Half-life and radioactive decay explained

A sample has an activity of 640 Bq and a half-life of 2 hours. After 8 hours, that's $8 \div 2 = 4$ half-lives:

$640 \to 320 \to 160 \to 80 \to 40$ Bq.

As a fraction: after 4 half-lives, $\left(\tfrac{1}{2}\right)^4 = \tfrac{1}{16}$ is left. $640 \div 16 = 40$ Bq.

1. Read the starting activity from the graph.
2. Halve it and find that value on the curve.
3. Read down to the time axis: that's one half-life.
4. Repeat from there to check: each halving takes the same time.

Real data are a little scattered because decay is random, so draw a smooth curve of best fit first.

• Alpha decay: the mass number falls by 4 and the atomic number by 2. For example, uranium-238 becomes thorium-234.
• Beta decay: a neutron becomes a proton, so the atomic number rises by 1 and the mass number stays the same.
• Gamma emission: no change to mass or atomic number; the nucleus loses energy.

Check that mass numbers and atomic numbers balance on both sides.

Background radiation comes from natural sources such as rocks and cosmic rays, and from human activity such as medical uses. Subtract the background count from measurements before working out half-life. Safety precautions include keeping sources in shielded containers, handling them with tongs, keeping exposure time short and staying at a distance.

• Subtracting half the original amount each time instead of halving what's left.
• Forgetting to subtract background radiation.
• Saying half-life is "half the time for all of it to decay".

1. A source has an activity of 1,200 Bq and a half-life of 3 hours. What is its activity after 9 hours?
2. A sample's activity falls from 400 Bq to 50 Bq in 21 days. What is its half-life?
3. What fraction of the original nuclei remain after 5 half-lives?

Answers: 150 Bq; 7 days (3 half-lives); 1/32.