Radioactive Half-life

The definition of half-life is the time taken for the count rate from a sample to decrease to half the initial value. If we use a radiation detector, such as a Geiger-Muller tube, we can measure the radiation being emitted from a a sample and calculate the radioactive half life from the results. 

First, you need to plot a graph of the counts per minute against the time. Then, extrapolate the time taken for the counts to reduce by a half. In this example, the original counts was measured to be 300 \text{ counts per minute} and so half the counts is 150 \text{ counts per minute}. You can see from the graph that this corresponds to 9 \text{ days}. Therefore the half-life of this sample is 9\text{ days}. 

If we know the half-life of a sample we can determine how much smaller the count rate will be after a given number of half-lives. 

For example, after 2\text{ half-lives}, the radioactivity of a sample will be \dfrac{1}{2}\times \dfrac{1}{2} = \bold{\color{f21cc2}{\dfrac{1}{4}}} of the original radioactivity. This is the same as saying it is 4 times smaller. 

After 3\text{ half-lives}, the radioactivity will be \dfrac{1}{2} \times \dfrac{1}{2} \times \dfrac{1}{2} = \bold{\color{f21cc2}{\dfrac{1}{8}}} of the original activity, or 8 times smaller.