Scientist can determine the age of ancient objects by a method called radiocarbo

Question

Scientist can determine the age of ancient objects by a method called radiocarbon dating. The bombardment of the upper atmosphere by cosmic rays converts nitrogen to a radioactive isotope of carbon, 14C, with a half-life of about 5730 years. Vegetation absorbs carbon dioxide through the atmosphere and animal life assimilates 14C through food chains. When a plant or animal dies, it stops replacing its carbon and the amount of 14C begins to decrease through radioactive decay. Therefore, the level of radioactivity must also decay exponentially.

A parchment fragment was discovered that had about 68% as much 14C radioactivity as does plant material on Earth today. Estimate the age of the parchment. (Round your answer to the nearest hundred years.)

Explanation / Answer

Start with the formula P = Pinitial * 2^-n , where n is the number of half lives.
You know that P = .68Pinitial, so plug that in for P.
.68Pinitial = Pinitial * 2^-n
.68 = 2^-n
Take the Ln of both sides.
Ln .68 = Ln (2^-n)
Ln .68 = -n Ln 2
n = - Ln .68 / Ln 2
n = 0.556 half-lives
n equals the total time in years (t) divided by the time for a single half-life (h)
n = t/h
t = nh
t = .556(5730 years)
t = 3188 years

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