Students should be able to determine the half-life of a radioactive…

The idea

Half-life is the time taken for the number of unstable nuclei in a radioactive sample to halve, or for the count rate to fall to half its initial value. To determine it from given information, identify the starting count rate, halve it, and read the time at which that value occurs. For example, if a source starts at 800 counts per minute and falls to 400 counts per minute after 6 hours, the half-life is 6 hours. If data are given at intervals, you may need to halve repeatedly: 800 → 400 → 200 → 100 counts per minute, each step taking one half-life. On a graph, find the time for the count rate to halve, or use the time for the activity to fall to half. Always state the unit of time and remember that half-life is constant for a given isotope, regardless of the starting amount.

What earns the marks

• Identify the initial count rate or activity from the data, graph or table before halving it.
• Halve the initial value correctly and read the corresponding time from the graph or table to obtain one half-life.
• For data given at intervals, count the number of halvings needed to reach the stated value and divide the total time by that number.
• State the half-life with the correct unit of time, such as seconds, minutes, hours, days or years.
• Recognise that the half-life is constant for a given isotope and does not depend on the starting count rate or sample size.
• Use a graph correctly by reading across from half the initial count rate to the curve and down to the time axis.

Common mistakes and how to put them right

• Halving the time instead of the count rate.

  Put it right: Halve the count rate or activity and find the time at which that value occurs.

• Reading the time at which the count rate reaches zero.

  Put it right: Use the point at which the count rate has fallen to half its starting value.

• Forgetting the unit or using the wrong unit.

  Put it right: Include the unit shown in the data, such as hours or days.

Exam tips

• Underline the initial count rate and the time interval in the question before starting any calculation.
• Show each halving step clearly, for example 800 → 400 → 200 counts per minute, so the examiner can follow your method.
• If the value does not halve exactly, estimate the half-life from the graph and give the unit; do not round the count rate to zero.