### What is half life

Half life is a term which is used to describe a quantity that drops in a way described in maths as exponential, which sounds hard and complicated, but it isn’t. We can’t see radioactivity so let’s use a completely different example of something that goes down exponentially.

There’s a hole in the bottom of this can which is full of water. As the water runs out the pressure at the bottom of the can falls so the water runs more slowly.

If we plotted the rate of flow on a graph, it would look like this. This curve shows an exponential change. Here’s a bit to concentrate on, an exponential change is one where the rate of change of a quantity (that is the rate of flow in this example) depends on the amount of that quantity (in this case the amount of water remaining in the bucket). The time the water takes to run out to fall from the twenty mark to the ten is about the same as to run from the ten to the five.

### The unpredictable atoms

Radioactivity is very similar to this, although a little bit less predictable. Radioactive decay is a random process, over a short period we cannot predict which atoms might decay and when we listen to a geiger counter recording radioactivity the rate of click is not steady.

The nuclei of radioactive atoms are unstable. That may be because they are too big, have too many protons or too many neutrons. To become more stable they might emit an alpha particle, beta plus or beta minus or others. There is more detail about this here.

We have some understanding of why some atoms are unstable and break down but we cannot predict when, or even if, a particular atom will break down and emit a particle or energy. If we have a large number of atoms we can predict roughly how many will break down in a given time but not which ones. The process is predictable with large numbers but quite random with individual atoms.

It is just like spinning a coin. If we do this 100 times we are fairly sure we will get about 50 heads but it is unlikely to be exactly 50. If we spin a coin once there is no way to accurately predict the outcome. Over a long period of time and with a lot of atoms the predictability is more certain and we can measure the half life. The easiest way to do that is from the graph.

### Working out the half life

#### Graphs of radioactive decay and measuring half life

If we plot a graph of how the amount of radioactivity changes with time we get something like this:

Because of the random nature of decay, the curve of the graph plotting the the number of atoms remaining against time, is not always smooth. Once the points are plotted a smooth line is drawn to even out the irregularities.

The **half life is the time taken for the amount of radioactivity to fall to half of its original value**. There is no such thing as a full life. The amount of radioactivity fall and falls again but never really completely disappears (although the level may drop so far that it is insignificant).

The half life should be measured in several places on the graph and an average taken. This again is because radioactive decay is random and subject to slight unpredictable variation. Because of the random nature of radioactive decay one value of the half-life is not reliable, so we take an average of several.

Those we have taken here are: 18.4! 21.6! 19.5! 21.8 which to 3 significant figures averages out to 20.3 seconds.

**There are more useful pages about different aspects and uses of radioactivity here:**