Understanding Half-life:

Half-life is the time it takes for half the radioactive atoms in a sample to decay.
It is a measure of the rate of decay of a radioactive material.
To calculate the half-life, you count the time between the point when a sample has 100% of the original amount of material, and the point at which it has 50%.

Properties of Half-life:

The half-life of a radioactive substance is constant. This means it doesn’t change, even if the temperature, pressure or any other environmental conditions change.
This is different from most chemical reactions, which speed up when the temperature increases.
The half-life does not depend on the amount of the material. This means that if you have a large amount of a radioactive substance, it decays at the same rate as a small amount.

If you’re given a graph of the number of radioactive atoms against time, the half-life is the length of time over which the number of radioactive atoms decreases by half.
To calculate the half-life from a graph, find the starting number of radioactive atoms (usually the number at time = 0), and then find the time at which it decreases to half this value.
Remember that in each successive half life, the number of radioactive atoms halves. So after one half-life, there is half left; after two half-lives, there’s a quarter left; after three half-lives, there’s an eighth left, and so on.

Half-life is really useful in applications such as medical tracers. A radioactive isotope with a short half-life can be injected into a patient, and it will quickly decay and become non-radioactive.
Geologists use the half-lives of naturally-occurring radioactive isotopes to date rocks and fossils, by looking at the proportions of the original radioactive isotope and the decay product in the sample.
Understanding half-life also helps us manage radioactive waste effectively, by estimating how long it will remain dangerous and need careful storage.