5.–/1 points SCalcET8 3.8.011. Ask Your Teacher My Notes Question Part Points Submissions Used Scientist can determine the age o
f 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 74% 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.) yr
These steps explain how you estimate the age of the parchment:
1) Carbon - 14 half-life: τ = 5730 years
2) Number of half-lives elapsed: n
3) Age of the parchment = τ×n = 5730×n years = 5730n
4) Exponential decay:
The ratio of the final amount of the radioactive isotope C-14 to the initial amount of the same is one half (1/2) raised to the number of half-lives elapsed (n):
A / Ao = (1/2)ⁿ
5) The parchment fragment had about 74% as much C-14 radioactivity as does plant material on Earth today:
⇒ A / Ao = 74% = 0.74
⇒ A / Ao = 0.74 = (1/2)ⁿ
⇒ ln (0.74) = n ln (1/2) [apply natural logarithm to both sides]
⇒ n = ln (1/2) / ln (0.74)
⇒ n ≈ - 0.693 / ( - 0.301) = 2.30
Hence, 2.30 half-lives have elapsed and the age of the parchment is:
