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Half-Life (Edexcel IGCSE Physics: Double Science)
Revision Note
Half life
- It is impossible to know when a particular unstable nucleus will decay
- It is possible to find out the rate at which the activity of a sample decreases
- This is known as the half-life
- Half-life is defined as:
The time it takes for the number of nuclei of a sample of radioactive isotopes to decrease by half
- In other words, the time it takes for the activity of a sample to fall to half its original level
- Different isotopes have different half-lives and half-lives can vary from a fraction of a second to billions of years in length
Measuring half life
- To determine the half-life of a sample, the procedure is:
- Measure the initial activity A0 of the sample
- Determine the half-life of this original activity
- Measure how the activity changes with time
- The time taken for the activity to decrease to half its original value is the half-life
Half life calculations
- Scientists can measure the half-lives of different isotopes accurately
- Uranium-235 has a half-life of 704 million years
- This means it would take 704 million years for the activity of a uranium-235 sample to decrease to half its original amount
- Carbon-14 has a half-life of 5700 years
- So after 5700 years, there would be 50% of the original amount of carbon-14 remaining
- After two half-lives or 11 400 years, there would be just 25% of the carbon-14 remaining
- With each half-life, the amount remaining decreases by half
A graph can be used to make half-life calculations
The graph shows how the activity of a radioactive sample changes over time. Each time the original activity halves, another half-life has passed
- The time it takes for the activity of the sample to decrease from 100% to 50% is the half-life
- It is the same length of time as it would take to decrease from 50% activity to 25% activity
- The half-life is constant for a particular isotope
- The following table shows that as the number of half-life increases, the proportion of the isotope remaining halves
Half life calculation table
| number of half lives | proportion of isotope remaining |
| 0 |  or 100% |
| 1 |  or 50% |
| 2 |  or 25% |
| 3 |  or 12.5% |
| 4 |  or 6.25% |
Worked example
The activity of a particular radioactive sample is 880 Bq. After a year, the activity has dropped to 220 Bq.
What is the half-life of this material?
Answer:
Step 1: Calculate how many times the activity has halved
- Initially, the activity was 880 Bq
- After 1 half-life the activity would be 440 Bq
- After 2 half-lives, the activity would be 220 Bq
- Therefore, 2 half-lives have passed
Step 2: Divide the time period by the number of half-lives
- The time period is a year
- The number of half-lives is 2
- 1 year divided by 2 is half of a year or 6 months
- Therefore, the half-life of the sample is 6 months
Worked example
The radioisotope technetium is used extensively in medicine. The graph below shows how the activity of a sample varies with time.
Determine the half-life of this material.
Answer:
Step 1: Draw lines on the graph to determine the time it takes for technetium to drop to half of its original activity
Step 2: Read the half-life from the graph
- In the diagram above the initial activity, A0, is 8 × 107 Bq
- The time taken to decrease to 4 × 107 Bq, or ½ A0, is 6 hours
- Therefore, the half-life of this isotope is 6 hours
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