Question

If the half-life of carbon is about 5,730 years, then a fossil that has one-sixteenth the normal proportion of carbon-14 to carbon-12 should be about how many years old?

Answer 1

1 -> 1/2 -> 1/4 -> 1/8 -> 1/16

Four half-lives ^

5,730*4=22,920 years.

Answer 2

The age of fossil is approximately 21480 years

The  half-life of a radioactive isotope is the time which it will take for half the amount of the radioactive isotope to decay to form more stable isoopes.

Carbon-14 is a radioactive isotope of carbon which has a half-life of 5370 years, after which half of it decays and half remains.

If a fossil sample has one-sixteenth the normal proportion of carbon-14 to carbon-12, the number of half-lives the carbon-14 isotope in the fossil has undergone will give the approximate age of the fossil.

Number of half-lives undergone is obtained as follows:

$(\frac{1}{2})^n = \frac{1}{16}$

$(\frac{1}{2})^n = (\frac{1}{2})^4$

n = 4

Therefore, the carbon-14 isotope has undergone four half-lives

Age of the fossil = 4 * 5370 years

Age of fossil = approximately 21480 years

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