Half-life as the time for activity to halve, reading half-life from a decay curve, and calculations of remaining activity or mass.

What this dot point is asking

CCEA wants you to define half-life, read a half-life from a decay curve, and calculate the activity or mass of a source remaining after a number of half-lives. This builds directly on the random nature of decay.

The answer

What half-life means

Activity is the number of decays per second, measured in becquerels ($\text{Bq}$), and it falls over time as fewer unstable nuclei remain.

The decay curve

A graph of activity (or count rate) against time gives a decay curve that falls steeply at first and then levels off, never quite reaching zero.

Calculating remaining activity

To find the activity after a whole number of half-lives, halve the starting value once for each half-life. After $n$ half-lives the activity is $\left(\tfrac{1}{2}\right)^n$ of the original.

Worked example: counting half-lives

Examples in context

Example 1. Carbon dating

Carbon-14 has a half-life of about 5700 years. By measuring how much carbon-14 is left in once-living material and counting the half-lives, scientists estimate the age of ancient remains.

Example 2. Medical tracers

A tracer used in a hospital scan needs a short half-life (often a few hours) so it gives a clear signal but decays quickly, limiting the patient's exposure once the scan is done.

Example 3. Storing nuclear waste

Some isotopes in nuclear waste have very long half-lives (thousands of years), so they stay radioactive for an extremely long time. This is why such waste must be sealed and stored securely for many generations until its activity has fallen to a safe level.

A useful check on a half-life answer is the fraction remaining. After one half-life a half remains, after two a quarter, after three an eighth, and so on. If a question gives the fraction left, you can work backwards: a quarter remaining means two half-lives have passed, an eighth means three, and so on. Linking the number of half-lives to the fraction $\left(\tfrac{1}{2}\right)^n$ remaining makes these questions quick and reliable.

Try this

Q1. Define half-life. [1 mark]

• Cue. The time for the activity (or number of undecayed nuclei) to fall to half its value.

Q2. A source of activity $240\ \text{Bq}$ has a half-life of $2$ hours. Find its activity after $6$ hours. [2 marks]

• Cue. Three half-lives: $240 \rightarrow 120 \rightarrow 60 \rightarrow 30\ \text{Bq}$.

Q3. Why must background radiation be subtracted from a count rate? [1 mark]

• Cue. To find the true activity of the source alone.