An Archaeologist in Turkey discovers a spear head that contains 80% of its original amount of c-14. Find the age of the spear head to the nearest year.
Hint : half-life of c(Carbon)-14 is 5730 years.
0.5^(t/5730) = 0.80
t = 5730 * log0.8/log0.5
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To determine the age of the spearhead, we can use the concept of radioactive decay and the half-life of carbon-14.
First, let's understand the concept of half-life. The half-life of a radioactive substance is the amount of time it takes for half of the substance to decay. In the case of carbon-14, its half-life is 5730 years. This means that after 5730 years, half of the original amount of carbon-14 will have decayed.
Now, let's use this information to find the age of the spearhead. We know that the spearhead contains 80% of its original amount of carbon-14. This implies that 20% of the carbon-14 has decayed.
To find the age, we need to determine the number of half-lives that have passed. Since each half-life is 5730 years, we can calculate the number of half-lives by dividing the percent of carbon-14 that remains (80%) by the percent of carbon-14 that decays during each half-life (20%):
Number of half-lives = log(remaining carbon-14 / original carbon-14) / log(0.5)
Substituting the values, we get:
Number of half-lives = log(0.80) / log(0.5)
Using a scientific calculator, we find that the number of half-lives is approximately 0.32.
Finally, we multiply the number of half-lives by the half-life of carbon-14 (5730 years) to find the age of the spearhead:
Age = Number of half-lives * Half-life of carbon-14
Age = 0.32 * 5730 years ≈ 1834 years
Therefore, the age of the spearhead, to the nearest year, is approximately 1834 years.