Radioactive isotopes have a very wide range of half-life values.

The idea

Half-life values span an extraordinary range, from tiny fractions of a second to billions of years. Uranium-238 has a half-life of about 4.5 billion years, carbon-14 about 5730 years, technetium-99m about 6 hours and some isotopes decay in microseconds. The consequence matters more than the numbers: a short half-life means each nucleus is very likely to decay soon, so for the same number of nuclei the activity is high and the decay curve is steepest at the start. A long half-life means a low activity that persists for a very long time. In a sample holding equal numbers of polonium-209, half-life 125 years, and polonium-210, half-life 138 days, the polonium-209 has the lower activity precisely because its half-life is longer.

What earns the marks

• The range running from fractions of a second to millions or billions of years.
• A short half-life giving a high activity from the same number of nuclei.
• The isotope with the shortest half-life having the steepest curve at the start.
• A comparison in the correct direction, such as polonium-209 having a lower activity than polonium-210 in the same sample.

Common mistakes and how to put them right

• Assuming a long half-life automatically means a more dangerous source.

• Comparing half-lives given in different units, such as 125 years and 138 days, without converting.

• Reading a steeper decay curve as a longer half-life.

• Saying an isotope with more nuclei remaining later must be decaying faster.

• Stating the comparison of activities without giving the half-life as the reason, when the reason mark depends on it.

Exam tips

• Convert to a common unit before comparing two half-lives; days against years catches people out.
• State the activity comparison first and then the half-life reason, matching the order the mark scheme expects.
• Remember that comparisons of activity only work directly when the numbers of atoms are equal, which the question will usually tell you.