Models in physics make predictions, and evidence either supports a model or it does not. In this lesson you test a nuclear model (radioactive decay with a constant half-life) and a space model (a planet in a circular orbit) against supplied numbers.
This is the closing physics lesson in integrated physical reasoning. It practises a skill that every science section tests: use the data given, not memory, to reach a conclusion.
How do I test a model against evidence?
A model has a prediction. The evidence has numbers. Your answer states the prediction, shows the matching numbers, and says whether they agree.
- Correct the data first. For count rates, subtract the background count.
- State the model’s prediction. For constant half-life, each equal time interval halves the corrected count rate.
- Check it with the numbers. Compare ratios across equal intervals, not single values.
- Use the model to predict. Halve once for every half-life that passes.
- Give a conclusion that says what the evidence shows and, where needed, what limits it, such as few readings or random variation.
Worked example (invented data)
A student records the count rate from a sample of a radioactive isotope. The background count rate is 20 counts per minute. The student’s readings are invented for this lesson.
| Time (h) | 0 | 2 | 4 | 6 |
|---|---|---|---|---|
| Measured count rate (counts/min) | 820 | 420 | 220 | 120 |
Does the evidence support a constant half-life? Find it, and predict the measured count rate at 10 h.
Step 1, correct the data. Subtract 20 from each reading: 800, 400, 200, 100.
Step 2, check the ratio. 800 → 400 → 200 → 100. Each 2 hour interval halves the corrected count rate. The model is supported by all three intervals.
Step 3, half-life. The half-life is 2.0 h.
Step 4, predict at 10 h. 10 h is 5 half-lives. Corrected rate = 800 ÷ 2⁵ = 800 ÷ 32 = 25 counts/min. The detector also counts background, so the measured rate is 25 + 20 = 45 counts/min.
Re-check: halving five times: 800, 400, 200, 100, 50, 25. Correct.
A space model with evidence. Earth’s orbit radius is about 1.5 × 10¹¹ m and its period about 3.15 × 10⁷ s. The model of a circular orbit gives v = 2πr ÷ T = (2 × 3.14 × 1.5 × 10¹¹) ÷ (3.15 × 10⁷) = 9.42 × 10¹¹ ÷ 3.15 × 10⁷ = 3.0 × 10⁴ m/s. That is about 30 km/s.
The mistake to watch for
A student ignores the background and predicts a reading of 25 counts/min at 10 h.
Mistaken answer: “820 ÷ 32 is about 26 counts/min at 10 h.”
This halves the measured value, which includes background. Background does not decay, so only the corrected part is halved. The detector would read about 45 counts/min.
The correction is to subtract first, halve second, add the background back last when the question asks for a measured reading.
Check yourself
All data are invented.
1. A sample’s corrected count rate falls from 640 counts/min to 40 counts/min in 12 h. What is its half-life?
Show answer
640 → 320 → 160 → 80 → 40 takes 4 halvings. 12 h ÷ 4 = 3.0 h.
2. What fraction of the original unstable nuclei remains after 3 half-lives?
Show answer
(½)³ = 1/8, or 12.5%.
3. A satellite orbits at radius 7.0 × 10⁶ m with period 5.8 × 10³ s. Find its orbital speed.
Show answer
v = 2πr ÷ T = (2 × 3.14 × 7.0 × 10⁶) ÷ (5.8 × 10³) = 4.40 × 10⁷ ÷ 5.8 × 10³ ≈ 7.6 × 10³ m/s, so 7.6 × 10³ m/s to 2 significant figures.
Where this leads next
Revisit staged energy problems to see how the same evidence-first habit applies to motion, then take the integrated practice set. Real radioactive sources are handled only under strict supervision, so this lesson uses supplied data. The scientific investigation critic helps you judge such data.
If tables of readings still feel like a wall of numbers, our teachers can show you how to pull out the pattern. That is a regular part of online one-to-one Co-ordinated Sciences tuition.