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Scientists look at half-life decay rates of radioactive isotopes to estimate when a particular atom might decay.
A useful application of half-lives is radioactive dating.
It might take a millisecond, or it might take a century. But if you have a large enough sample, a pattern begins to emerge.
It takes a certain amount of time for half the atoms in a sample to decay.
It then takes the same amount of time for half the remaining radioactive atoms to decay, and the same amount of time for half of those remaining radioactive atoms to decay, and so on. The amount of time it takes for one-half of a sample to decay is called the half-life of the isotope, and it’s given the symbol: It’s important to realize that the half-life decay of radioactive isotopes is not linear.
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.
Knowing about half-lives is important because it enables you to determine when a sample of radioactive material is safe to handle.The rule is that a sample is safe when its radioactivity has dropped below detection limits. So, if radioactive iodine-131 (which has a half-life of 8 days) is injected into the body to treat thyroid cancer, it’ll be “gone” in 10 half-lives, or 80 days.This stuff is important to know when using radioactive isotopes as medical tracers, which are taken into the body to allow doctors to trace a pathway or find a blockage, or in cancer treatments.They need to be active long enough to treat the condition, but they should also have a short enough half-life so that they don’t injure healthy cells and organs.Radioactive dating is helpful for figuring out the age of ancient things.Carbon-14 (C-14), a radioactive isotope of carbon, is produced in the upper atmosphere by cosmic radiation.The primary carbon-containing compound in the atmosphere is carbon dioxide, and a very small amount of carbon dioxide contains C-14.Plants absorb C-14 during photosynthesis, so C-14 is incorporated into the cellular structure of plants.Plants are then eaten by animals, making C-14 a part of the cellular structure of all living things.As long as an organism is alive, the amount of C-14 in its cellular structure remains constant.But when the organism dies, the amount of C-14 begins to decrease.