Question

Anthropologists can estimate the age of a bone or other sample of organic matter by its carbon-14 content. The carbon-14 in a living organism is constant until the organism dies, after which carbon- 14 decays with first-order kinetics and a half-life of 5730 years. Suppose a bone from an ancient human contains 19.5% of the C-14 found in living organisms. How old is the bone?

Answer 1

The bone is approximately 17,190 years old.

Step-by-step explanation:

The age of the bone can be determined by using the concept of carbon dating. Carbon-14 (C-14) is a radioactive isotope of carbon that is present in living organisms.

When an organism dies, the amount of C-14 in its body gradually decreases over time due to radioactive decay. The half-life of C-14 is 5730 years, which means that after 5730 years, only half of the original amount of C-14 remains.

In the case of the bone from the ancient human, it contains 19.5% of the C-14 found in living organisms. This means that the bone has undergone approximately 3 half-lives of decay (since 19.5% is close to 1/2^3, or 1/8).

Therefore, we can calculate the age of the bone by multiplying 5730 years by the number of half-lives that have passed, which is 3. The bone is approximately 17,190 years old.