693 / 5.04 × 10¹⁰ ✓ = 1.4 × 10⁻¹¹ s⁻¹ ✓
- (e)No ✓; each decay involves the same nuclei and the same mass change, so the energy per decay is fixed; only the number of decays per second falls ✓
The lesson's own checks as a quiz
The quick-check and exam-style questions from the student lesson, printable with the key.
Radioactive decay is described as random and spontaneous because:
- Ayou cannot predict which nucleus decays next, and the rate is unaffected by external conditions
- Bevery nucleus decays at exactly the same time
- Cheating the source speeds it up
- Donly the heaviest nucleus decays first
The activity of a radioactive source is given by:
- AA = λN
- BA = N / λ
- CA = λ / N
- DA = λ + N
The decay constant λ and the half-life t½ are related by:
- Aλ t½ = ln2
- Bλ t½ = 1
- Cλ = t½
- Dλ = 2 t½
After three half-lives, the fraction of the original nuclei still undecayed is:
- Aone eighth
- Bone third
- Cone half
- Dzero
Quiz key
Random: the moment of decay of any one nucleus is unpredictable. Spontaneous: the decay rate is not changed by temperature, pressure or chemical state.
Activity = decay constant × number of undecayed nuclei: A = λN, measured in becquerel (decays per second).
Substituting N = N₀/2 at t = t½ into N = N₀e⁻λᵗ gives λt½ = ln2, so λ = 0.693 / t½.
Each half-life halves the number: N₀ → N₀/2 → N₀/4 → N₀/8. After n half-lives the fraction is (½)ⁿ.
What to project
The student lesson embeds these tabs. Open them full screen on the projector; every slider has a drag handle on the stage.
Slides for this lesson
A projectable deck for every pack is on the way. Until then, present the student lesson full screen: its sections, figure and lab tabs follow the same order as the plan above.