For example, you can’t find the remaining amount of an isotope as 7.5 half-lives by finding the midpoint between 7 and 8 half-lives.
This decay is an example of an exponential decay, shown in the figure below.
A useful application of half-lives is radioactive dating.
This has to do with figuring out the age of ancient things.
If you could watch a single atom of a radioactive isotope, U-238, for example, you wouldn’t be able to predict when that particular atom might decay.
It might take a millisecond, or it might take a century. But if you have a large enough sample, a pattern begins to emerge.
Animals eating those plants in turn absorb carbon-14 as well as the stable isotopes.
So, in turn, at the next half life carbon-14 would be only 25% of its original mass because at each half life, half the isotope has vanished.When an organism dies, it ceases to absorb Carbon $ from the atmosphere and the Carbon $ within the organism decays exponentially, becoming Nitrogen $, with a half-life of approximately 30$ years.Carbon $, however, is stable and so does not decay over time.It falls through the atmosphere and is picked up by Earth’s atmosphere and spread around.Because it reacts identically to carbon-12 and carbon-13, carbon-14 becomes attached to plants using photosynthesys and becomes part of their molecular makeup.