Half life dating formula
Substituting the initial condition \(t = 0\), \(m = 100\) gives \(C = 100\), so \[ m(t) = 100 \, e^.
\] With this formula, we can calculate the amount \(m\) of carbon-14 over the years. But after 5000 years, however, almost half of the carbon-14 has decayed.
Depending on the isotope, its Half Life may range from a few fractions of a second to several billion years. The Half Life of Uranium-238 is 4,500,000,000 years.
There is even a radioactive isotope of carbon, carbon-14. C-14 has two extra neutrons and a half-life of 5730 years.
At any particular time all living organisms have approximately the same ratio of carbon 12 to carbon 14 in their tissues.
When an organism dies it ceases to replenish carbon in its tissues and the decay of carbon 14 to nitrogen 14 changes the ratio of carbon 12 to carbon 14.
Experts can compare the ratio of carbon 12 to carbon 14 in dead material to the ratio when the organism was alive to estimate the date of its death.
Scientists use C-14 in a process called carbon dating.
Carbon dating is when scientists try to measure the age of very old substances.
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So, the fossil is 8,680 years old, meaning the living organism died 8,680 years ago.