activity and half-life of a radioactive source

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Activity of a radioactive source

The activity of a radioactive source is the number of ionising radiations it emits per second. Activity is measured in becquerels. The symbol for the becquerel is Bq. One becquerel is one ionising radiation emitted per second, i.e. an alpha, a beta particle or a gamma ray emitted per second. The activity of a radioactive source decreases with time.

Half-life

It is not possible to predict when an individual atom might decay, but it is possible to measure how long it takes for half the nuclei to decay. This is called the half-life of the radioactive isotope.

Here are three definitions of the half-life of a radioactive isotope, but they mean essentially the same thing; choose the one you like best:

  1. The time it takes for the number of nuclei in a sample containing the isotope to halve.
  2. The time it takes for the count rate from a sample containing the isotope to fall to half its starting level.
  3. The time taken for the activity of a radioactive source to reduce by half.

Different radioactive isotopes have different half-lives. For example, the half-life of carbon-14 is 5,715 years, but the half-life of francium-223 is just 20 minutes.

Measuring half-life

The half-life could be measured as follows.

Diagram of use of GM tube to detect radiationFirst of all the background count rate is measured using a GM tube connected to a counter. The count rate from the source is measured at regular fixed intervals over a period of time.

The background count rate is subtracted from each measurement and the actual count rate from the source is measured. A graph of the count rate of the source against time is plotted. From the graph, the time taken for the count rate to fall by half is measured. A number of measurements are made and an average value is calculated. The average value is the half-life of the radioactive source.

A typical half-life graph

You can see from the graph that the half life is 2 days, since this is the time taken for the counts per minute to halve from 80 to 40 (or from 40 to 20, or from 20 to 10, etc).

 

 

 

 

 

 

 

Question
A radioactive source has a half-life of 15 minutes. At a particular time the activity of the source is 16 kBq. What is the activity of the source 1 hour later?

Solution
1 hour = 60 minutes
60 minutes = 4 x 15 minutes = 4 half-lifes
Activity after 1 half-life = 16 x 0.5 = 8 kBq
Activity after 2 half-lifes = 8 x 0.5 = 4 kBq
Activity after 3 half-lifes = 4 x 0.5 = 2 kBq
Activity after 4 half-lifes = 2 x 0.5 = 1 kBq

Answer
Activity of the radioactive source 1 hour later = 1 kBq

[ This page has been adapted from www.bbc.co.uk/schools/gcsebitesize/science ]