Higher tier: Half-life
Radioactive decay is a spontaneous and random process.
A block of radioactive material will contain many trillions of nuclei and not all nuclei will decay at the same time so it is impossible to tell when a particular nucleus will decay.
A spontaneous process means that it is not possible to say which particular nucleus will decay next, but given that there are so many of them, it is possible to say that a certain number will decay in a certain time.
It also means that the process of radioactive decay cannot be speeded up or slowed down by any physical changes such as a change of temperature or pressure.
A random process means that scientists cannot tell when a particular nucleus will decay, but they can use statistical methods to tell when half the unstable nuclei in a sample will have decayed.
This is called the half-life.
The illustration below shows how a radioactive sample is decaying over time.
Image caption, In this example, the starting activity is 80 counts per minute.
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It takes two days for the count to halve from 80 counts per minute down to 40 counts per minute.
It takes another two days for the count rate to halve again, this time from 40 counts per minute to 20 counts per minute.
The half-life of this source is 2 days.
Note that this second two days does not see the count drop to zero, only that it halves again.
A third, two-day period from four days to six days sees the count rate halving again from 20 counts per minute to 10 counts per minute .
This process continues and although the count rate might get very small, it does not drop to zero completely.
The half-life of radioactive carbon-14 is 5,730 years.
If a sample of a tree (for example) originally contained 64 grams (g) of radioactive carbon, then after 5,730 years it will contain 32 g, after another 5,730 years that will have halved again to 16 g.
Question
If a sample with a half-life of 2 days has a count rate of 3,200 Bq at the start, what is its count rate after 8 days?
8 days = 4 half lives.
After 1 half-life the count rate = 1600 Bq.
After 2 half-lives the count rate = 800 Bq.
After 3 half-lives the count rate = 400 Bq.
After 4 half-lives the count rate = 200 Bq
After 8 days the count rate is 200 Bq.
Question
The half-life of cobalt-60 is 5 years. If there are 100 g of cobalt-60 in a sample, how much will be left after 15 years?
15 years is three half-lives.
After 1 half-life the mass of cobalt 60 remaining = 50 g.
After 2 half-lives the mass of cobalt 60 remaining = 25 g.
After 3 half-lives the mass of cobalt 60 remaining = 12.5 g.
The mass of cobalt-60 remaining after 15 years is 12.5 g.
Question
What is the half-life of this radioactive source?
It takes five days for the count to halve from 80 counts per minute to 40 counts per minute.
It takes another five days for the count rate to halve again, this time from 40 counts per minute to 20 counts per minute.
The half-life of this source is 5 days.