Earth’s History — Investigation · Earth & Space Science, Grade 9
Use relative order, isotope evidence, and planetary records to reconstruct Earth’s past.
Model Radioactive Decay and Date an Event
Investigate
How does repeated random decay produce a predictable population pattern?
Plan three teaching sessions: define the model and comparison; run or analyze repeated supplied/collected records; then graph, explain, revise and submit the notebook. These independent home-study routes do not certify the school’s mandated investigations or laboratory minutes.
Materials
- About 80 coins or two-sided paper counters
- Tray
- Graph paper
- Calculator; supplied data if needed
Before you begin
This is a paper-and-data investigation. Use supplied illustrative data or teacher-approved observations. Do not enter hazardous sites to collect evidence.
Plan a fair test
Each round represents one equal interval with a one-half removal probability. Number remaining is the outcome. Keep the removal rule constant; individual atoms cannot be assigned a scheduled decay time.
Method
- Count counters and label them parent atoms. Predict the population after three rounds.
- Toss all remaining counters; remove the chosen face and record the remaining count.
- Repeat for at least five rounds, recording even unexpected results.
- Graph fraction remaining versus round and compare with (1/2)^n.
- Repeat the simulation or compare supplied data; explain the variability.
- Apply the ideal fractions to a rock with a 10-million-year half-life and 25% parent remaining, stating dating assumptions.
Open the investigation data (illustrative)
Illustrative data created for this activity; these are not measurements from an actual site or an official reference table.
| Round | Ideal remaining out of 80 | One illustrative trial remaining |
|---|---|---|
| 0 | 80 | 80 |
| 1 | 40 | 43 |
| 2 | 20 | 19 |
| 3 | 10 | 11 |
| 4 | 5 | 6 |
| 5 | 2.5 | 2 |
Analyze and explain
- Why does the ideal curve allow 2.5 while a physical trial has whole counters?
- Date the stated sample and identify the event being dated.
- Why should a sedimentary rock’s inherited grains not automatically date deposition?
- Identify the system boundary, units and conditions held comparable.
- Explain how the graph or figure supports the mechanism rather than merely repeat its trend.
- State one uncertainty or scale limitation and design a follow-up comparison that could challenge the explanation.
What a strong explanation includes
- Graph uses fractions or clearly labeled counts
- Distinguishes probability from fixed individual lifetimes
- Connects parent fraction to elapsed half-lives and age
- States closed-system and initial-condition assumptions
- Keep observations separate from model-generated or supplied illustrative records.
- Explain a revision using the evidence and a stated model limitation.
Parent / teacher guide: discuss after the investigation
The ideal curve describes an expected population, so it can have fractional counts. A real trial fluctuates and has whole counters. Under suitable initial-parent/daughter and closed-system assumptions, 25% parent implies two half-lives, or 20 Ma since the mineral’s dating clock began, often crystallization or cooling. Inherited grains can be older than their deposition. Counter rounds illustrate probability, not the physics of nuclear transformation. A complete notebook also specifies the boundary, measurement units and matched conditions. Describe a mechanism connecting the pattern to the claim, then state a limitation and an additional comparison. Supplied illustrative outcomes are not a claim about your collected results; differences must be interpreted rather than corrected to match the example.
Compare this model with the learner’s actual evidence. Different measurements can support a different conclusion; check the reasoning and limitations, not matching wording.