Question

Charcoal used to make prehistoric drawings on cave walls in France was analyzed. The results were 4 mg carbon-14 (parent isotope) and 60 mg nitrogen (daughter isotope). The half-life of carbon-14 is 5,730 years. How old are the cave drawings?

Answer 1

The cave drawings are 22920 years old.

Explanation:

`A = A_o * (1/2)^(t/h)`, where `A` is the final amount of radioactive anything, `A_o` is the initial amount, `t` is the elapsed time, and `h` is the half-life of the radioactive material.

At the time of the drawing, there were 0 g of nitrogen 14 and 64 g of Carbon 14.

There are now 4 g.

Plugging everything in, we have:

`4=64*(1/2)^(t/5730) -> 1/16 = (1/2)^(t/5730) ->`
`log_(1/2)(1/16)=log_(1/2) (1/2)^(t/5730) -> 4=t/5730 -> 22920 = t`.

The cave drawings are 22920 years old.