Use the concept of half-life to carry out simple calculations on the decay…

The idea

Half-life is the time taken for the count rate, activity or number of undecayed nuclei of a radioactive isotope to halve. To calculate, divide the starting value by 2 repeatedly, once per half-life, or find how many halvings fit into the elapsed time. For example, a source of activity 800 Bq with a half-life of 5 days falls to 400 Bq after 5 days, 200 Bq after 10 days and 100 Bq after 15 days. Working backwards, count how many halvings separate two values and multiply by the half-life. On a decay graph, activity or count rate plotted against time falls as a curve; read the time for the value to halve, then check the next halving takes the same time. Background radiation must be subtracted before halving measured count rates.

What earns the marks

• Halves the starting activity or count rate once for each half-life that elapses.
• Divides the elapsed time by the half-life to find the number of halvings.
• Multiplies the number of halvings by the half-life to find the elapsed time.
• Reads the half-life from a decay curve as the time for the value to fall to half.
• Subtracts background count rate before applying halving to measured data.

Common mistakes and how to put them right

• Halves the value only once regardless of how many half-lives have passed.

  Put it right: Divide the elapsed time by the half-life first.

• Forgets to subtract background radiation from measured count rates.

  Put it right: Subtract it before halving.

• Reads the half-life from the wrong point on a graph.

  Put it right: Use the time for the activity to fall to half its initial value.

Exam tips

• Write down the number of half-lives before doing any arithmetic so the number of halvings is clear.
• Show each halving step by step rather than jumping to a final value.
• Check a graph answer by confirming the second halving takes the same time as the first.