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,^14 C, with a half-life of about 5730 years. Vegetation absorbs carbon dioxide through the atmosphere and animal life assimilates^14 C through food chains. When a plant or animal dies, it stops replacing its carbon and the amount of^14 C 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^14 C radioactivity as does plant material on Earth today. Estimate the age of the parchment. (Round your answer to the nearest hundred years.) yr

Explanation / Answer

we know that

for radioactivity

so

ln (A/Ao) = -kt

given

final amount (A) = 0.68 Ao (initial amount)

so

A/Ao = 0.68

so

ln 0.68 = -kt

kt = 0.38566

now

decay constant (k) = 0.693 / half life

given

half life = 5730

so

k = 0.693 / 5730

now

kt = 0.38566

so

0.693 x t / 5730 = 0.38566

t = 3188

so

the age of the parchment is 3188 years

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