6.1.10Radiation
Half-Life
5 min read 5 parts Lesson 10 of 14
Section 1 of 5What Half-Life Means
Each half-life reduces the remaining activity by a factor of two.
Definition
- The half-life of a radioactive isotope is the time taken for its activity,
- or the number of undecayed nuclei, to fall to half of its starting value.
Random but predictable
- We cannot predict when a single nucleus will decay, but a large sample always halves in activity in the same time.
Different isotopes
- Half-lives range from fractions of a second to billions of years, depending on the isotope.
Not affected
- Temperature, pressure and chemical state do not alter the half-life of a given isotope.
Count rate
- The corrected count rate halves in each half-life too, since it is proportional to the activity.
Section 2 of 5Using Half-Life
Using Half-Life
Repeated halving
- After n half-lives the activity is the original value divided by 2ⁿ.
Number of half-lives
- Divide the total elapsed time by the half-life to find how many half-lives have passed.
From a graph
- Read the time for the activity to fall from any value to half that value;
- repeating at different points should give the same answer.
From a table
- Look for the time interval over which the activity halves, then check that it halves again in the same interval.
Background
- Before finding half-life from count rates, subtract background so that the corrected values are used.
| Number of half-lives | Fraction remaining | Activity from 800 Bq |
|---|---|---|
| 0 | 1 | 800 Bq |
| 1 | ½ | 400 Bq |
| 2 | ¼ | 200 Bq |
| 3 | ⅛ | 100 Bq |
Section 3 of 5Solving Half-Life Problems
1
Write down the starting activity, the half-life and the total time, making sure all times use the same unit.
2
Divide the total time by the half-life to find the number of half-lives that have elapsed.
3
Halve the activity once for each half-life, or divide by 2ⁿ for n half-lives.
4
To find the half-life instead, count how many halvings take the activity from the initial to the final value.
5
Divide the elapsed time by the number of halvings to get the half-life, and quote the unit.
Section 4 of 5Worked Example
Question
- A source has an activity of 640 Bq and a half-life of 3.0 hours.
- (a) Calculate its activity after 12 hours.
- (b) A different source falls from 800 Bq to 100 Bq in 15 days;
- find its half-life.
- (a) Number of half-lives = 12 ÷ 3.0 = 4.
- Activity = 640 ÷ 2⁴ = 640 ÷ 16 = 40 Bq.
- 1(b) 800240032004100 is three halvings
- Half-life = 15 ÷ 3 = 5.0 days.
Answer (a) 40 Bq; (b) 5.0 days.
Section 5 of 5Exam Checklist & Tips
6.1.10 – Key Points for the Exam
- Half-life The time taken for the activity of a source to halve.
- Isotope A form of an element with a particular number of neutrons.
- Decay curve A graph of activity or count rate against time for a radioactive source.
- Undecayed nuclei Nuclei that have not yet emitted radiation.
- Corrected count rate The count rate after background has been subtracted.
Common Mistakes
- Thinking that after two half-lives all the nuclei have decayed.
- Using elapsed time directly instead of dividing by the half-life.
- Reading a half-life from a graph without subtracting background first.
- Believing the half-life depends on the starting amount of the source.