Radioactive Decay and Half Life

Some materials contain unstable isotopes. 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 various forms.

Radioactive material will typically contain a large number of unstable isotopes. As radioactive decay is a random process, we cannot 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.

  • We measure activity in becquerels: 1 Bq = 1 decay per second.

2. The half-life

  • We use the activity of the sample to calculate the half-life


Half-life refers to the time it takes for half of a sample of unstable nuclei to decay. There are two ways to define half-life:

  • The time taken for the number of isotopes to halve – For example, a drop from 100,000 unstable nuclei to 50,000 unstable nuclei
  • The time taken for the number of decays per second to halve – For example, a drop from 500 decays per second to 250 decays per second

So when a half-life passes, the activity and the number of unstable nuclei will halve.

Over time, as the number of unstable isotopes decreases, there are fewer unstable nuclei 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.

Calculating half-life

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, the half-life is 20 days

Detecting radioactivity

In practice, to find the activity, we use a detector, such as 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.

Calculating The Remaining Isotope – Higher

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?

There are two half-lives in 11,460 years. So the remaining carbon-14 will be:

$\left( \frac{1}{2} \right)^{2}=\frac{1}{4}$

$\frac{1}{4} \times 100\:g=25 \:g$

So, after 11,460 years, 25g of the initial 100g of carbon-14 remains.