# How is Carbon 14 dating used?

Feb 23, 2016

One can use formula $t = \left(\frac{5730}{-} 0.693\right) \ln \left({N}_{t} / {N}_{0}\right)$

#### Explanation:

Carbon-14 dating is used for (i) carbon-14 decays slowly in a living organism to nitrogen (half life 5730 years) (ii) amount of carbon-14 lost is continually replenished as long as the organism takes in air or food (however, once the organism dies, it ceases to absorb carbon-14).

Hence, it is a good way of determining the age of certain archaeological artifacts of biological origin (could be bone, fiber, wood, plant remnants etc.) up to about 50,000 years old.

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.