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The half-life is always the same regardless of how many nuclei you have left, and this very useful property lies at the heart of radiocarbon dating. The graph below shows the decay curve (you may recognize it as an exponential decay) and it shows the amount, or percent, of carbon-14 remaining.
You will notice that after around 40,000 years (or 8 half-lives), the amount left is starting to become very small, less than 1%.
For the record, a beta-particle is a specific type of nuclear decay. Image 1 shows carbon-14 production by high energy neutrons hitting nitrogen-14 atoms, while in Image 2, carbon-14 naturally decomposes through beta-particle production.
Notice that the nitrogen-14 atom is recreated and goes back into the cycle.
Because of the carbon cycle, there is always carbon-14 present in both the air and in living organisms.
The half-life is the time required for half of the original sample of radioactive nuclei to decay.
For example, if you start off with 1000 radioactive nuclei with a half-life of 10 days, you would have 500 left after 10 days; you would have 250 left after 20 days (2 half-lives); and so on.
Then the radiocarbon dating measures remaining radioactivity.
By knowing how much carbon-14 is left in a sample, the age of the organism and when it died can be worked out.
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