Define half-life and use it in simple calculations, and describe everyday uses and dangers of radioactivity

What this dot point is asking

SEAB wants you to define the half-life of a radioactive source, to use it in simple calculations by repeated halving, and to describe how radioactivity is used in everyday life along with its dangers and how to handle it safely. The big idea is that a radioactive sample fades away in a steady, predictable pattern (each half-life it halves), and that this useful behaviour also brings real risks.

The answer

What half-life means

Although we cannot predict when a single nucleus will decay, a large sample fades away in a very regular way. The half-life is the time taken for half of the radioactive nuclei in a sample to decay. It is also the time for the count rate (the reading on a detector) to fall to half its value.

Different sources have very different half-lives, from a fraction of a second to thousands of years. A short half-life means the source decays quickly; a long half-life means it stays radioactive for a long time.

Using half-life in calculations

To find how much is left after a whole number of half-lives, you halve the amount each time:

• After $1$ half-life: half is left ($\tfrac{1}{2}$).
• After $2$ half-lives: a quarter is left ($\tfrac{1}{4}$).
• After $3$ half-lives: an eighth is left ($\tfrac{1}{8}$).

The quick method is: work out how many half-lives have passed (divide the total time by the half-life), then halve the starting amount that many times. The count rate never quite reaches zero; it just keeps halving.

Uses of radioactivity

Radioactivity is useful in many ways:

• Tracers: a small amount of a source is added to a fluid so its path can be followed with a detector, for example to find a leak in an underground pipe or to follow blood flow in the body.
• Thickness control: a beta source on one side of a sheet and a detector on the other measure the thickness of paper or metal; if the sheet gets thicker, fewer particles get through.
• Sterilising: gamma rays kill bacteria on medical equipment and on some food.
• Treating cancer: carefully aimed gamma rays can destroy cancer cells.

The right type of radiation is chosen for each job; for example, a tracer to be detected from outside the body uses gamma because it can pass out through tissue.

Dangers and safe handling

Radiation can damage or kill living cells. A large dose can cause radiation burns, and exposure over time can cause cancer. Because of this, sources must be handled carefully. The three main precautions are:

• Distance: keep the source as far away as possible, using tongs instead of bare hands.
• Time: limit the time you spend near the source.
• Shielding: store the source in a lead-lined container and use shielding such as lead or concrete.

Examples in context

Example 1. Carbon dating old objects. Living things take in a tiny amount of the radioactive isotope carbon-14. When they die they stop taking it in, and the carbon-14 decays with a known half-life. By measuring how much is left, scientists work out how many half-lives have passed and so estimate the age of wood, bone or cloth. This uses the steady halving pattern directly.

Example 2. A thickness gauge in a factory. A beta source sits above a moving metal sheet with a detector below. The detector reading depends on how much radiation gets through, so it depends on the thickness. If the sheet gets too thick the count drops and the rollers adjust automatically. Beta is chosen because alpha would be stopped completely and gamma would pass through almost unchanged.

Try this

• Cue. Define the half-life of a radioactive source. [1 mark] It is the time taken for half of the radioactive nuclei in the sample to decay (or for the count rate to fall to half its value).

• Cue. A source has a half-life of $3\ \text{years}$ and a starting count rate of $640\ \text{counts per minute}$. Find the count rate after $9\ \text{years}$. [2 marks] $9 \div 3 = 3$ half-lives; halve three times: $640 \to 320 \to 160 \to 80\ \text{counts per minute}$.

• Cue. State two ways to reduce the danger when handling a radioactive source. [2 marks] Keep the source as far away as possible (use tongs and limit your time near it) and store or shield it with lead.