CIE IGCSE Physics (0625) Half-life Study Notes - New Syllabus
CIE IGCSE Physics (0625) Half-life Study Notes
LEARNING OBJECTIVE
- Understanding the concepts of Half-life
Key Concepts:
- Half-life
- Suitability of a radioactive isotope
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)