Chemistry • Year 11 • Module 1 • Lesson 20
Nuclear Chemistry
Apply nuclear equation balancing and half-life calculations to data, scenarios and a reasoning challenge on radioisotope selection.
1. Interpret experimental data, a decaying radioisotope sample
A 240 mg sample of a radioisotope with an unknown half-life is monitored over time. The table below shows the mass remaining. 8 marks
| Time elapsed (hours) | Mass remaining (mg) | Half-lives elapsed |
|---|---|---|
| 0 | 240 | 0 |
| 6 | 120 | |
| 12 | 60 | |
| 18 | 30 | |
| 24 | 15 |
1.1 Complete the “Half-lives elapsed” column. 2 marks
1.2 Determine the half-life of this radioisotope, showing your reasoning from the table. 2 marks
1.3 Calculate the mass remaining after 36 hours. 2 marks
1.4 Explain why the mass remaining approaches, but never mathematically reaches, exactly zero. 2 marks
2. Interpret graph, decay curve of a 100 mg sample
The graph below shows the decay of a 100 mg sample of a radioisotope with a half-life of 4 days. 7 marks
Figure 2. Decay curve, 100 mg sample, half-life = 4 days.
2.1 Read the graph to state the mass remaining at day 8 and day 12. 2 marks
2.2 Calculate the mass remaining at day 16 using (1/2)ⁿ, and compare it to the value the graph shows. 3 marks
2.3 Explain why the curve gets flatter (loses less mass per day) as time goes on, even though the half-life itself never changes. 2 marks
3. Compare alpha decay and beta decay
Complete the two-column table contrasting alpha decay and beta decay. 8 marks (1 per cell)
| Feature | Alpha decay | Beta decay |
|---|---|---|
| Particle emitted | ||
| Change in mass number (A) | ||
| Change in atomic number (Z) | ||
| Penetrating power |
4. Predict and justify, choosing a radioisotope for a hospital scan
A hospital needs a radioisotope for a same-day diagnostic scan of a patient's kidney function. Two candidates are available: Radioisotope X (gamma emitter, half-life 6 hours) and Radioisotope Y (gamma emitter, half-life 8 years). A student claims: “Radioisotope Y is the better choice because its much longer half-life means it will keep working for longer, giving a clearer scan.” 5 marks
4.1 Identify the error in the student's claim. 2 marks
4.2 Explain which radioisotope is actually the better choice for this scan, and why. 3 marks
Q1.1, Half-lives elapsed column
6 h → 1; 12 h → 2; 18 h → 3; 24 h → 4.
Q1.2, Half-life determination
The mass halves every 6 hours (240 → 120 → 60 → 30 → 15) [1]. Therefore the half-life of this radioisotope is 6 hours [1].
Q1.3, Mass at 36 hours
n = 36 ÷ 6 = 6 half-lives [1]. Mass remaining = 240 × (1/2)⁶ = 240 ÷ 64 = 3.75 mg [1].
Q1.4, Why mass never reaches exactly zero
Each half-life only removes half of whatever mass is currently present, not a fixed absolute amount [1]. Since you are always halving a smaller and smaller remaining quantity, the mass approaches zero but never mathematically reaches it, in principle a tiny fraction of the original nuclei always remain undecayed [1].
Q2.1, Reading the graph
At day 8: 25 mg remaining. At day 12: ~12.5 mg remaining.
Q2.2, Calculating day 16
n = 16 ÷ 4 = 4 half-lives [1]. Mass remaining = 100 × (1/2)⁴ = 100 ÷ 16 = 6.25 mg [1]. This matches the graph, which shows the curve levelling off close to this value by day 16 [1].
Q2.3, Why the curve flattens
Because each half-life halves whatever mass remains, and the remaining mass keeps getting smaller, the actual amount of mass lost in each successive 4-day interval keeps shrinking (50 mg lost in the first interval, but only ~3 mg lost between day 12 and day 16) [1]. The half-life itself (4 days) never changes, only the shrinking absolute quantity being halved changes, which is why the curve flattens rather than continuing in a straight line [1].
Q3, Compare and contrast table
Particle emitted: Alpha, a helium nucleus (⁴₂He); Beta, a high-speed electron (⁰₋₁e). Change in A: Alpha, decreases by 4; Beta, unchanged. Change in Z: Alpha, decreases by 2; Beta, increases by 1. Penetrating power: Alpha, low (stopped by paper); Beta, moderate (stopped by aluminium).
Q4.1, Error in student's claim
The student has the logic backwards. A radioisotope with a much longer half-life (8 years) would still be significantly radioactive long after the scan is finished, delivering a far larger cumulative radiation dose to the patient with no additional diagnostic benefit [1]. For a same-day diagnostic scan, a short half-life is actually preferred, long enough to complete the scan, but short enough to decay away quickly afterwards and minimise the patient's radiation exposure [1].
Q4.2, Better choice and why
Radioisotope X (half-life 6 hours) is the better choice [1]. It remains active for long enough to complete a same-day diagnostic scan, but decays away within about a day, meaning the total radiation dose absorbed by the patient is minimised [1]. This is exactly the same principle behind the real-world choice of technetium-99m (half-life about 6 hours) for medical imaging [1].