Half-lives and the random nature of radioactive decay — AQA GCSE Physics
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Half-lives and the random nature of radioactive decay explained
There are three routes to a half-life and the data decides which one you use.
Read the full explanation
From a graph: correct for background, halve the initial count rate, read across to the curve and down to the time axis. From a table: find the time interval over which the count rate falls to half, do it again for a second interval and take the mean. From a start and end value: count how many halvings take you from one to the other, then divide the total time by that number. For example, 800 Bq falling to 100 Bq is three halvings, 800 to 400 to 200 to 100, so if this took 24 minutes the half-life is 8 minutes. Always check the unit on the time axis, and quote the answer in the same unit.
Your focus
- Determine a half-life from a decay curve by halving the corrected count rate and reading off the interval.
- Calculate a half-life from a start value, an end value and a total time by counting the halvings.
- Decide when a set of readings needs a background correction before a half-life can be found.
Half-lives and the random nature of radioactive decay exam tips
Marking Points
- one mark for halving the corrected initial count rate and reading the time for that fall
- one mark for counting the number of halvings between the two values given
- one mark for dividing the total time by the number of half-lives
- one mark for the half-life with the correct unit taken from the data
Examiner Tips
- 💡Write the halving chain out in full, such as 800, 400, 200, 100, so the number of half-lives is on the page for a method mark.
- 💡If a background count rate is quoted anywhere in the question, subtract it from every value before you start.
- 💡Show the reading lines you draw on a printed graph; examiners credit the construction even if the final number is slightly out.
Common Mistakes
- dividing the total time by the ratio of the counts, for example by 8 rather than by the 3 halvings it represents
- using raw counts when a background count rate has been given in the question
- reading the time at which the count rate reaches zero, which it never does
- taking the half-life from the flat tail of the curve where the readings are least reliable
- quoting the answer in seconds when the axis is in minutes or years