Question

This exercise uses the radioactive decay model. A wooden artifact from an ancient tomb contains 80% of the carbon-14 that is present in living trees. How long ago was the artifact made?

a) 5730 years
b) 11460 years
c) 17190 years
d) 22920 years

Answer 1

a) 5730 years.The wooden artifact that contains 80% of the carbon-14 present in living trees is approximately 5730 years old, as this time period represents less than one half-life of carbon-14 decay.

Step-by-step explanation:

The age of a wooden artifact that contains 80% of the carbon-14 present in living trees can be determined using radiocarbon dating. The half-life of carbon-14 (¹⁴C) is approximately 5730 years, which is the time it takes for half of the original amount of carbon-14 in a sample to decay.

Since the artifact in question has 80% of the carbon-14 remaining, it does not represent a full half-life decay. Instead, since a half-life would leave 50% of carbon-14, and the artifact has more than this, we can infer that it has been less than one half-life since the artifact was made.

Given that the decrease from 100% to 80% is not as great as the decrease from 100% to 50%, it is logical to choose the answer that represents a time less than 5730 years.

Therefore, looking at the options given, such as 5730 years, 11460 years, 17190 years, and 22920 years, the correct answer is option (a) 5730 years, as the other options represent multiples of the half-life period which would result in a lesser percentage of carbon-14 remaining than is observed in the artifact.