Question

Radioactive isotopes can be used to find the age of rocks, fossils, or other artifacts. Carbon-14 has a half-life of 5,730 years. Suppose a sample of charcoal from a primitive fire pit contains one eighth of its original amount of carbon-14. How old is the sample?
A. 716 years
B. 17,190 years
C. 22,920 years
D. 45,840 years

Answer 1

Explanation:

 1/8 of carbon-14 which means it divided...3 times 

1/2 x 1/2 x 1/2 = 1/8 

3 x 5730 = 17190 years old

Answer 2

Given :

Half-life of C-14 ($t_{1/2}$) = 5730 years.

a sample of charcoal from a primitive fire pit contains one eighth of its original amount of carbon-14.

To Find :

How old is the sample

Solution :

Half life ($t_{1/2}$) of C-14 isotope = 5730 years

In 5730 years the concentration of carbon reduces to half

The concentration of carbon becomes half in 5730 years

The concentration of carbon will become $\frac{1}{8}$th or $\frac{1}{2^{3} }$ in (5730 × 3) years

                                                                                    = 17190 years

∴ The sample is 17190 years old.

The correct option is (B) 17190 years.