How do scientists work out the half-lives of radioactive atoms that have ones billions of years long, ie too long to

Question: How do scientists work out the half-lives of radioactive atoms that have ones billions of years long, ie too long to observe in a lab?
- Keywords:
  half-life,
  half-lives,
  isotope,
  radioactive
Asked by bridget to Amy, Drew, Julia, Kimberley, Sara on 20 Jun 2011.
- Sara Imari Walker answered on 20 Jun 2011:
  
  Hi Bridget!! Fantastic question! Radioactivity is all about probabilities. In fact, half life is only meaninful if we talk about populations of atoms. An individual atom may have a low probability of decay, such that the half life of a population of such atoms is billions of years. However, since atoms are so small, it is easy to take billions of atoms to study!! As long as our sample is large enough we can expect to see decays. So if we take an atom with a billion year half life, but have billions of that atom to study, a few are bound to decay while we are observing them. From that we can get the half life of the entire population. Pretty smart and pretty cool!
- Drew Rae answered on 20 Jun 2011:
  
  Hi Bridget – Cool question, and Sara has given a good answer. The half-life is just an average (the time for half of the atoms to decay, with each individual atom decaying at random) so we don’t have to wait for half of them to decay to know how fast they are decaying on average. You do need a big enough sample to get a reliable answer though.
  
  At my home university they have a container full of pitch (tar) which drips about once every fifty years. Because it has only dripped a few times, they can’t be perfectly sure exactly when the next drop will happen.
- Amy MacQueen answered on 20 Jun 2011:
  
  Hey bridget! This is a brilliant question and one I thought about for a long time – because its not like there’s a “positive control” so you kind of think…yeah but how do they know how long it is?!
  
  The others have given really good answers – sample size is important!
  
  In the simplest of terms it is possible to measure the rate at which the radioactivity of a radioactive material decreases because even materials with a very long half-life will have a measureable rate of decay. It is then possible to work out how long it would take for half of the atoms in that material to decay and therefore to know the half-life!

Question: How do scientists work out the half-lives of radioactive atoms that have ones billions of years long, ie too long to observe in a lab?

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