# How is the half life of carbon 14 dating used?

Feb 29, 2016

Carbon-14 dating is used for determining the age of archaeological artifacts of biological origin (could be bone, fiber, wood, plant remnants etc.) up to about 50,000 years old.

For this, If a fossil has say 25% of carbon-14 as compared to living sample than it is 11460 years old (as it has one-fourth carbon it is 5730*2=11460 years old).

General formula for time $t$ is $\left(\frac{5730}{-} 0.693\right) \ln \left({N}_{t} / {N}_{0}\right)$. As in the above example $\left({N}_{t} / {N}_{0} = 0.25\right)$ and $\ln 0.25 = - 1.386$

$t = \left(\frac{5730}{-} 0.693\right) \cdot \left(- 1.386\right) = 5730 \cdot 2 = 11460$ years.