From Scientific American:
So, what is a half-life? What’s the math behind it? And what does it have to do with the amount of caffeine left in your body at the end of the day … and even with calculating the ages of archeological artifacts and the entire solar system?
Let’s find out.
Some types of atoms do a really weird thing—they spontaneously decay into other types of atoms. A bit more precisely, some unstable isotopes of certain atoms (meaning certain versions of certain atoms that have certain, shall we say, non-standard numbers of neutrons in their nuclei) will spontaneously turn into different elements and in so doing release other particles and light along the way.