An archaeologist in Turkey discovers a spear that contains 80% of its original amount of C-14. Find the age of the spear head to the nearest year.
Incomplete. We need to know the half-life of C-14
To find the age of the spearhead, we can use the concept of radioactive decay and the half-life of carbon-14 (C-14).
The half-life of C-14 is approximately 5730 years, which means that every 5730 years, the amount of C-14 in a sample reduces by half.
We know that the spearhead contains 80% of its original amount of C-14. This means that 20% (100% - 80%) of the C-14 has decayed.
To determine the number of half-lives that have occurred, we can use the formula:
(Number of half-lives) = (log(remaining percentage) / log(0.5))
Plugging in the values, we get:
(Number of half-lives) = (log(0.20) / log(0.5))
(Number of half-lives) ≈ 2.726
Since each half-life is approximately 5730 years, we can multiply the number of half-lives by the half-life duration to get the age of the spearhead:
Age = (Number of half-lives) * (half-life duration)
Age ≈ 2.726 * 5730
Age ≈ 15,625 years
Therefore, the age of the spearhead is approximately 15,625 years.