Some materials contain unstable isotopes. For them to become more stable, they emit nuclear radiation. For example, they can emit an alpha particle, a beta particle or a gamma ray. We call these materials radioactive and they come in many different forms.
Radioactive material will typically contain a large number of unstable isotopes. As radioactive decay is a random process, we can not tell when an individual isotope will decay. However, there are two useful things we can find out:
1. The activity of the sample – which is the overall rate of decay of all the isotopes in the sample.
2. The half-life
Half-life is a statistical technique that is used to find out when half the sample of unstable nuclei has decayed. There are two definitions for half-life:
So when a half-life passes, the activity and the number of unstable nuclei will halve.
As time goes on, the number of unstable isotopes remaining decreases, so there are fewer unstable nuclei of those isotopes left to decay. This means that the overall rate of decay will also decrease.
The number of nuclei remaining is positively correlated to the activity of the sample because less radioactive nuclei result in lower activity.
A useful way to show the decay process is by using a graph that plots activity (in becquerels) against time.
As time goes on, the number of particles remaining and the activity of the sample will decrease. However, the graph is curved because the rate of decline will also fall. The activity will continue to reduce to a very small value, but it will not reach 0.
To calculate the half-life by using the graph, we first find the time it takes for the activity to halve. In this case, the activity drops from 160 to 80 in 20 days. If we check again, we can see that it drops from 80 to 40 in another 20 days. So we know that the half-life is 20 days
In reality, we would have to find the activity by using a detector, for example, a Geiger-Muller tube.
A Geiger-Muller tube records all the decays that reach it each second (the alpha particles, beta particles and gamma rays). This value is recorded as the count rate. The count rate is then used to estimate the activity.
When provided with the half-life, it should be possible to calculate the remaining amount of the sample. The amount of sample remaining can be expressed as a fraction, decimal or ratio.
Let’s look at an example.
The half-life of carbon-14 is 5,730 years. How much is remaining from a 100g sample of carbon-14 after 11,460 years?