Half-lifeIB MYP Physics: Revision notes

Radioactive decay is random, but for a large number of nuclei the rate of decay is predictable. The half-life is the time taken for the activity of a sample (or the number of undecayed nuclei) to fall to half of its original value.

Activity is the number of decays per second, measured in becquerels (Bq). Each isotope has its own half-life, from a fraction of a second to billions of years. A long half-life does not mean a nucleus waits that long: it means that, in that time, half of the nuclei in a large sample are expected to decay.

Halve the amount once for each half-life that passes.

1. Work out the number of half-lives: time / half-life.
2. Halve the starting value that many times.

Worked example: a sample has an activity of 800 Bq and a half-life of 3 days. What is the activity after 12 days?

• Number of half-lives = 12 / 3 = 4
• 800, 400, 200, 100, 50
• The activity is 50 Bq.

You can also write it as the fraction left: after 4 half-lives, $\frac{1}{2^4} = \frac{1}{16}$ remains, and 800 / 16 = 50.

A decay curve is a graph of activity (or count rate) against time. It falls steeply at first and then more slowly.

To find the half-life:

1. Read the starting activity at time 0.
2. Work out half of this value.
3. Find the time on the curve when the activity has fallen to this value.
4. That time is the half-life. Check by finding the time to fall from this value to half of it again: it should be the same.

If background radiation is present, subtract it from the readings first.

The half-life and type of radiation must suit the job.

• Medical tracers (for example technetium-99m): a short half-life (hours) and gamma rays, so the radiation leaves the body to be detected and the patient is not exposed for long.
• Smoke alarms (americium-241): an alpha source with a long half-life (hundreds of years), so the activity stays steady for years.
• Thickness gauges (for example for paper or metal foil): a beta source with a long enough half-life so that the source activity stays steady, and the count rate changes only if thickness changes.
• Carbon dating: carbon-14 has a half-life of 5730 years. Living things keep a constant fraction of carbon-14; after death it decays. Comparing the fraction left with that in living material gives the age, up to about 50 000 years.