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 75% 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

amount of original carbnC14 after t years N=N0 ert where N0 =initial amount of carbonC14 by the time animal dies

half-life of about 5730 years

at half life amount of C14 present N=(1/2)N0

(1/2)N0=N0 er*5730

er*5730=(1/2)

5730r =ln(1/2)

r =(ln(1/2))/5730

r =-0.000121

N=N0 e-0.000121t

parchment fragment was discovered that had about 75% as much 14C radioactivity as does plant material on Earth todayN=(0.75)N0

(0.75)N0=N0 e-0.000121*t

e-0.000121*t=0.75

-0.000121t =ln(0.75)

t =2400 years

age of the parchment. =2400 years

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