Definition for exams: half-life is the time taken for half of the radioactive atoms now present to decay.
It is very useful as there is a problem measuring how quickly the activity drops off for some isotopes, as they can last millions of years, so the half-life is used to measure how quickly activity falls off.
It is different for different isotopes as each isotope has a different amount of activity to expel. A short half-life means the activity fall quickly, because lots of the nuclei is decaying quickly (the half-life is short as it does not take up much time). A long half-life means the activity falls more slowly because most of the nuclei don't decay for a long time (the half-life is long as it takes a very very long time).
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