Half Life and Radioactive Decay
Half life for Cambridge IGCSE Physics 0625. What half life means, how to read it off a graph, background radiation and the calculations examiners set.
What you need to know
- Half life is the time taken for half the undecayed nuclei in a sample to decay, or for the count rate to fall to half.
- Decay is random and spontaneous. Nothing you do to the sample changes the half life.
- Always subtract the background count rate from the measured rate before you start.
- From a graph, pick a starting count rate, find half of it, and read off the time between them. Do it twice from different starting points to check.
- After n half lives the activity is the original divided by 2 to the power n.
Equations
- corrected count = measured count minus background count
- activity after n half lives = original activity / 2^n
- number of half lives = total time / half life
Half Life and Radioactive Decay questions students ask
What is half life?
The time taken for half the undecayed nuclei in a sample to decay, or equivalently for the count rate to fall to half its value.
How do you read half life from a graph?
Pick a count rate on the curve, find half of it, and read off the time between the two points. Repeat from a different starting point to check you get the same answer.
Why do you subtract the background count?
The detector records background radiation as well as the source. If you do not remove it, the count rate never appears to halve properly and your half life comes out wrong.
How do you calculate activity after several half lives?
Divide the original activity by 2 for each half life that passes. After n half lives the activity is the original divided by 2 to the power n.
Can you change the half life of a source?
No. Heating it, cooling it, compressing it or putting it under pressure makes no difference. Half life is a fixed property of the isotope.
Is radioactive decay random?
Yes, and it is spontaneous. You cannot predict which nucleus decays next, only the average behaviour of a large number of them.
Does a radioactive source ever stop being radioactive?
In practice the activity falls until it is indistinguishable from background, but mathematically it never reaches exactly zero.
What is count rate?
The number of decays detected per unit time, usually counts per second or counts per minute. It is proportional to the number of undecayed nuclei present.
Mistakes that cost marks
- Forgetting the background subtraction. It changes the answer and examiners test it deliberately.
- Reading the time to reach zero instead of the time to reach half.
- Saying the sample stops being radioactive after two half lives.
- Thinking heating or compressing the sample changes the half life.
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