7.10-7.13 - Background radiation and half-life calculations

Background sources

Background radiation is the ionising radiation that is always present in the environment. It is not usually from one obvious source in the room; it is the small amount of radiation arriving from many natural sources around us.

The Edexcel specification asks you to explain sources from Earth and space. Earth sources include naturally radioactive materials in rocks, soil and building materials. Uranium and thorium in rocks can decay through chains that include radon gas, which can move through soil and into air in buildings. Food, water and living things also contain small amounts of naturally radioactive isotopes, such as carbon-14 and potassium-40.

Space sources are mainly cosmic rays from the Sun and other stars. The amount reaching a detector can depend on altitude and shielding by the atmosphere, but for this lesson the key point is simpler: some background ionising radiation comes from beyond Earth.

Do not confuse this with the uses of radioactive sources in medicine or industry. Those applications are a later topic. Here, "background" means the radiation already present from the environment.

Activity and becquerels

The activity of a radioactive source is the rate at which unstable nuclei in it decay. A source with a high activity has many decays each second. A source with a low activity has fewer decays each second.

Activity is measured in becquerels, symbol Bq.

1 Bq = 1 radioactive decay per second

So a source with activity 300 Bq has, on average, 300 decays each second. The phrase "on average" matters because radioactive decay is random: you cannot predict exactly which nucleus will decay next. However, for a large sample, the overall activity follows a predictable decrease over time.

As a source decays, there are fewer undecayed unstable nuclei left. Fewer unstable nuclei means fewer chances for decay each second, so the activity decreases. The source does not usually stop suddenly; its activity falls gradually.

What half-life means

Half-life is the time taken for the activity of a radioactive source to fall to half its previous value. It can also be described as the time taken for half the undecayed nuclei in a sample to decay.

For example, if a source has activity 200 Bq and its half-life is 10 minutes, then after 10 minutes its activity is 100 Bq. After another 10 minutes, it halves again to 50 Bq. It halves from whatever value it has at the start of that half-life; it does not lose the same number of becquerels each time.

Different radioactive isotopes have different half-lives. One isotope may have a half-life of seconds, another may have a half-life of years. The half-life is a property of the isotope. Changing the initial sample mass does not change it: a larger sample starts with greater activity, but the same fraction decays in each interval. Ordinary changes in temperature, pressure or chemical state do not change nuclear half-life.

This is why half-life is useful. Although individual decays are random, the time for a large sample's activity to halve is predictable for that isotope.

Activity calculations

Half-life calculations are easiest when you count how many half-lives have passed. Each half-life divides the activity by 2.

Here $A_0$ is the starting activity, $A$ is the activity after decay, and $n$ is the number of half-lives. For International GCSE questions in this cluster, you usually use whole numbers of half-lives and repeated halving is often clearer than trying to use a more advanced decay equation.

Worked example: a source starts at 640 Bq. Its half-life is 3 days. Calculate its activity after 9 days.

number of half-lives = 9 days / 3 days = 3
640 Bq → 320 Bq → 160 Bq → 80 Bq

After 9 days, the activity is 80 Bq.

You can also work backwards from the halving chain. Suppose a source falls from 720 Bq to 90 Bq, and its half-life is 5 minutes.

720 Bq → 360 Bq → 180 Bq → 90 Bq

That is 3 half-lives, so the time taken is:

3 × 5 minutes = 15 minutes

The same chain also finds an unknown half-life. If you are told the fall from 720 Bq to 90 Bq took 15 minutes, divide the time by the number of half-lives:

half-life = 15 minutes / 3 = 5 minutes