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

Remember what *half*-life means. It’s the average time for *half* a sample to decay. We use half-life because the decay is exponential, so we can’t meaningfully measure the “full life.” After X amount of time, half the sample will have decayed, and after another X time, half of what was left will have decayed, etc.

So now that we’ve refreshed our memories on half-life:

It takes hundreds of years for *half* the sample to decay. But *some* of the sample will decay in a few years. So maybe we can’t directly measure the half-life, but we can measure the 0.01%-life. Then we can use that to calculate the half-life.