Question

A fossilized tooth is found to have approximately 12.5% of its original radioactive carbon atoms. If the half-life of this radioactive carbon is 5730 years, how old is the fossil?

A) 17,190 years
B) 11,460 years
C) 22,920 years
D) 34,380 years

Answer 1

The age of the fossil is 17,190 years, which is determined by calculating three half-lives of carbon-14 (C-14) since the fossil has 12.5% of its original radioactive carbon atoms left.

Step-by-step explanation:

To determine the age of the fossil based on the current percentage of its original radioactive carbon atoms (12.5%), the concept of half-life, which is characteristic of radioactive decay, needs to be applied. The half-life of carbon-14 (C-14) is given as 5730 years. With 12.5% of the original C-14 remaining, we can infer that there have been three half-lives since the fossil was part of a living organism, because with each half-life, the amount of C-14 is reduced by half (100% to 50% to 25% to 12.5%).

Calculating three half-lives :

• First half-life: 5730 years (50% remaining)
• Second half-life: 5730 years (25% remaining)
• Third half-life: 5730 years (12.5% remaining)

By adding the years for each half-life (5730 + 5730 + 5730), the total age of the fossil is calculated to be 17,190 years. Therefore, the correct answer is A) 17,190 years.