CIE IGCSE Physics (0625) Half-life Study Notes - New Syllabus
CIE IGCSE Physics (0625) Topic 5.2.4 Half-life Study Notes
Key Concepts:
Core
- Define the half-life of a particular isotope as the time taken for half the nuclei of that isotope in any sample to decay; recall and use this definition in simple calculations, which might involve information in tables or decay curves (calculations will not include background radiation)
Supplement
- Calculate half-life from data or decay curves from which background radiation has not been subtracted
- Explain how the type of radiation emitted and the half-life of an isotope determine which isotope is used for applications including: (a) household fire (smoke) alarms (b) irradiating food to kill bacteria (c) sterilisation of equipment using gamma rays (d) measuring and controlling thicknesses of materials (e) diagnosis and treatment of cancer using gamma rays
Half-Life
Half-Life
The half-life of a radioactive isotope is the time taken for half the nuclei in a sample to decay.
- It is a measure of how quickly a radioactive substance decays.
- The half-life is always the same for a particular isotope, regardless of the sample size.
- After each half-life, the number of undecayed nuclei is halved.
Example:
A sample contains 800 radioactive atoms of isotope X. The half-life of isotope X is 2 hours.
How many radioactive atoms remain after:
- (a) 2 hours
- (b) 4 hours
- (c) 6 hours
▶️ Answer / Explanation
(a) After 2 hours (1 half-life):
\( \frac{800}{2} = \boxed{400} \) atoms remain
(b) After 4 hours (2 half-lives):
\( \frac{400}{2} = \boxed{200} \) atoms remain
(c) After 6 hours (3 half-lives):
\( \frac{200}{2} = \boxed{100} \) atoms remain
Example :
The graph below shows the number of undecayed atoms of a radioactive substance over time:
Time (hours): 0 2 4 6 8
Atoms: 800 400 200 100 50
Use the data to determine the half-life of the substance.
▶️ Answer / Explanation
Step 1: Find two points where the number of atoms halves:
From 800 → 400 → 200 → 100 → 50
Step 2: Time for each halving:
800 to 400: 2 hours
400 to 200: 2 more hours
Half-life = \( \boxed{2 \text{ hours}} \)
Example:
A radioactive substance decays over time as shown in the table:
| Time (minutes) | Remaining Atoms |
|---|---|
| 0 | 3200 |
| 10 | 1600 |
| 20 | 800 |
| 30 | 400 |
What is the half-life of the substance?
▶️ Answer / Explanation
Step 1: Look at when the number of atoms halves:
- 3200 → 1600 at 10 minutes
- 1600 → 800 at 20 minutes
- 800 → 400 at 30 minutes
Half-life = \( \boxed{10 \text{ minutes}} \)
Note: When calculating half-life from experimental data, you must:
- Identify and subtract background radiation (if it hasn’t been removed).
- Use the corrected counts to find when the activity reduces to half its value.
Example:
A radioactive sample is measured over time using a Geiger counter. The background radiation is 20 counts/min. The readings are:
| Time (minutes) | Measured Count Rate (counts/min) |
|---|---|
| 0 | 220 |
| 5 | 140 |
| 10 | 90 |
| 15 | 65 |
Estimate the half-life of the sample using the data provided.
▶️ Answer / Explanation
Step 1: Subtract background radiation (20 counts/min) from all values:
- 0 min: \( 220 – 20 = 200 \)
- 5 min: \( 140 – 20 = 120 \)
- 10 min: \( 90 – 20 = 70 \)
- 15 min: \( 65 – 20 = 45 \)
Step 2: Find time when corrected count falls from 200 to 100 (i.e., halves)
At 0 min: 200
At 5 min: 120
At 10 min: 70
So, count reaches 100 sometime between 0 and 5 minutes.
Use linear estimation:
From 0 to 5 min, count falls 200 → 120 (drop of 80 in 5 min)
200 → 100 is a drop of 100
Proportion: \( \frac{100}{80} = 1.25 \times 5 = 6.25 \text{ min} \)
Estimated Half-life ≈ \( \boxed{6.25 \text{ minutes}} \)
Example:
A Geiger counter records the decay rate of a radioactive sample. The background radiation is constant at 20 counts/minute. The graph shows the following measured count rates:
| Time (minutes) | Measured Count Rate |
|---|---|
| 0 | 420 |
| 5 | 220 |
| 10 | 120 |
| 15 | 70 |
Estimate the half-life of the radioactive substance using the graph data. Do not forget to account for background radiation.
▶️ Answer / Explanation
Step 1: Subtract the background radiation (20 counts/min):
- 0 min: \( 420 – 20 = 400 \)
- 5 min: \( 220 – 20 = 200 \)
- 10 min: \( 120 – 20 = 100 \)
- 15 min: \( 70 – 20 = 50 \)
Step 2: Find when the count drops to half its original value:
Start = 400 → Half = 200 at 5 minutes → Half = 100 at 10 minutes → Half = 50 at 15 minutes
Each halving occurs every 5 minutes.
Half-life = \( \boxed{5 \text{ minutes}} \)
Suitability of a radioactive isotope
Suitability of a radioactive isotope
The suitability of a radioactive isotope for a particular application depends on:
- Type of radiation emitted (alpha, beta, gamma)
- Penetrating power and ionising ability of that radiation
- Half-life – long enough to be useful, but not so long as to be hazardous
(a) Household Fire Alarms
- Isotope Used: Americium-241
- Radiation Type: Alpha particles
- Half-Life: ~432 years (long-lasting, stable)
- Why Alpha? Alpha particles ionise air inside the detector to allow a small current to flow. Smoke particles disrupt this current and trigger the alarm.
- Why Long Half-Life? So the detector functions reliably for many years without replacement.
(b) Irradiating Food to Kill Bacteria
- Isotope Used: Cobalt-60 or Cesium-137
- Radiation Type: Gamma rays
- Half-Life: Several years (Cobalt-60 = 5.3 years)
- Why Gamma? Gamma rays are highly penetrating and can pass through food packaging to kill bacteria and parasites without making food radioactive.
- Why Medium Half-Life? Long enough to allow continuous use before replacement, but not permanent.
(c) Sterilisation of Equipment Using Gamma Rays
- Isotope Used: Cobalt-60
- Radiation Type: Gamma rays
- Half-Life: ~5.3 years
- Why Gamma? Penetrates deep into surgical instruments or bandages to destroy all microorganisms, even inside packaging.
- Why Medium Half-Life? Provides a balance between effectiveness and safety for repeated sterilisation cycles.
(d) Measuring and Controlling Thickness of Materials
- Radiation Type: Depends on material thickness:
- Beta emitters (like Strontium-90) used for medium thickness materials like paper or plastic.
- Gamma emitters used for thicker materials like metal sheets.
- Why Beta or Gamma? Their penetration depends on thickness. Less radiation detected = thicker material. Automated systems use this to control rollers.
- Half-Life: Moderate (not too short to avoid frequent replacement).
(e) Diagnosis and Treatment of Cancer Using Gamma Rays
- Isotope Used: Technetium-99m (diagnosis), Cobalt-60 (treatment)
- Radiation Type: Gamma rays
- Why Gamma?
- Gamma rays penetrate body tissues and can be directed to specific areas (focused beams).
- For diagnosis (e.g., medical scans), the gamma source is injected into the body, and emitted rays are detected outside.
- Half-Life:
- Technetium-99m: Short half-life (~6 hours) — enough for scanning but quickly decays to reduce exposure.
- Cobalt-60: Longer half-life (~5.3 years) — used in gamma ray machines to kill cancer cells.
Example:
Americium-241 is used in household smoke detectors. Which statement best explains why?
- A. It emits gamma radiation that can penetrate walls
- B. It emits alpha particles that ionise the air between two electrodes
- C. It emits beta particles that detect smoke by scattering off molecules
- D. It emits neutrons which trigger a current
▶️ Answer / Explanation
B. It emits alpha particles that ionise the air between two electrodes
Alpha particles ionise air to allow current to flow; smoke disrupts this, triggering the alarm.
Example:
Which radioactive source would be most suitable for sterilising surgical equipment sealed in plastic packaging?
- A. Alpha emitter with a short half-life
- B. Beta emitter with a medium half-life
- C. Gamma emitter with a long half-life
- D. Neutron emitter with a short half-life
▶️ Answer / Explanation
C. Gamma emitter with a long half-life
Gamma rays can penetrate packaging and sterilise contents. A long half-life ensures long-term use without frequent replacement.
Example:
Explain why Technetium-99m is suitable for medical imaging but not for treating cancer, while Cobalt-60 is used for cancer treatment but not imaging.
▶️ Answer / Explanation
Technetium-99m:
- Emits gamma rays (ideal for detection outside the body)
- Short half-life (~6 hours) → reduces long-term radiation exposure
- Used for diagnosis, not strong enough for treatment
Cobalt-60:
- Emits high-energy gamma rays
- Long half-life (~5.3 years) → consistent for long-term treatment machines
- Strong enough to destroy cancer cells (radiotherapy)