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If the life of a radioactive substance is taken to mean the time that elapses before the activity drops to zero, then it is clear from the graph below that we would be waiting forever! A much more useful quantity for dealing with the life of radioactive substances is the half-life.
Half-life (or t1/2) is defined as the time taken for the activity of the sample to halve. Note that the half-life remains the same throughout the life of the sample.
As the activity of a sample is proportional to the number of radioactive nuclides present it is also possible to say that the half-life is the time taken for half of the radioactive nuclides in a sample to decay.
We can also plot a graph of ln (that's small L and small N) N against t (Note ln N is the natural logarithm of N. To find it, type the N into your calculator and press the ln button)
It is possible to show from this graph that the gradient is equal to -l called the decay constant. As you can see from the graph, the steeper the gradient the more quickly the substance will decay and hence a shorter half-life.
Carbon-14 Dating is a useful example of the concept of half-life in practice. Carbon-14 is a radioactive isotope of carbon with a half-life of 5730 years.
All living matter takes in carbon-14 during its lifetime as it naturally occurs in nature. Upon death this uptake ceases, and levels of carbon-14 decay. It is possible to compare the activity of a living sample of material with an ancient specimen (of the same mass) and estimate the age. For example if a specimen has half the activity of a living sample of equal mass it is around 5730 years old i.e. 1 half-life. If the activity were quarter it would be 2 x 5730 = 11460 years old i.e. 2 half-life's and so on.
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