What is meant by the half-life of a radioactive substance? - Leaving Cert Physics - Question i - 2015

The half-life of a radioactive substance is the time required for the quantity of radioactive material to reduce to half its initial amount. This means that after one half-life, half of the original radioactive atoms will have decayed into different atoms or isotopes.

Mathematically, the half-life ( extit{T}_rac{1}{2}) can be expressed using the decay constant ( extit{k}) as:

extit{T}_rac{1}{2} = rac{ ext{ln}(2)}{k}

In practice, this concept is crucial in fields such as nuclear medicine, radiometric dating, and understanding natural radioactivity.