Question

Carbon-14 is a radioactive isotope of carbon that has a half-life of about 5,730

years. You have discovered a fossil and want to know how old the fossil is. You count
the parent and daughter atoms and calculate that you have about 6.25% of the
parent atom (carbon-14) left. How old is the fossil? (Provide units (years) for your
final answer. You must show your work.
2 points for showing work
1 point for final answer with units

Answer 1

22,920 years

Step-by-step explanation:

When the fossil first started to decay, it must have had 100% of its parent carbon-14 atoms. Every 5,730 years, that amount gets cut in half. Let's travel back a ways, to the very beginning, 0 years into the decay. We'll keep track of the time elapsed, the number of half-lifes, and the percent of carbon-14 remaining:

• 0 years (0 half-lives) - 100%
• 5,730 years (1 half-life) - 50%
• 11,460 years (2 half-lives) - 25%
• 17,190 years (3 half-lives) - 11.5%
• 22,920 years (4 half-lives) - 6.25%

That last one represents our situation, so the fossil is 22,920 years old.