How do we determine half life for elements that have half life in billions of years

Question

It’s been little over 100 years since we discovered radioactivity. How then do we know the half life of elements that have half lives in hundreds plus years?

In: 21

Answer 1

It’s a prediction, which we made with math.

Essentially, all the ones short enough for us to observe follow the same formula, and there’s no reason to think there’s a fundamental difference, so we apply that formula to the other atoms too.

And then from what observations we do have, like comparing carbon dating (which uses the formula) to other methods of measuring the age of rocks, it all lines up.