Question

How is Carbon 14 dating used?

Answer 1

One can use formula `t=(5730/-0.693)ln(N_t/N_0)`

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 `(5730/-0.693)ln(N_t/N_0)`. As in the above example `(N_t/N_0=0.25)` and `ln0.25=-1.386`

`t=(5730/-0.693)*(-1.386)=5730*2=11460` years.