We’re going to see what 'half-life' means and why radioactivity changes with time. It doesn’t depend on the size of the sample and it doesn’t change with time. So we imagine going in forward one half-life at a time from ZERO years: 10 years, 20 years, 30 years, etc.We’ll also see how carbon dating can be used to date ancient remains. If we had a bigger sample of the same isotope then the count would be higher, say 200 becquerels. Then we halve the count for each half-life: 100 Bq after 10 years; 50 Bq after 20 years; 25 Bq after 30 years So we can see the radioactivity would be 25 becquerels afer 30 years.It's useful because it has a half-life of the order of a minute and a pure sample can be prepared simply by shaking a bottle of liquid.It's not that radioactive isotopes 'have' a half-life.Even though carbon-14 causes around half of the internal radioactivity of living things, it’s only around 0.25 Bq per gram.A common way to isolate the carbon is to carefully burn a piece of the wood and use the carbon dioxide given off.This means a human adult has a radioactivity of around 3000-4000 becquerels due to carbon-14. When a living thing dies the cells are no longer replaced so no new carbon enters it.The radioactivity of the carbon-14 begins to decrease. By measuring the radioactivity we can tell how long ago the living thing died.
It is mostly carbon-12 with tiny amounts of the radioactive carbon-14. For example, a sample with a count of only 25% of atmospheric carbon dioxide must be two half-lives old: 100% - 50% takes 1 half-life 50% - 25% takes a second half-life If the half-life is 5600 years then the sample must be 5600 x 2 = 11 200 years old.We measure the radioactivity of the carbon dioxide in a special chamber to shield it from background radiation. You can use a much smaller sample of the material you want to test if you count the carbon-14 atoms directly rather than having to wait for them to decay.We can then compare it with the radioactivity of the same amount of carbon dioxide from the atmosphere. Even this kind of carbon dating can only be used to date things that were once alive and died less than about 60 000 years ago.Other radio-dating techniques are used to date ancient rocks.We can plot a graph of radioactivity against time for our sample that had a half-life of 10 years.Carbon dating can only be used to find the age of things that were once alive, like wood, leather, paper and bones.