LuduminaAT-05 · AT-U2 · Planned
Half-life and random decay data
Learning objectives
Determine half-life from data/graphs; explain aggregate predictability versus individual randomness; H calculate net decline over half-lives.
8463 §§4.4.2.3 / 8464 §§6.4.2.3
DfE single-science pp.43–44 / Combined pp.35–36. Evidence checked 30 September–1 October 2026. Skills: WS1.2,3.4,3.7; MS1c,3d,4a.
Needs firstAT-03; P0 fractions
Explanation
Half-life is the time for the undecayed population or activity to fall to half its value. It describes aggregate behaviour, not a schedule for one nucleus. Correct measured counts for background before estimating a source half-life. Higher calculations distinguish remaining fraction from net decline.
Concepts, equations and units: Half-life in s or labelled time; corrected count rate after background subtraction; H fractions N=N0(½)^n and decline=N0−N, integer n practice.
Prediction, demonstration and game exercise
Predict, observe, explain
Run repeat stochastic populations then plot count rate; compare large versus small samples.
Planned learner game exercise
Choose a half-life and estimate it from noisy model measurements; separate background from source counts.
Independent practice
Read two half-lives; H two remaining/declined fraction problems; estimate range from repeats.
Original practice example · Shared
A source-only count-rate graph falls from 80 to 40 counts/s in 5 minutes. Estimate half-life.
Show working and model answer
Working / reasoning
A halving interval is 5 minutes; compare another halving interval if the graph permits.
Answer
5 minutes.
Exit check and success criteria
Correct graph interval and randomness explanation; H distinguishes remaining from declined proportion.
During practice, compare the prediction with evidence and give an error-specific prompt. The exit item uses a fresh context or fresh values, answered independently.
Misconceptions, practical links and mastery
Check these misconceptions
After two half-lives nothing remains; half-life is half the total decay time; every nucleus decays at the half-life.
Practical preparation
No RP; random-decay model/supplied counts.
Virtual preparation and revision only. Required hands-on activities and school records remain separate.
Proposed mastery
0: not yet evidenced. 1: supported. 2: independent exit criteria met. 3: successful changed-context transfer. Advance at 2; revisit with fresh retrieval. These are not GCSE grades.