What is the relationship between half-life and the activity of the scource?

Answer 1

In general, the shorter the half-life of a radioactive substance, the more active it is. Think about it. Say you have two samples of radioactive material the size of sugar cubes. And let's say they have about the same number of atoms of the radioactive substance in them initially, but the substances are different. Substance A has a very short half-life. Substance B has an extremely long half-life. Let's look at what happens. In substance A, the material with the short half-life, atoms will be disintegrating at a high rate. There will be lots of radiation (with the type being determined by the method of decay), and it will have a high activity. It will be "hot" in the language of the physicist. Substance B will be taking its sweet time decaying. One atom here and one atom there will be decaying, and you could hold it in your hand for a while without doing much damage to yourself. In contrast, substance A would have to be kept in a containment cask to keep people who work around it safe from the radiation. For similar amounts of radioactive material, shorter half-lives mean higher activity. Having read this far, it should be simple and easy to see.

Answer 2

The activity of a radioactive source decreases over time due to radioactive decay. The half-life is the time it takes for half of the radioactive atoms in a sample to decay. As the half-life increases, the rate of decay slows down, resulting in a lower activity of the source.