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

Scale.

Sure Uranium 238 has a half life of 4.5 billion years, but you’re not staring at one atom waiting for it to decay – that could take an eternity.

Instead you slap a brick of U-238 on the table, and it contains 10^24 atoms.

Any one atom may have a vanishingly small 0.00000000001% chance decay today, but you have 1000000000000000000000000 atoms.

So you’ll record *millions* of decay events today, and can use that value to calculate the half life.