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Quick subject briefing
Before this lesson: Consolidation after pupils have met radioactive decay, count rate and half-life graphs. HOD/teacher assigns one tier route before handing over. Shared pages 1-6 and 9; Foundation page 7 OR Higher page 8.
Half-life is the elapsed time for a sample’s expected undecayed nuclei, activity or corrected source count rate to halve. It is a statistical trend; one nucleus has no predictable decay deadline. A measured detector rate includes background. Subtract background from each reading before halving; add it back only if a measured target is requested.
Words and symbols you will need
- Half-life
- Time for one halving of the sample quantity, measured between two corresponding times.
- Activity, Bq
- Number of nuclear decays per second in the source.
- Count rate
- Detector events per unit time. It is not automatically the activity in Bq.
- Measured / corrected
- Measured includes background. Corrected subtracts the supplied background, using the same rate unit.
- Higher: decrease ratio
- Decrease = initial - remaining. Decrease : initial differs from remaining : initial.
Help pupils choose a method
- Check the graph label: already corrected, or measured including background? Correct each measured value once.
- For a graph half-life, choose a corrected level and half that level; subtract the corresponding times.
- For several halvings count intervals, then multiply by known half-life or divide a known total time. Higher: name the requested ratio numerator before simplifying.
Use the supplied model — pupil page 2
Use pupil page 2: 9 h contains three 3 h intervals, so 640 Bq halves three times to 80 Bq. The separate detector example subtracts 12 from 90 to give 78 counts/min. These examples deliberately use different quantities and units.
A source has activity 640 Bq and half-life 3 h. Find activity after 9 h. In a separate detector test, measured rate is 90 counts/min and background is 12 counts/min. Find corrected source count rate.
Worked answer: 9 / 3 = 3 half-lives: 640 → 320 → 160 → 80 Bq. In the separate detector test, corrected count rate = 90 - 12 = 78 counts/min. Activity uses Bq; detector count rate uses counts per unit time. Do not automatically equate them.
If pupils are still stuck
Read the matching Say/Ask/Expect coaching and direct the named fresh retry in its replacement time. If still insecure, help label measured/corrected values and the time interval, then record the exact difficulty. For Higher ratio errors, use the page 8 model, ask whether 100 : 400 describes remaining or decrease (remaining), then let pupils retry their own ratio working.
KEEP THIS OPEN DURING THE LESSON
Timed teacher run sheet
- Print one complete 9-page pupil booklet per pupil, stapled in order; double-sided printing is fine. Keep the 11-page teacher guide separate.
- Confirm the HOD/teacher-assigned tier and tick it on pupil page 1. Everyone uses pages 1-6 and 9. Foundation completes page 7; Higher completes page 8 instead. Never assign both tier pages.
- Read teacher page 1, then use the timed run sheet on page 2. Pupils need pens, a ruler and calculator. All figures and data are supplied; no login, devices or radioactive materials are required.
0-5 minPupil page / Q
1 / 1-3
Read aloud / check: Assign and tick one tier route. Everyone starts from memory; check at 5 minutes.
Next: If insecure, use Try again A in the first 2 reading minutes.
Answers: 1, 2, 3.
Open check 1 and its coaching →
5-15 minPupil page / Q
2 / reading
Read aloud / check: Read the quantity table and both models. Name measured versus corrected rates.
Next: Check A if used, then continue reading.
15-20 minPupil page / Q
3 / 4
Read aloud / check: Choose a letter and show correction, halving and the measured target. Pause.
Next: If insecure, Try again B replaces questions 5-6.
Answers: 4.
Open check 2 and its coaching →
20-30 minPupil page / Q
3-4 / 5-12
Read aloud / check: Complete the definitions, separate test and corrected graph questions.
Next: If B was used, leave 5-6 blank. Figure 1 is already corrected.
Answers: 5, 6, 7, 8, 9, 10, 11, 12.
30-33 minPupil page / Q
5 / 13
Read aloud / check: Complete question 13 independently, then pause.
Next: If insecure, Try again C replaces questions 14-15.
Answers: 13.
Open check 3 and its coaching →
33-45 minPupil page / Q
5-8 / 14-22
Read aloud / check: Use the Sample B graph for 14-18. At 41 minutes Foundation uses page 7; Higher uses page 8 instead.
Next: If C was used, leave 14-15 blank. Do not assign both tier pages. Higher: distinguish remaining from decrease.
Answers: 14, 15, 16, 17, 18, 19, 20, 21, 22.
45-55 minPupil page / Q
9 / 23
Read aloud / check: Correct assigned practice and explain one correction.
Next: Share only assigned practice answers. Keep the exit hidden. For Higher, check numerator/order in both ratios.
Answers: 23.
55-60 minPupil page / Q
9 / 24
Read aloud / check: Cover earlier pages. Everyone completes shared question 24 independently.
Next: Collect every booklet; check afterwards. D is next lesson only. Record Higher ratio practice separately.
Answers: 24.
Open check 4 and its coaching →
Estimated 60 minutes. Practice: 10 minutes, a 3-minute check, 8 minutes shared background work and 4 minutes on ONE tier page. A uses reading time; B replaces 5-6; C replaces 14-15; D is next lesson only. Timings are not classroom-trialled.
Check entry, hinge and mid-practice at the marked pauses. At 45 minutes share only shared and assigned-tier practice answers. Keep question 24 and follow-up answers hidden until submission.
Download teacher guide & answers ↓If several pupils are stuck
Use the matching page 2 method and coaching. Direct the named retry within its replacement time. If still insecure, help pupils set up corrected values and a halving chain, then report the exact difficulty; do not improvise an experiment.
Estimated 60 minutes. Practice: 10 minutes, a 3-minute check, 8 minutes shared background work and 4 minutes on ONE tier page. A uses reading time; B replaces 5-6; C replaces 14-15; D is next lesson only. Timings are not classroom-trialled.
ENTRY CHECK
Check 1: Question 1, Question 2, Question 3
Look for: Question 1: 48 counts/s; question 2: 50 counts/s; question 3 rejects an exact individual deadline because decay is random.
If secure: Continue to reading and models on pupil page 2.
If: Does not halve 96, or adds background to 62 instead of subtracting it.Open coaching
Likely issue: The relevant source contribution or arithmetic step is insecure.
- Say
- Background adds detector events unrelated to this sample. Subtract it to isolate the sample contribution; a half-life then halves that corrected contribution.
- Ask
- For questions 1-2, what are 96 divided by 2 and 62 minus 12?
- Expect
- 48 counts/s and 50 counts/s. Keep detector rate units.
Next: Use the quantity table and methods on page 2. Direct Try again A on page 1 in the first 2 reading minutes.
Pupil page 2, corrected rate and halving; Try again A on page 1.
If: Agrees that every individual nucleus must decay after exactly one half-life.Open coaching
Likely issue: A sample trend is being treated as an individual timetable.
- Say
- We cannot predict the exact decay time of one nucleus. Half-life describes the expected halving of a large population, not a deadline for each member.
- Ask
- In question 3, can knowing the sample half-life identify which nucleus decays next?
- Expect
- No. Individual decays are random, even though the large sample follows a statistical trend.
Next: Use page 2, the opening paragraph. Direct Try again A during reading time and check the reason as well as the numbers.
Pupil page 2, random individual decay; Try again A on page 1.
HINGE CHECK
Check 2: Question 4
Look for: C, with 110 - 10 = 100, then 50, then 50 + 10 = 60 counts/s. A letter alone is insufficient.
If secure: Start questions 5-12 and require quantities and units in working.
If: A halves the entire measured 110 counts/s to get 55.Open coaching
Likely issue: The unchanged background has incorrectly been halved.
- Say
- Only the sample contribution halves. The constant background stays at 10 counts/s, so remove it before halving and add it back for a measured target.
- Ask
- In question 4, which part of 110 comes from the sample, and what remains of that part after one half-life?
- Expect
- 100 counts/s comes from the sample and halves to 50; adding background gives 60 counts/s.
Next: Use the three-step method on page 2. Complete Try again B on page 3 instead of questions 5-6.
Pupil page 2, Measured or corrected?; Try again B on page 3.
If: B reports the corrected 50 counts/s as the measured target.Open coaching
Likely issue: The pupil has not restored background to the detector reading.
- Say
- Fifty is the corrected sample contribution. A detector still counts the unchanged background as well, so the measured target is larger.
- Ask
- In question 4, what does the detector record in addition to the sample’s 50 counts/s?
- Expect
- The background 10 counts/s, making measured rate 60 counts/s.
Next: Use page 2, the last step of the measured-target method. Complete Try again B instead of questions 5-6.
Pupil page 2, Measured or corrected?; Try again B on page 3.
If: D stops at 100, or C is chosen without all three steps.Open coaching
Likely issue: The halving step is missing or the correct letter may be a guess.
- Say
- Name each step: initial sample contribution, halved sample contribution, final detector reading. A corrected starting value alone is not the final measured result.
- Ask
- Show all three numbers for question 4 and explain what each describes.
- Expect
- 100 counts/s initially from the sample, 50 after halving, and 60 including background.
Next: Ask for the three named quantities. If insecure, use the page 2 method and Try again B instead of questions 5-6.
Pupil page 2, three-step measured-target method; Try again B on page 3.
MID PRACTICE CHECK
Check 3: Question 13
Look for: Question 13: corrected rates 100, 50, 25 counts/s; two successive halving intervals each last 3 min.
If secure: Continue questions 14-18, then one assigned tier page at about 41 minutes.
If: Uses raw rates 110, 60 and 35 directly for halving, or subtracts background only once.Open coaching
Likely issue: Each measured reading needs its own correction.
- Say
- Every measured reading includes the same supplied background. Subtract it separately from every reading before comparing the sample.
- Ask
- For question 13, what are 110 - 10, 60 - 10 and 35 - 10?
- Expect
- 100, 50 and 25 counts/s. Those corrected values show the halving pattern.
Next: Use page 2, corrected-rate definition. Complete Try again C on page 5 instead of questions 14-15, then continue 16-18.
Pupil page 2, Measured or corrected?; Try again C on page 5.
If: Gives 6 min, a final graph time, or a count-rate value as half-life.Open coaching
Likely issue: Half-life is an elapsed halving interval, not the end time or height.
- Say
- One half-life is the interval for a single halving. A fourfold fall contains two halvings. Subtract the paired times or divide the total interval by two.
- Ask
- In question 13, between which times does corrected rate go from 100 to 50, then 50 to 25?
- Expect
- 0-3 min and 3-6 min. Each lasts 3 min; half-life is 3 min.
Next: Use page 2, Count halvings, then use elapsed time. Complete Try again C instead of questions 14-15.
Pupil page 2, elapsed-time method; Try again C on page 5.
EXIT CHECK
Check 4: Question 24
Look for: Question 24: corrected rates 160 and 40 counts/s; two half-lives in 4.0 min gives 2.0 min; individual decay remains unpredictable. For Higher ratio evidence, also inspect questions 21-22; the exit checks shared objectives.
If secure: Record independently secure shared skills and the exact remaining difficulty. Report assigned tier practice separately.
If: Incorrect corrected rates, only one halving, or 4 min given as half-life.Open coaching
Likely issue: Background correction or counting halving intervals needs follow-up.
- Say
- Correct both readings first. Then count the halving steps between them before sharing the total elapsed time equally between those steps.
- Ask
- In question 24, what are the corrected values and how many halvings connect them?
- Expect
- 160 and 40 counts/s; 160 → 80 → 40 is two halvings, so 4.0 / 2 = 2.0 min.
Next: Next lesson, revisit page 2, then direct Try again D independently on page 9.
Pupil page 2, correction and elapsed-time methods; Try again D on page 9, next lesson.
If: Claims the calculated half-life predicts one nucleus’s exact decay time.Open coaching
Likely issue: Random individual decay and a sample trend are still confused.
- Say
- A statistical population trend does not tell us when a particular nucleus will decay. The corrected sample rate can halve while individual events remain unpredictable.
- Ask
- Does the 2.0 min half-life in question 24 identify the next nucleus to decay? Explain.
- Expect
- No. Decay of an individual nucleus is random; 2.0 min describes the sample trend.
Next: Next lesson, use the opening explanation on page 2 before Try again D. Keep this outside today’s 60 minutes.
Pupil page 2, random individual decay; Try again D on page 9, next lesson.
Answers keyed to the pupil handout
- Question 1
Pupil page 1 - 96 / 2 = 48 counts/s.
- Question 2
Pupil page 1 - 62 - 12 = 50 counts/s.
- Question 3
Pupil page 1 - No. Individual decay times are random; half-life describes the statistical trend for a sample, not a deadline for one nucleus.
- Question 4
Pupil page 3 - C. Initial source contribution = 110 - 10 = 100 counts/s; half is 50 counts/s; add unchanged background: 50 + 10 = 60 counts/s.
- Question 5
Pupil page 3 - The time taken for the number of undecayed nuclei of the isotope in a sample to halve. Accept time for its activity or background-corrected source count rate to fall to half its initial value. A nucleus does not split in half.
- Question 6
Pupil page 3 - Radioactive decay is random; the exact decay time of an individual nucleus cannot be predicted. A predictable large-sample trend is not an individual timetable.
- Question 7
Pupil page 4 - 8.0 / 4.0 = 2 half-lives: 640 → 320 → 160 counts/s. This is a separate test from Sample A in Figure 1.
- Question 8
Pupil page 4 - 160 counts/s. Accept approximately 155-165 counts/s from the supplied graph.
- Question 9
Pupil page 4 - The times are 0 and 4.0 min; half-life = 4.0 - 0 = 4.0 min. Half-life is an elapsed time, not a count rate.
- Question 10
Pupil page 4 - Times are 8.0 and 12 min; half-life = 12 - 8.0 = 4.0 min. Do not report the final clock reading, 12 min, as the interval.
- Question 11
Pupil page 4 - 80 → 40 → 20 is two half-lives. Time = 2 × 4.0 = 8.0 min. Equivalently the graph times are 8 and 16 min, separated by 8 min.
- Question 12
Pupil page 4 - 120 → 60 → 30 → 15 is three half-lives. Half-life = 18 / 3 = 6.0 min.
- Question 13
Pupil page 5 - Corrected rates: 100, 50 and 25 counts/s. They halve from 0 to 3 min and again from 3 to 6 min. Half-life = 3 min; it is not 6 min or a count rate.
- Question 14
Pupil page 5 - 100 counts/s. Accept approximately 96-104 counts/s.
- Question 15
Pupil page 5 - Corrected rate = measured - background = 100 - 20 = 80 counts/s. Allow follow-through from the graph reading.
- Question 16
Pupil page 6 - At 4.0 h: 60 - 20 = 40 counts/s. At 6.0 h: 40 - 20 = 20 counts/s. Allow sensible graph-reading tolerance and consistent follow-through.
- Question 17
Pupil page 6 - Corrected rate halves from 80 to 40 counts/s between 2.0 h and 4.0 h. Half-life = 4.0 - 2.0 = 2.0 h = 120 min.
- Question 18
Pupil page 6 - Initial source contribution = 180 - 20 = 160 counts/s. Half is 80 counts/s. The background stays at 20 counts/s, so the measured target is 80 + 20 = 100 counts/s. Halving the full measured rate incorrectly halves the background too.
- Question 19
Pupil page 7 - Two half-lives: 320 → 160 → 80 counts/s.
- Question 20
Pupil page 7 - 320 → 160 → 80 → 40 → 20 requires four half-lives. Earliest time = 4 × 3.0 = 12 min. At 9 min the expected rate is still 40 counts/s.
- Question 21
Pupil page 8 - 320 → 160 → 80 → 40 counts/s. Remaining : initial = 40 : 320 = 1 : 8.
- Question 22
Pupil page 8 - Decrease = 320 - 40 = 280 counts/s. Decrease : initial = 280 : 320 = 7 : 8. Alternatively initial 8 units, remaining 1 unit, decrease 7 units. 1 : 8 describes what remains, not the decrease.
- Question 23
Pupil page 9 - Accept a corrected answer with a valid reason, not a copied final value. All-correct route: only the sample contribution halves; subtract background, halve that corrected value, then add the unchanged background to recover a measured target. Higher pupils should also explain any remaining/decrease ratio error.
- Question 24
Pupil page 9 - (a) 170 - 10 = 160 counts/s; 50 - 10 = 40 counts/s. (b) 160 → 80 → 40 is two half-lives in 4.0 min, so half-life = 4.0 / 2 = 2.0 min. (c) No. Individual decay is random; half-life describes a statistical sample trend.
- Try again A
- (a) 42 counts/s. (b) 77 - 7 = 70 counts/s. (c) No: an individual nucleus decays randomly, while half-life describes a sample trend.
- Try again B
- Initial corrected rate = 150 - 10 = 140 counts/s. After one half-life it is 70 counts/s. Measured target = 70 + 10 = 80 counts/s.
- Try again C
- Corrected rates: 80, 40 and 20 counts/s. Each halving takes 4 min, so half-life = 4 min.
- Try again D
- Corrected rates: 192 and 48 counts/s. 192 → 96 → 48 is two half-lives in 12 min, so half-life = 6 min. It cannot predict an individual decay time because decay is random.
Worksheet selection and marking
Shared selected source parts total 18 marks; each tier alternative adds 3, giving 21 selected-source marks per route. Accept stated graph-reading tolerances and sensible follow-through. Ratios are Higher only. The shared exit checks shared skills; it is not an independent Higher-ratio check. Supplied background correction is data handling, not assessment of Separate-only background origins or hazards.
Selection: Shared Q1(a,b), Q2(a,c,e,f,g,h), Q3(a-e). Foundation Q5(a,b) OR Higher Q6(a,b); source pages 1-4, 6-7.
Open the maintained worked solutions →Collect and follow up: Collect all named booklets with the assigned tier ticked. One tier page should be blank. Record shared half-life, correction and randomness evidence from question 24; use Higher questions 21-22 separately for ratio evidence. Tell the usual teacher the precise error and who needs Try again D.
