7.2.5Acids, Bases and Salts
Half-Life — Cambridge IGCSE Chemistry 0620 Revision Notes & Topical Questions
5 min read 5 parts Lesson 6 of 11 Unit quiz
Curriculum Equation Key Radioactive Decay & Half-Life FormulasFast Exam Solution
N(t) = N₀ × (1/2)^(t / t½) | λ = ln(2) / t½ ≈ 0.693 / t½ | E = Δm × c²
Section 1 of 5Defining Half-Life
Half-life
- The average time taken for the number of undecayed nuclei in a sample, or its count rate, to fall to half its original value.
Constant value
- Each isotope has its own fixed half-life, which is not changed by temperature, pressure or chemical state.
Range
- Half-lives vary from a fraction of a second to billions of years, depending on the isotope.
Prediction
- Individual nuclei decay randomly, but a large sample decays in a predictable pattern described by the half-life.
Section 2 of 5Finding Half-Life from a Graph
1
Read the initial count rate from the graph, then halve it to find the count rate after one half-life.
2
Find the time at which the curve reaches this halved count rate, and note the time taken.
3
Repeat the process for the next halving and check that the time interval is the same each time.
4
The time taken for the first halving is the half-life, because the half-life is constant for the isotope.
Section 3 of 5Using Half-Life
Using Half-Life
Each half-life
- Every half-life halves the number of undecayed nuclei, so after n half-lives the fraction left is (1/2)ⁿ.
Carbon-14
- Carbon-14 has a half-life of 5700 years, so after 11 400 years only a quarter of the original amount remains.
Activity
- A sample with a short half-life has a high activity that falls quickly, while a long half-life gives a low, steady activity.
Uncertainty
- Measured count rates include background, so the background count should be subtracted before reading the half-life.
Section 4 of 5Worked Example
Question
- A sample has a count rate of 800 counts per minute.
- After 3 hours the count rate is 100 counts per minute.
- What is the half-life?
- 1800240032004100 counts per minute takes 3 halvings
- Half-life = total time ÷ number of half-lives = 3 hours ÷ 3 = 1 hour.
Answer 1 hour
Section 5 of 5Exam Checklist & Tips
7.2.5 – Key Points for the Exam
- Half-life The time for the activity or number of undecayed nuclei to halve.
- Count rate The number of decays detected each second or each minute.
- Undecayed nuclei Nuclei in a sample that have not yet undergone radioactive decay.
- Random decay Decay in which the moment a single nucleus decays cannot be predicted.
Common Mistakes
- Dividing the total time by the starting count rate instead of by the number of half-lives counted.
- Stating that half-life is the time for the sample to disappear completely; it only halves in each interval.
- Measuring from 50 % to 25 % and assuming it is a different length from 100 % to 50 %;
- both intervals are the same length.
- Forgetting to subtract background count rate when the readings are low and background is significant.
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